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# 线性回归
让我们从经典的线性回归（Linear Regression \[[1](#参考文献)\]）模型开始这份教程。在这一章里，你将使用真实的数据集建立起一个房价预测模型，并且了解到机器学习中的若干重要概念。
本教程源代码目录在[book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/01.fit_a_line)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## 背景介绍
给定一个大小为$n$的数据集 ${\{y_{i}, x_{i1}, ..., x_{id}\}}_{i=1}^{n}$，其中$x_{i1}, \ldots, x_{id}$是第$i$个样本$d$个属性上的取值，$y_i$是该样本待预测的目标。线性回归模型假设目标$y_i$可以被属性间的线性组合描述，即
$$y_i = \omega_1x_{i1} + \omega_2x_{i2} + \ldots + \omega_dx_{id} + b, i=1,\ldots,n$$
例如，在我们将要建模的房价预测问题里，$x_{ij}$是描述房子$i$的各种属性（比如房间的个数、周围学校和医院的个数、交通状况等），而 $y_i$是房屋的价格。
初看起来，这个假设实在过于简单了，变量间的真实关系很难是线性的。但由于线性回归模型有形式简单和易于建模分析的优点，它在实际问题中得到了大量的应用。很多经典的统计学习、机器学习书籍\[[2,3,4](#参考文献)\]也选择对线性模型独立成章重点讲解。
## 效果展示
我们使用从[UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing)获得的波士顿房价数据集进行模型的训练和预测。下面的散点图展示了使用模型对部分房屋价格进行的预测。其中，每个点的横坐标表示同一类房屋真实价格的中位数，纵坐标表示线性回归模型根据特征预测的结果，当二者值完全相等的时候就会落在虚线上。所以模型预测得越准确，则点离虚线越近。
<p align="center">
<img src = "image/predictions.png" width=400><br/>
图1. 预测值 V.S. 真实值
</p>
## 模型概览
### 模型定义
在波士顿房价数据集中，和房屋相关的值共有14个：前13个用来描述房屋相关的各种信息，即模型中的 $x_i$；最后一个值为我们要预测的该类房屋价格的中位数，即模型中的 $y_i$。因此，我们的模型就可以表示成：
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
$\hat{Y}$ 表示模型的预测结果，用来和真实值$Y$区分。模型要学习的参数即：$\omega_1, \ldots, \omega_{13}, b$。
建立模型后，我们需要给模型一个优化目标，使得学到的参数能够让预测值$\hat{Y}$尽可能地接近真实值$Y$。这里我们引入损失函数（[Loss Function](https://en.wikipedia.org/wiki/Loss_function)，或Cost Function）这个概念。 输入任意一个数据样本的目标值$y_{i}$和模型给出的预测值$\hat{y_{i}}$，损失函数输出一个非负的实值。这个实值通常用来反映模型误差的大小。
对于线性回归模型来讲，最常见的损失函数就是均方误差（Mean Squared Error， [MSE](https://en.wikipedia.org/wiki/Mean_squared_error)）了，它的形式是：
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
即对于一个大小为$n$的测试集，$MSE$是$n$个数据预测结果误差平方的均值。
### 训练过程
定义好模型结构之后，我们要通过以下几个步骤进行模型训练
1. 初始化参数，其中包括权重$\omega_i$和偏置$b$，对其进行初始化（如0均值，1方差）。
2. 网络正向传播计算网络输出和损失函数。
3. 根据损失函数进行反向误差传播 （[backpropagation](https://en.wikipedia.org/wiki/Backpropagation)），将网络误差从输出层依次向前传递, 并更新网络中的参数。
4. 重复2~3步骤，直至网络训练误差达到规定的程度或训练轮次达到设定值。
## 数据集
### 数据集接口的封装
首先加载需要的包
```python
import paddle.v2 as paddle
import paddle.v2.dataset.uci_housing as uci_housing
```
我们通过uci_housing模块引入了数据集合[UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing)
其中，在uci_housing模块中封装了：
1. 数据下载的过程。下载数据保存在~/.cache/paddle/dataset/uci_housing/housing.data。
2. [数据预处理](#数据预处理)的过程。
### 数据集介绍
这份数据集共506行，每行包含了波士顿郊区的一类房屋的相关信息及该类房屋价格的中位数。其各维属性的意义如下：
| 属性名 | 解释 | 类型 |
| ------| ------ | ------ |
| CRIM | 该镇的人均犯罪率 | 连续值 |
| ZN | 占地面积超过25,000平方呎的住宅用地比例 | 连续值 |
| INDUS | 非零售商业用地比例 | 连续值 |
| CHAS | 是否邻近 Charles River | 离散值，1=邻近；0=不邻近 |
| NOX | 一氧化氮浓度 | 连续值 |
| RM | 每栋房屋的平均客房数 | 连续值 |
| AGE | 1940年之前建成的自用单位比例 | 连续值 |
| DIS | 到波士顿5个就业中心的加权距离 | 连续值 |
| RAD | 到径向公路的可达性指数 | 连续值 |
| TAX | 全值财产税率 | 连续值 |
| PTRATIO | 学生与教师的比例 | 连续值 |
| B | 1000(BK - 0.63)^2，其中BK为黑人占比 | 连续值 |
| LSTAT | 低收入人群占比 | 连续值 |
| MEDV | 同类房屋价格的中位数 | 连续值 |
### 数据预处理
#### 连续值与离散值
观察一下数据，我们的第一个发现是：所有的13维属性中，有12维的连续值和1维的离散值（CHAS）。离散值虽然也常使用类似0、1、2这样的数字表示，但是其含义与连续值是不同的，因为这里的差值没有实际意义。例如，我们用0、1、2来分别表示红色、绿色和蓝色的话，我们并不能因此说“蓝色和红色”比“绿色和红色”的距离更远。所以通常对一个有$d$个可能取值的离散属性，我们会将它们转为$d$个取值为0或1的二值属性或者将每个可能取值映射为一个多维向量。不过就这里而言，因为CHAS本身就是一个二值属性，就省去了这个麻烦。
#### 属性的归一化
另外一个稍加观察即可发现的事实是，各维属性的取值范围差别很大（如图2所示）。例如，属性B的取值范围是[0.32, 396.90]，而属性NOX的取值范围是[0.3850, 0.8170]。这里就要用到一个常见的操作-归一化（normalization）了。归一化的目标是把各位属性的取值范围放缩到差不多的区间，例如[-0.5,0.5]。这里我们使用一种很常见的操作方法：减掉均值，然后除以原取值范围。
做归一化（或 [Feature scaling](https://en.wikipedia.org/wiki/Feature_scaling)）至少有以下3个理由：
- 过大或过小的数值范围会导致计算时的浮点上溢或下溢。
- 不同的数值范围会导致不同属性对模型的重要性不同（至少在训练的初始阶段如此），而这个隐含的假设常常是不合理的。这会对优化的过程造成困难，使训练时间大大的加长。
- 很多的机器学习技巧/模型（例如L1，L2正则项，向量空间模型-Vector Space Model）都基于这样的假设：所有的属性取值都差不多是以0为均值且取值范围相近的。
<p align="center">
<img src = "image/ranges.png" width=550><br/>
图2. 各维属性的取值范围
</p>
#### 整理训练集与测试集
我们将数据集分割为两份：一份用于调整模型的参数，即进行模型的训练，模型在这份数据集上的误差被称为**训练误差**；另外一份被用来测试，模型在这份数据集上的误差被称为**测试误差**。我们训练模型的目的是为了通过从训练数据中找到规律来预测未知的新数据，所以测试误差是更能反映模型表现的指标。分割数据的比例要考虑到两个因素：更多的训练数据会降低参数估计的方差，从而得到更可信的模型；而更多的测试数据会降低测试误差的方差，从而得到更可信的测试误差。我们这个例子中设置的分割比例为$8:2$
在更复杂的模型训练过程中，我们往往还会多使用一种数据集：验证集。因为复杂的模型中常常还有一些超参数（[Hyperparameter](https://en.wikipedia.org/wiki/Hyperparameter_optimization)）需要调节，所以我们会尝试多种超参数的组合来分别训练多个模型，然后对比它们在验证集上的表现选择相对最好的一组超参数，最后才使用这组参数下训练的模型在测试集上评估测试误差。由于本章训练的模型比较简单，我们暂且忽略掉这个过程。
## 训练
`fit_a_line/trainer.py`演示了训练的整体过程。
### 初始化PaddlePaddle
```python
paddle.init(use_gpu=False, trainer_count=1)
```
### 模型配置
线性回归的模型其实就是一个采用线性激活函数（linear activation，`LinearActivation`）的全连接层（fully-connected layer，`fc_layer`）：
```python
x = paddle.layer.data(name='x', type=paddle.data_type.dense_vector(13))
y_predict = paddle.layer.fc(input=x,
size=1,
act=paddle.activation.Linear())
y = paddle.layer.data(name='y', type=paddle.data_type.dense_vector(1))
cost = paddle.layer.mse_cost(input=y_predict, label=y)
```
### 创建参数
```python
parameters = paddle.parameters.create(cost)
```
### 创建Trainer
```python
optimizer = paddle.optimizer.Momentum(momentum=0)
trainer = paddle.trainer.SGD(cost=cost,
parameters=parameters,
update_equation=optimizer)
```
### 读取数据且打印训练的中间信息
PaddlePaddle提供一个
[reader机制](https://github.com/PaddlePaddle/Paddle/tree/develop/doc/design/reader)
来读取数据。 Reader返回的数据可以包括多列，我们需要一个Python dict把列
序号映射到网络里的数据层。
```python
feeding={'x': 0, 'y': 1}
```
此外，我们还可以提供一个 event handler，来打印训练的进度：
```python
# event_handler to print training and testing info
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "Pass %d, Batch %d, Cost %f" % (
event.pass_id, event.batch_id, event.cost)
if isinstance(event, paddle.event.EndPass):
result = trainer.test(
reader=paddle.batch(
uci_housing.test(), batch_size=2),
feeding=feeding)
print "Test %d, Cost %f" % (event.pass_id, result.cost)
```
```python
# event_handler to print training and testing info
from paddle.v2.plot import Ploter
train_title = "Train cost"
test_title = "Test cost"
cost_ploter = Ploter(train_title, test_title)
step = 0
def event_handler_plot(event):
global step
if isinstance(event, paddle.event.EndIteration):
if step % 10 == 0: # every 10 batches, record a train cost
cost_ploter.append(train_title, step, event.cost)
if step % 100 == 0: # every 100 batches, record a test cost
result = trainer.test(
reader=paddle.batch(
uci_housing.test(), batch_size=2),
feeding=feeding)
cost_ploter.append(test_title, step, result.cost)
if step % 100 == 0: # every 100 batches, update cost plot
cost_ploter.plot()
step += 1
```
### 开始训练
```python
trainer.train(
reader=paddle.batch(
paddle.reader.shuffle(
uci_housing.train(), buf_size=500),
batch_size=2),
feeding=feeding,
event_handler=event_handler_plot,
num_passes=30)
```
![png](./image/train_and_test.png)
## 总结
在这章里，我们借助波士顿房价这一数据集，介绍了线性回归模型的基本概念，以及如何使用PaddlePaddle实现训练和测试的过程。很多的模型和技巧都是从简单的线性回归模型演化而来，因此弄清楚线性模型的原理和局限非常重要。
## 参考文献
1. https://en.wikipedia.org/wiki/Linear_regression
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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# Linear Regression
Let us begin the tutorial with a classical problem called Linear Regression \[[1](#References)\]. In this chapter, we will train a model from a realistic dataset to predict home prices. Some important concepts in Machine Learning will be covered through this example.
The source code for this tutorial lives on [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/01.fit_a_line). For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book).
## Problem Setup
Suppose we have a dataset of $n$ real estate properties. These real estate properties will be referred to as *homes* in this chapter for clarity.
Each home is associated with $d$ attributes. The attributes describe characteristics such the number of rooms in the home, the number of schools or hospitals in the neighborhood, and the traffic condition nearby.
In our problem setup, the attribute $x_{i,j}$ denotes the $j$th characteristic of the $i$th home. In addition, $y_i$ denotes the price of the $i$th home. Our task is to predict $y_i$ given a set of attributes $\{x_{i,1}, ..., x_{i,d}\}$. We assume that the price of a home is a linear combination of all of its attributes, namely,
$$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b, i=1,\ldots,n$$
where $\vec{\omega}$ and $b$ are the model parameters we want to estimate. Once they are learned, we will be able to predict the price of a home, given the attributes associated with it. We call this model **Linear Regression**. In other words, we want to regress a value against several values linearly. In practice, a linear model is often too simplistic to capture the real relationships between the variables. Yet, because Linear Regression is easy to train and analyze, it has been applied to a large number of real problems. As a result, it is an important topic in many classic Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
## Results Demonstration
We first show the result of our model. The dataset [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) is used to train a linear model to predict the home prices in Boston. The figure below shows the predictions the model makes for some home prices. The $X$-axis represents the median value of the prices of simlilar homes within a bin, while the $Y$-axis represents the home value our linear model predicts. The dotted line represents points where $X=Y$. When reading the diagram, the more precise the model predicts, the closer the point is to the dotted line.
<p align="center">
<img src = "image/predictions_en.png" width=400><br/>
Figure 1. Predicted Value V.S. Actual Value
</p>
## Model Overview
### Model Definition
In the UCI Housing Data Set, there are 13 home attributes $\{x_{i,j}\}$ that are related to the median home price $y_i$, which we aim to predict. Thus, our model can be written as:
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
where $\hat{Y}$ is the predicted value used to differentiate from actual value $Y$. The model learns parameters $\omega_1, \ldots, \omega_{13}, b$, where the entries of $\vec{\omega}$ are **weights** and $b$ is **bias**.
Now we need an objective to optimize, so that the learned parameters can make $\hat{Y}$ as close to $Y$ as possible. Let's refer to the concept of [Loss Function (Cost Function)](https://en.wikipedia.org/wiki/Loss_function). A loss function must output a non-negative value, given any pair of the actual value $y_i$ and the predicted value $\hat{y_i}$. This value reflects the magnitutude of the model error.
For Linear Regression, the most common loss function is [Mean Square Error (MSE)](https://en.wikipedia.org/wiki/Mean_squared_error) which has the following form:
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
That is, for a dataset of size $n$, MSE is the average value of the the prediction sqaure errors.
### Training
After setting up our model, there are several major steps to go through to train it:
1. Initialize the parameters including the weights $\vec{\omega}$ and the bias $b$. For example, we can set their mean values as $0$s, and their standard deviations as $1$s.
2. Feedforward. Evaluate the network output and compute the corresponding loss.
3. [Backpropagate](https://en.wikipedia.org/wiki/Backpropagation) the errors. The errors will be propagated from the output layer back to the input layer, during which the model parameters will be updated with the corresponding errors.
4. Repeat steps 2~3, until the loss is below a predefined threshold or the maximum number of repeats is reached.
## Dataset
### Python Dataset Modules
Our program starts with importing necessary packages:
```python
import paddle.v2 as paddle
import paddle.v2.dataset.uci_housing as uci_housing
```
We encapsulated the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) in our Python module `uci_housing`. This module can
1. download the dataset to `~/.cache/paddle/dataset/uci_housing/housing.data`, if not yet, and
2. [preprocesses](#preprocessing) the dataset.
### An Introduction of the Dataset
The UCI housing dataset has 506 instances. Each instance describes the attributes of a house in surburban Boston. The attributes are explained below:
| Attribute Name | Characteristic | Data Type |
| ------| ------ | ------ |
| CRIM | per capita crime rate by town | Continuous|
| ZN | proportion of residential land zoned for lots over 25,000 sq.ft. | Continuous |
| INDUS | proportion of non-retail business acres per town | Continuous |
| CHAS | Charles River dummy variable | Discrete, 1 if tract bounds river; 0 otherwise|
| NOX | nitric oxides concentration (parts per 10 million) | Continuous |
| RM | average number of rooms per dwelling | Continuous |
| AGE | proportion of owner-occupied units built prior to 1940 | Continuous |
| DIS | weighted distances to five Boston employment centres | Continuous |
| RAD | index of accessibility to radial highways | Continuous |
| TAX | full-value property-tax rate per $10,000 | Continuous |
| PTRATIO | pupil-teacher ratio by town | Continuous |
| B | 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town | Continuous |
| LSTAT | % lower status of the population | Continuous |
| MEDV | Median value of owner-occupied homes in $1000's | Continuous |
The last entry is the median home price.
### Preprocessing
#### Continuous and Discrete Data
We define a feature vector of length 13 for each home, where each entry corresponds to an attribute. Our first observation is that, among the 13 dimensions, there are 12 continuous dimensions and 1 discrete dimension.
Note that although a discrete value is also written as numeric values such as 0, 1, or 2, its meaning differs from a continuous value drastically. The linear difference between two discrete values has no meaning. For example, suppose $0$, $1$, and $2$ are used to represent colors *Red*, *Green*, and *Blue* respectively. Judging from the numeric representation of these colors, *Red* differs more from *Blue* than it does from *Green*. Yet in actuality, it is not true that extent to which the color *Blue* is different from *Red* is greater than the extent to which *Green* is different from *Red*. Therefore, when handling a discrete feature that has $d$ possible values, we usually convert it to $d$ new features where each feature takes a binary value, $0$ or $1$, indicating whether the original value is absent or present. Alternatively, the discrete features can be mapped onto a continuous multi-dimensional vector through an embedding table. For our problem here, because CHAS itself is a binary discrete value, we do not need to do any preprocessing.
#### Feature Normalization
We also observe a huge difference among the value ranges of the 13 features (Figure 2). For instance, the values of feature *B* fall in $[0.32, 396.90]$, whereas those of feature *NOX* has a range of $[0.3850, 0.8170]$. An effective optimization would require data normalization. The goal of data normalization is to scale te values of each feature into roughly the same range, perhaps $[-0.5, 0.5]$. Here, we adopt a popular normalization technique where we substract the mean value from the feature value and divide the result by the width of the original range.
There are at least three reasons for [Feature Normalization](https://en.wikipedia.org/wiki/Feature_scaling) (Feature Scaling):
- A value range that is too large or too small might cause floating number overflow or underflow during computation.
- Different value ranges might result in varying *importances* of different features to the model (at least in the beginning of the training process). This assumption about the data is often unreasonable, making the optimization difficult, which in turn results in increased training time.
- Many machine learning techniques or models (e.g., *L1/L2 regularization* and *Vector Space Model*) assumes that all the features have roughly zero means and their value ranges are similar.
<p align="center">
<img src = "image/ranges_en.png" width=550><br/>
Figure 2. The value ranges of the features
</p>
#### Prepare Training and Test Sets
We split the dataset in two, one for adjusting the model parameters, namely, for model training, and the other for model testing. The model error on the former is called the **training error**, and the error on the latter is called the **test error**. Our goal in training a model is to find the statistical dependency between the outputs and the inputs, so that we can predict new outputs given new inputs. As a result, the test error reflects the performance of the model better than the training error does. We consider two things when deciding the ratio of the training set to the test set: 1) More training data will decrease the variance of the parameter estimation, yielding more reliable models; 2) More test data will decrease the variance of the test error, yielding more reliable test errors. One standard split ratio is $8:2$.
When training complex models, we usually have one more split: the validation set. Complex models usually have [Hyperparameters](https://en.wikipedia.org/wiki/Hyperparameter_optimization) that need to be set before the training process, such as the number of layers in the network. Because hyperparameters are not part of the model parameters, they cannot be trained using the same loss function. Thus we will try several sets of hyperparameters to train several models and cross-validate them on the validation set to pick the best one; finally, the selected trained model is tested on the test set. Because our model is relatively simple, we will omit this validation process.
## Training
`fit_a_line/trainer.py` demonstrates the training using [PaddlePaddle](http://paddlepaddle.org).
### Initialize PaddlePaddle
```python
paddle.init(use_gpu=False, trainer_count=1)
```
### Model Configuration
Logistic regression is essentially a fully-connected layer with linear activation:
```python
x = paddle.layer.data(name='x', type=paddle.data_type.dense_vector(13))
y_predict = paddle.layer.fc(input=x,
size=1,
act=paddle.activation.Linear())
y = paddle.layer.data(name='y', type=paddle.data_type.dense_vector(1))
cost = paddle.layer.mse_cost(input=y_predict, label=y)
```
### Create Parameters
```python
parameters = paddle.parameters.create(cost)
```
### Create Trainer
```python
optimizer = paddle.optimizer.Momentum(momentum=0)
trainer = paddle.trainer.SGD(cost=cost,
parameters=parameters,
update_equation=optimizer)
```
### Feeding Data
PaddlePaddle provides the
[reader mechanism](https://github.com/PaddlePaddle/Paddle/tree/develop/doc/design/reader)
for loadinng training data. A reader may return multiple columns, and we need a Python dictionary to specify the mapping from column index to data layers.
```python
feeding={'x': 0, 'y': 1}
```
Moreover, an event handler is provided to print the training progress:
```python
# event_handler to print training and testing info
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "Pass %d, Batch %d, Cost %f" % (
event.pass_id, event.batch_id, event.cost)
if isinstance(event, paddle.event.EndPass):
result = trainer.test(
reader=paddle.batch(
uci_housing.test(), batch_size=2),
feeding=feeding)
print "Test %d, Cost %f" % (event.pass_id, result.cost)
```
```python
# event_handler to print training and testing info
from paddle.v2.plot import Ploter
train_title = "Train cost"
test_title = "Test cost"
plot_cost = Ploter(train_title, test_title)
step = 0
def event_handler_plot(event):
global step
if isinstance(event, paddle.event.EndIteration):
if step % 10 == 0: # every 10 batches, record a train cost
plot_cost.append(train_title, step, event.cost)
if step % 100 == 0: # every 100 batches, record a test cost
result = trainer.test(
reader=paddle.batch(
uci_housing.test(), batch_size=2),
feeding=feeding)
plot_cost.append(test_title, step, result.cost)
if step % 100 == 0: # every 100 batches, update cost plot
plot_cost.plot()
step += 1
```
### Start Training
```python
trainer.train(
reader=paddle.batch(
paddle.reader.shuffle(
uci_housing.train(), buf_size=500),
batch_size=2),
feeding=feeding,
event_handler=event_handler_plot,
num_passes=30)
```
![png](./image/train_and_test.png)
## Summary
This chapter introduces *Linear Regression* and how to train and test this model with PaddlePaddle, using the UCI Housing Data Set. Because a large number of more complex models and techniques are derived from linear regression, it is important to understand its underlying theory and limitation.
## References
1. https://en.wikipedia.org/wiki/Linear_regression
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.
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# Recognize Digits # 识别数字
The source code for this tutorial is live at [book/recognize_digits](https://github.com/PaddlePaddle/book/tree/develop/02.recognize_digits). For instructions on getting started with Paddle, please refer to [installation instructions](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book). 本教程源代码目录在[book/recognize_digits](https://github.com/PaddlePaddle/book/tree/develop/02.recognize_digits)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## Introduction ## 背景介绍
When one learns to program, the first task is usually to write a program that prints "Hello World!". In Machine Learning or Deep Learning, the equivalent task is to train a model to recognize hand-written digits on the dataset [MNIST](http://yann.lecun.com/exdb/mnist/). Handwriting recognition is a classic image classification problem. The problem is relatively easy and MNIST is a complete dataset. As a simple Computer Vision dataset, MNIST contains images of handwritten digits and their corresponding labels (Fig. 1). The input image is a $28\times28$ matrix, and the label is one of the digits from $0$ to $9$. All images are normalized, meaning that they are both rescaled and centered. 当我们学习编程的时候，编写的第一个程序一般是实现打印"Hello World"。而机器学习（或深度学习）的入门教程，一般都是 [MNIST](http://yann.lecun.com/exdb/mnist/) 数据库上的手写识别问题。原因是手写识别属于典型的图像分类问题，比较简单，同时MNIST数据集也很完备。MNIST数据集作为一个简单的计算机视觉数据集，包含一系列如图1所示的手写数字图片和对应的标签。图片是28x28的像素矩阵，标签则对应着0~9的10个数字。每张图片都经过了大小归一化和居中处理。
<p align="center"> <p align="center">
<img src="image/mnist_example_image.png" width="400"><br/> <img src="image/mnist_example_image.png" width="400"><br/>
Fig. 1. Examples of MNIST images 图1. MNIST图片示例
</p> </p>
The MNIST dataset is created from the [NIST](https://www.nist.gov/srd/nist-special-database-19) Special Database 3 (SD-3) and the Special Database 1 (SD-1). The SD-3 is labeled by the staff of the U.S. Census Bureau, while SD-1 is labeled by high school students the in U.S. Therefore the SD-3 is cleaner and easier to recognize than the SD-1 dataset. Yann LeCun et al. used half of the samples from each of SD-1 and SD-3 to create the MNIST training set (60,000 samples) and test set (10,000 samples), where training set was labeled by 250 different annotators, and it was guaranteed that there wasn't a complete overlap of annotators of training set and test set. MNIST数据集是从 [NIST](https://www.nist.gov/srd/nist-special-database-19) 的Special Database 3（SD-3）和Special Database 1（SD-1）构建而来。由于SD-3是由美国人口调查局的员工进行标注，SD-1是由美国高中生进行标注，因此SD-3比SD-1更干净也更容易识别。Yann LeCun等人从SD-1和SD-3中各取一半作为MNIST的训练集（60000条数据）和测试集（10000条数据），其中训练集来自250位不同的标注员，此外还保证了训练集和测试集的标注员是不完全相同的。
Yann LeCun, one of the founders of Deep Learning, have previously made tremendous contributions to handwritten character recognition and proposed the **Convolutional Neural Network** (CNN), which drastically improved recognition capability for handwritten characters. CNNs are now a critical concept in Deep Learning. From the LeNet proposal by Yann LeCun, to those winning models in ImageNet competitions, such as VGGNet, GoogLeNet, and ResNet (See [Image Classification](https://github.com/PaddlePaddle/book/tree/develop/03.image_classification) tutorial), CNNs have achieved a series of impressive results in Image Classification tasks. Yann LeCun早先在手写字符识别上做了很多研究，并在研究过程中提出了卷积神经网络（Convolutional Neural Network），大幅度地提高了手写字符的识别能力，也因此成为了深度学习领域的奠基人之一。如今的深度学习领域，卷积神经网络占据了至关重要的地位，从最早Yann LeCun提出的简单LeNet，到如今ImageNet大赛上的优胜模型VGGNet、GoogLeNet、ResNet等（请参见[图像分类](https://github.com/PaddlePaddle/book/tree/develop/03.image_classification) 教程），人们在图像分类领域，利用卷积神经网络得到了一系列惊人的结果。
Many algorithms are tested on MNIST. In 1998, LeCun experimented with single layer linear classifier, Multilayer Perceptron (MLP) and Multilayer CNN LeNet. These algorithms quickly reduced test error from 12% to 0.7% \[[1](#references)\]. Since then, researchers have worked on many algorithms such as **K-Nearest Neighbors** (k-NN) \[[2](#references)\], **Support Vector Machine** (SVM) \[[3](#references)\], **Neural Networks** \[[4-7](#references)\] and **Boosting** \[[8](#references)\]. Various preprocessing methods like distortion removal, noise removal, and blurring, have also been applied to increase recognition accuracy. 有很多算法在MNIST上进行实验。1998年，LeCun分别用单层线性分类器、多层感知器（Multilayer Perceptron, MLP）和多层卷积神经网络LeNet进行实验，使得测试集上的误差不断下降（从12%下降到0.7%）\[[1](#参考文献)\]。此后，科学家们又基于K近邻（K-Nearest Neighbors）算法\[[2](#参考文献)\]、支持向量机（SVM）\[[3](#参考文献)\]、神经网络\[[4-7](#参考文献)\]和Boosting方法\[[8](#参考文献)\]等做了大量实验，并采用多种预处理方法（如去除歪曲、去噪、模糊等）来提高识别的准确率。
In this tutorial, we tackle the task of handwritten character recognition. We start with a simple **softmax** regression model and guide our readers step-by-step to improve this model's performance on the task of recognition. 本教程中，我们从简单的模型Softmax回归开始，带大家入门手写字符识别，并逐步进行模型优化。
## Model Overview ## 模型概览
Before introducing classification algorithms and training procedure, we define the following symbols: 基于MNIST数据训练一个分类器，在介绍本教程使用的三个基本图像分类网络前，我们先给出一些定义：
- $X$ is the input: Input is a $28\times 28$ MNIST image. It is flattened to a $784$ dimensional vector. $X=\left (x_0, x_1, \dots, x_{783} \right )$. - $X$是输入：MNIST图片是$28\times28$ 的二维图像，为了进行计算，我们将其转化为$784$维向量，即$X=\left ( x_0, x_1, \dots, x_{783} \right )$。
- $Y$ is the output: Output of the classifier is 1 of the 10 classes (digits from 0 to 9). $Y=\left (y_0, y_1, \dots, y_9 \right )$. Each dimension $y_i$ represents the probability that the input image belongs to class $i$. - $Y$是输出：分类器的输出是10类数字（0-9），即$Y=\left ( y_0, y_1, \dots, y_9 \right )$，每一维$y_i$代表图片分类为第$i$类数字的概率。
- $L$ is the ground truth label: $L=\left ( l_0, l_1, \dots, l_9 \right )$. It is also 10 dimensional, but only one entry is $1$ and all others are $0$s. - $L$是图片的真实标签：$L=\left ( l_0, l_1, \dots, l_9 \right )$也是10维，但只有一维为1，其他都为0。
### Softmax Regression ### Softmax回归(Softmax Regression)
In a simple softmax regression model, the input is first fed to fully connected layers. Then, a softmax function is applied to output probabilities of multiple output classes\[[9](#references)\]. 最简单的Softmax回归模型是先将输入层经过一个全连接层得到的特征，然后直接通过softmax 函数进行多分类\[[9](#参考文献)\]。
The input $X$ is multiplied by weights $W$ and then added to the bias $b$ to generate activations. 输入层的数据$X$传到输出层，在激活操作之前，会乘以相应的权重 $W$ ，并加上偏置变量 $b$ ，具体如下：
$$ y_i = \text{softmax}(\sum_j W_{i,j}x_j + b_i) $$ $$ y_i = \text{softmax}(\sum_j W_{i,j}x_j + b_i) $$
where $ \text{softmax}(x_i) = \frac{e^{x_i}}{\sum_j e^{x_j}} $ 其中 $ \text{softmax}(x_i) = \frac{e^{x_i}}{\sum_j e^{x_j}} $
For an $N$-class classification problem with $N$ output nodes, Softmax normalizes the resulting $N$ dimensional vector so that each of its entries falls in the range $[0,1]\in\math{R}$, representing the probability that the sample belongs to a certain class. Here $y_i$ denotes the predicted probability that an image is of digit $i$. 对于有 $N$ 个类别的多分类问题，指定 $N$ 个输出节点，$N$ 维结果向量经过softmax将归一化为 $N$ 个[0,1]范围内的实数值，分别表示该样本属于这 $N$ 个类别的概率。此处的 $y_i$ 即对应该图片为数字 $i$ 的预测概率。
In such a classification problem, we usually use the cross entropy loss function: 在分类问题中，我们一般采用交叉熵代价损失函数（cross entropy），公式如下：
$$ \text{crossentropy}(label, y) = -\sum_i label_ilog(y_i) $$ $$ \text{crossentropy}(label, y) = -\sum_i label_ilog(y_i) $$
Fig. 2 illustrates a softmax regression network, with the weights in blue, and the bias in red. `+1` indicates that the bias is $1$. 图2为softmax回归的网络图，图中权重用蓝线表示、偏置用红线表示、+1代表偏置参数的系数为1。
<p align="center"> <p align="center">
<img src="image/softmax_regression_en.png" width=400><br/> <img src="image/softmax_regression.png" width=400><br/>
Fig. 2. Softmax regression network architecture<br/> 图2. softmax回归网络结构图<br/>
</p> </p>
### Multilayer Perceptron ### 多层感知器(Multilayer Perceptron, MLP)
The softmax regression model described above uses the simplest two-layer neural network. That is, it only contains an input layer and an output layer, with limited regression capability. To achieve better recognition results, consider adding several hidden layers\[[10](#references)\] between the input layer and the output layer. Softmax回归模型采用了最简单的两层神经网络，即只有输入层和输出层，因此其拟合能力有限。为了达到更好的识别效果，我们考虑在输入层和输出层中间加上若干个隐藏层\[[10](#参考文献)\]。
1. After the first hidden layer, we get $ H_1 = \phi(W_1X + b_1) $, where $\phi$ denotes the activation function. Some [common ones](###list-of-common-activation-functions) are sigmoid, tanh and ReLU. 1. 经过第一个隐藏层，可以得到 $ H_1 = \phi(W_1X + b_1) $，其中$\phi$代表激活函数，常见的有sigmoid、tanh或ReLU等函数。
2. After the second hidden layer, we get $ H_2 = \phi(W_2H_1 + b_2) $. 2. 经过第二个隐藏层，可以得到 $ H_2 = \phi(W_2H_1 + b_2) $。
3. Finally, the output layer outputs $Y=\text{softmax}(W_3H_2 + b_3)$, the vector denoting our classification result. 3. 最后，再经过输出层，得到的$Y=\text{softmax}(W_3H_2 + b_3)$，即为最后的分类结果向量。
Fig. 3. shows a Multilayer Perceptron network, with the weights in blue, and the bias in red. +1 indicates that the bias is $1$.
图3为多层感知器的网络结构图，图中权重用蓝线表示、偏置用红线表示、+1代表偏置参数的系数为1。
<p align="center"> <p align="center">
<img src="image/mlp_en.png" width=500><br/> <img src="image/mlp.png" width=500><br/>
Fig. 3. Multilayer Perceptron network architecture<br/> 图3. 多层感知器网络结构图<br/>
</p>
### 卷积神经网络(Convolutional Neural Network, CNN)
在多层感知器模型中，将图像展开成一维向量输入到网络中，忽略了图像的位置和结构信息，而卷积神经网络能够更好的利用图像的结构信息。[LeNet-5](http://yann.lecun.com/exdb/lenet/)是一个较简单的卷积神经网络。图4显示了其结构：输入的二维图像，先经过两次卷积层到池化层，再经过全连接层，最后使用softmax分类作为输出层。下面我们主要介绍卷积层和池化层。
<p align="center">
<img src="image/cnn.png"><br/>
图4. LeNet-5卷积神经网络结构<br/>
</p> </p>
### Convolutional Neural Network #### 卷积层
#### Convolutional Layer 卷积层是卷积神经网络的核心基石。在图像识别里我们提到的卷积是二维卷积，即离散二维滤波器（也称作卷积核）与二维图像做卷积操作，简单的讲是二维滤波器滑动到二维图像上所有位置，并在每个位置上与该像素点及其领域像素点做内积。卷积操作被广泛应用与图像处理领域，不同卷积核可以提取不同的特征，例如边沿、线性、角等特征。在深层卷积神经网络中，通过卷积操作可以提取出图像低级到复杂的特征。
<p align="center"> <p align="center">
<img src="image/conv_layer.png" width='750'><br/> <img src="image/conv_layer.png" width='750'><br/>
Fig. 4. Convolutional layer<br/> 图5. 卷积层图片<br/>
</p> </p>
The **convolutional layer** is the core of a Convolutional Neural Network. The parameters in this layer are composed of a set of filters, also called kernels. We could visualize the convolution step in the following fashion: Each kernel slides horizontally and vertically till it covers the whole image. At every window, we compute the dot product of the kernel and the input. Then, we add the bias and apply an activation function. The result is a two-dimensional activation map. For example, some kernel may recognize corners, and some may recognize circles. These convolution kernels may respond strongly to the corresponding features. 图5给出一个卷积计算过程的示例图，输入图像大小为$H=5,W=5,D=3$，即$5 \times 5$大小的3通道（RGB，也称作深度）彩色图像。这个示例图中包含两（用$K$表示）组卷积核，即图中滤波器$W_0$和$W_1$。在卷积计算中，通常对不同的输入通道采用不同的卷积核，如图示例中每组卷积核包含（$D=3）$个$3 \times 3$（用$F \times F$表示）大小的卷积核。另外，这个示例中卷积核在图像的水平方向（$W$方向）和垂直方向（$H$方向）的滑动步长为2（用$S$表示）；对输入图像周围各填充1（用$P$表示）个0，即图中输入层原始数据为蓝色部分，灰色部分是进行了大小为1的扩展，用0来进行扩展。经过卷积操作得到输出为$3 \times 3 \times 2$（用$H_{o} \times W_{o} \times K$表示）大小的特征图，即$3 \times 3$大小的2通道特征图，其中$H_o$计算公式为：$H_o = (H - F + 2 \times P)/S + 1$，$W_o$同理。 而输出特征图中的每个像素，是每组滤波器与输入图像每个特征图的内积再求和，再加上偏置$b_o$，偏置通常对于每个输出特征图是共享的。输出特征图$o[:,:,0]$中的最后一个$-2$计算如图5右下角公式所示。
Fig. 4 illustrates the dynamic programming of a convolutional layer, where depths are flattened for simplicity. The input is $W_1=5$, $H_1=5$, $D_1=3$. In fact, this is a common representation for colored images. $W_1$ and $H_1$ correspond to the width and height in a colored image. $D_1$ corresponds to the 3 color channels for RGB. The parameters of the convolutional layer are $K=2$, $F=3$, $S=2$, $P=1$. $K$ denotes the number of kernels; specifically, $Filter$ $W_0$ and $Filter$ $W_1$ are the kernels. $F$ is kernel size while $W0$ and $W1$ are both $F\timesF = 3\times3$ matrices in all depths. $S$ is the stride, which is the width of the sliding window; here, kernels move leftwards or downwards by 2 units each time. $P$ is the width of the padding, which denotes an extension of the input; here, the gray area shows zero padding with size 1. 在卷积操作中卷积核是可学习的参数，经过上面示例介绍，每层卷积的参数大小为$D \times F \times F \times K$。在多层感知器模型中，神经元通常是全部连接，参数较多。而卷积层的参数较少，这也是由卷积层的主要特性即局部连接和共享权重所决定。
#### Pooling Layer - 局部连接：每个神经元仅与输入神经元的一块区域连接，这块局部区域称作感受野（receptive field）。在图像卷积操作中，即神经元在空间维度（spatial dimension，即上图示例H和W所在的平面）是局部连接，但在深度上是全部连接。对于二维图像本身而言，也是局部像素关联较强。这种局部连接保证了学习后的过滤器能够对于局部的输入特征有最强的响应。局部连接的思想，也是受启发于生物学里面的视觉系统结构，视觉皮层的神经元就是局部接受信息的。
<p align="center"> - 权重共享：计算同一个深度切片的神经元时采用的滤波器是共享的。例如图4中计算$o[:,:,0]$的每个每个神经元的滤波器均相同，都为$W_0$，这样可以很大程度上减少参数。共享权重在一定程度上讲是有意义的，例如图片的底层边缘特征与特征在图中的具体位置无关。但是在一些场景中是无意的，比如输入的图片是人脸，眼睛和头发位于不同的位置，希望在不同的位置学到不同的特征 (参考[斯坦福大学公开课]( http://cs231n.github.io/convolutional-networks/))。请注意权重只是对于同一深度切片的神经元是共享的，在卷积层，通常采用多组卷积核提取不同特征，即对应不同深度切片的特征，不同深度切片的神经元权重是不共享。另外，偏重对同一深度切片的所有神经元都是共享的。
<img src="image/max_pooling_en.png" width="400px"><br/>
Fig. 5 Pooling layer using max-pooling<br/>
</p>
A **pooling layer** performs downsampling. The main functionality of this layer is to reduce computation by reducing the network parameters. It also prevents over-fitting to some extent. Usually, a pooling layer is added after a convolutional layer. Pooling layer can use various techniques, such as max pooling and average pooling. As shown in Fig.5, max pooling uses rectangles to segment the input layer into several parts and computes the maximum value in each part as the output. 通过介绍卷积计算过程及其特性，可以看出卷积是线性操作，并具有平移不变性（shift-invariant），平移不变性即在图像每个位置执行相同的操作。卷积层的局部连接和权重共享使得需要学习的参数大大减小，这样也有利于训练较大卷积神经网络。
#### LeNet-5 Network #### 池化层
<p align="center"> <p align="center">
<img src="image/cnn_en.png"><br/> <img src="image/max_pooling.png" width="400px"><br/>
Fig. 6. LeNet-5 Convolutional Neural Network architecture<br/> 图6. 池化层图片<br/>
</p> </p>
[**LeNet-5**](http://yann.lecun.com/exdb/lenet/) is one of the simplest Convolutional Neural Networks. Fig. 6. shows its architecture: A 2-dimensional input image is fed into two sets of convolutional layers and pooling layers. This output is then fed to a fully connected layer and a softmax classifier. Compared to multilayer, fully connected perceptrons, the LeNet-5 can recognize images better. This is due to the following three properties of the convolution: 池化是非线性下采样的一种形式，主要作用是通过减少网络的参数来减小计算量，并且能够在一定程度上控制过拟合。通常在卷积层的后面会加上一个池化层。池化包括最大池化、平均池化等。其中最大池化是用不重叠的矩形框将输入层分成不同的区域，对于每个矩形框的数取最大值作为输出层，如图6所示。
- The 3D nature of the neurons: a convolutional layer is organized by width, height and depth. Neurons in each layer are connected to only a small region in the previous layer. This region is called the receptive field.
- Local connectivity: A CNN utilizes the local space correlation by connecting local neurons. This design guarantees that the learned filter has a strong response to local input features. Stacking many such layers generates a non-linear filter that is more global. This enables the network to first obtain good representation for small parts of input and then combine them to represent a larger region.
- Weight sharing: In a CNN, computation is iterated on shared parameters (weights and bias) to form a feature map. This means that all the neurons in the same depth of the output respond to the same feature. This allows the network to detect a feature regardless of its position in the input. In other words, it is shift invariant.
For more details on Convolutional Neural Networks, please refer to the tutorial on [Image Classification](https://github.com/PaddlePaddle/book/blob/develop/image_classification/README.md) and the [relevant lecture](http://cs231n.github.io/convolutional-networks/) from a Stanford open course.
### List of Common Activation Functions 更详细的关于卷积神经网络的具体知识可以参考[斯坦福大学公开课]( http://cs231n.github.io/convolutional-networks/ )和[图像分类](https://github.com/PaddlePaddle/book/blob/develop/image_classification/README.md)教程。
- Sigmoid activation function: $ f(x) = sigmoid(x) = \frac{1}{1+e^{-x}} $
- Tanh activation function: $ f(x) = tanh(x) = \frac{e^x-e^{-x}}{e^x+e^{-x}} $ ### 常见激活函数介绍
- sigmoid激活函数： $ f(x) = sigmoid(x) = \frac{1}{1+e^{-x}} $
In fact, tanh function is just a rescaled version of the sigmoid function. It is obtained by magnifying the value of the sigmoid function and moving it downwards by 1. - tanh激活函数： $ f(x) = tanh(x) = \frac{e^x-e^{-x}}{e^x+e^{-x}} $
- ReLU activation function: $ f(x) = max(0, x) $ 实际上，tanh函数只是规模变化的sigmoid函数，将sigmoid函数值放大2倍之后再向下平移1个单位：tanh(x) = 2sigmoid(2x) - 1 。
For more information, please refer to [Activation functions on Wikipedia](https://en.wikipedia.org/wiki/Activation_function). - ReLU激活函数： $ f(x) = max(0, x) $
## Data Preparation 更详细的介绍请参考[维基百科激活函数](https://en.wikipedia.org/wiki/Activation_function)。
PaddlePaddle provides a Python module, `paddle.dataset.mnist`, which downloads and caches the [MNIST dataset](http://yann.lecun.com/exdb/mnist/). The cache is under `/home/username/.cache/paddle/dataset/mnist`: ## 数据介绍
PaddlePaddle在API中提供了自动加载[MNIST](http://yann.lecun.com/exdb/mnist/)数据的模块`paddle.dataset.mnist`。加载后的数据位于`/home/username/.cache/paddle/dataset/mnist`下：
| File name | Description | Size |
|----------------------|--------------|-----------|
|train-images-idx3-ubyte| Training images | 60,000 |
|train-labels-idx1-ubyte| Training labels | 60,000 |
|t10k-images-idx3-ubyte | Evaluation images | 10,000 |
|t10k-labels-idx1-ubyte | Evaluation labels | 10,000 |
| 文件名称 | 说明 |
|----------------------|-------------------------|
|train-images-idx3-ubyte| 训练数据图片，60,000条数据 |
|train-labels-idx1-ubyte| 训练数据标签，60,000条数据 |
|t10k-images-idx3-ubyte | 测试数据图片，10,000条数据 |
|t10k-labels-idx1-ubyte | 测试数据标签，10,000条数据 |
## Model Configuration ## 配置说明
A PaddlePaddle program starts from importing the API package: 首先，加载PaddlePaddle的V2 api包。
```python ```python
import gzip import gzip
import paddle.v2 as paddle import paddle.v2 as paddle
``` ```
其次，定义三个不同的分类器：
We want to use this program to demonstrate three different classifiers, each defined as a Python function: - Softmax回归：只通过一层简单的以softmax为激活函数的全连接层，就可以得到分类的结果。
- Softmax regression: the network has a fully-connection layer with softmax activation:
```python ```python
def softmax_regression(img): def softmax_regression(img):
...@@ -188,26 +188,27 @@ def softmax_regression(img): ...@@ -188,26 +188,27 @@ def softmax_regression(img):
act=paddle.activation.Softmax()) act=paddle.activation.Softmax())
return predict return predict
``` ```
- 多层感知器：下面代码实现了一个含有两个隐藏层（即全连接层）的多层感知器。其中两个隐藏层的激活函数均采用ReLU，输出层的激活函数用Softmax。
- Multi-Layer Perceptron: this network has two hidden fully-connected layers, one with ReLU and the other with softmax activation:
```python ```python
def multilayer_perceptron(img): def multilayer_perceptron(img):
# 第一个全连接层，激活函数为ReLU
hidden1 = paddle.layer.fc(input=img, size=128, act=paddle.activation.Relu()) hidden1 = paddle.layer.fc(input=img, size=128, act=paddle.activation.Relu())
# 第二个全连接层，激活函数为ReLU
hidden2 = paddle.layer.fc(input=hidden1, hidden2 = paddle.layer.fc(input=hidden1,
size=64, size=64,
act=paddle.activation.Relu()) act=paddle.activation.Relu())
# 以softmax为激活函数的全连接输出层，输出层的大小必须为数字的个数10
predict = paddle.layer.fc(input=hidden2, predict = paddle.layer.fc(input=hidden2,
size=10, size=10,
act=paddle.activation.Softmax()) act=paddle.activation.Softmax())
return predict return predict
``` ```
- 卷积神经网络LeNet-5: 输入的二维图像，首先经过两次卷积层到池化层，再经过全连接层，最后使用以softmax为激活函数的全连接层作为输出层。
- Convolution network LeNet-5: the input image is fed through two convolution-pooling layers, a fully-connected layer, and the softmax output layer:
```python ```python
def convolutional_neural_network(img): def convolutional_neural_network(img):
# 第一个卷积-池化层
conv_pool_1 = paddle.networks.simple_img_conv_pool( conv_pool_1 = paddle.networks.simple_img_conv_pool(
input=img, input=img,
filter_size=5, filter_size=5,
...@@ -216,7 +217,7 @@ def convolutional_neural_network(img): ...@@ -216,7 +217,7 @@ def convolutional_neural_network(img):
pool_size=2, pool_size=2,
pool_stride=2, pool_stride=2,
act=paddle.activation.Relu()) act=paddle.activation.Relu())
# 第二个卷积-池化层
conv_pool_2 = paddle.networks.simple_img_conv_pool( conv_pool_2 = paddle.networks.simple_img_conv_pool(
input=conv_pool_1, input=conv_pool_1,
filter_size=5, filter_size=5,
...@@ -225,16 +226,17 @@ def convolutional_neural_network(img): ...@@ -225,16 +226,17 @@ def convolutional_neural_network(img):
pool_size=2, pool_size=2,
pool_stride=2, pool_stride=2,
act=paddle.activation.Relu()) act=paddle.activation.Relu())
# 以softmax为激活函数的全连接输出层，输出层的大小必须为数字的个数10
predict = paddle.layer.fc(input=conv_pool_2, predict = paddle.layer.fc(input=conv_pool_2,
size=10, size=10,
act=paddle.activation.Softmax()) act=paddle.activation.Softmax())
return predict return predict
``` ```
PaddlePaddle provides a special layer `layer.data` for reading data. Let us create a data layer for reading images and connect it to a classification network created using one of above three functions. We also need a cost layer for training the model. 接着，通过`layer.data`调用来获取数据，然后调用分类器（这里我们提供了三个不同的分类器）得到分类结果。训练时，对该结果计算其损失函数，分类问题常常选择交叉熵损失函数。
```python ```python
# 该模型运行在单个CPU上
paddle.init(use_gpu=False, trainer_count=1) paddle.init(use_gpu=False, trainer_count=1)
images = paddle.layer.data( images = paddle.layer.data(
...@@ -242,14 +244,17 @@ images = paddle.layer.data( ...@@ -242,14 +244,17 @@ images = paddle.layer.data(
label = paddle.layer.data( label = paddle.layer.data(
name='label', type=paddle.data_type.integer_value(10)) name='label', type=paddle.data_type.integer_value(10))
# predict = softmax_regression(images) # predict = softmax_regression(images) # Softmax回归
# predict = multilayer_perceptron(images) # uncomment for MLP # predict = multilayer_perceptron(images) #多层感知器
predict = convolutional_neural_network(images) # uncomment for LeNet5 predict = convolutional_neural_network(images) #LeNet5卷积神经网络
cost = paddle.layer.classification_cost(input=predict, label=label) cost = paddle.layer.classification_cost(input=predict, label=label)
``` ```
Now, it is time to specify training parameters. In the following `Momentum` optimizer, `momentum=0.9` means that 90% of the current momentum comes from that of the previous iteration. The learning rate relates to the speed at which the network training converges. Regularization is meant to prevent over-fitting; here we use the L2 regularization. 然后，指定训练相关的参数。
- 训练方法（optimizer)： 代表训练过程在更新权重时采用动量优化器 `Momentum` ，其中参数0.9代表动量优化每次保持前一次速度的0.9倍。
- 训练速度（learning_rate）： 迭代的速度，与网络的训练收敛速度有关系。
- 正则化（regularization）： 是防止网络过拟合的一种手段，此处采用L2正则化。
```python ```python
parameters = paddle.parameters.create(cost) parameters = paddle.parameters.create(cost)
...@@ -264,13 +269,13 @@ trainer = paddle.trainer.SGD(cost=cost, ...@@ -264,13 +269,13 @@ trainer = paddle.trainer.SGD(cost=cost,
update_equation=optimizer) update_equation=optimizer)
``` ```
Then we specify the training data `paddle.dataset.movielens.train()` and testing data `paddle.dataset.movielens.test()`. These two methods are *reader creators*. Once called, a reader creator returns a *reader*. A reader is a Python method, which, once called, returns a Python generator, which yields instances of data. 下一步，我们开始训练过程。`paddle.dataset.movielens.train()`和`paddle.dataset.movielens.test()`分别做训练和测试数据集。这两个函数各自返回一个reader——PaddlePaddle中的reader是一个Python函数，每次调用的时候返回一个Python yield generator。
`shuffle` is a reader decorator. It takes in a reader A as input and returns a new reader B. Under the hood, B calls A to read data in the following fashion: it copies in `buffer_size` instances at a time into a buffer, shuffles the data, and yields the shuffled instances one at a time. A large buffer size would yield very shuffled data. 下面`shuffle`是一个reader decorator，它接受一个reader A，返回另一个reader B —— reader B 每次读入`buffer_size`条训练数据到一个buffer里，然后随机打乱其顺序，并且逐条输出。
`batch` is a special decorator, which takes in reader and outputs a *batch reader*, which doesn't yield an instance, but a minibatch at a time. `batch`是一个特殊的decorator，它的输入是一个reader，输出是一个batched reader —— 在PaddlePaddle里，一个reader每次yield一条训练数据，而一个batched reader每次yield一个minibatch。
`event_handler_plot` is used to plot a figure like below： `event_handler_plot`可以用来在训练过程中画图如下：
![png](./image/train_and_test.png) ![png](./image/train_and_test.png)
...@@ -301,8 +306,7 @@ def event_handler_plot(event): ...@@ -301,8 +306,7 @@ def event_handler_plot(event):
cost_ploter.append(test_title, step, result.cost) cost_ploter.append(test_title, step, result.cost)
``` ```
`event_handler` is used to plot some text data when training. `event_handler` 用来在训练过程中输出训练结果
```python ```python
lists = [] lists = []
...@@ -334,7 +338,7 @@ trainer.train( ...@@ -334,7 +338,7 @@ trainer.train(
num_passes=5) num_passes=5)
``` ```
During training, `trainer.train` invokes `event_handler` for certain events. This gives us a chance to print the training progress. 训练过程是完全自动的，event_handler里打印的日志类似如下所示：
``` ```
# Pass 0, Batch 0, Cost 2.780790, {'classification_error_evaluator': 0.9453125} # Pass 0, Batch 0, Cost 2.780790, {'classification_error_evaluator': 0.9453125}
...@@ -345,20 +349,12 @@ During training, `trainer.train` invokes `event_handler` for certain events. Thi ...@@ -345,20 +349,12 @@ During training, `trainer.train` invokes `event_handler` for certain events. Thi
# Test with Pass 0, Cost 0.326659, {'classification_error_evaluator': 0.09470000118017197} # Test with Pass 0, Cost 0.326659, {'classification_error_evaluator': 0.09470000118017197}
``` ```
After the training, we can check the model's prediction accuracy. 训练之后，检查模型的预测准确度。用 MNIST 训练的时候，一般 softmax回归模型的分类准确率为约为 92.34%，多层感知器为97.66%，卷积神经网络可以达到 99.20%。
```
# find the best pass
best = sorted(lists, key=lambda list: float(list[1]))[0]
print 'Best pass is %s, testing Avgcost is %s' % (best[0], best[1])
print 'The classification accuracy is %.2f%%' % (100 - float(best[2]) * 100)
```
Usually, with MNIST data, the softmax regression model achieves an accuracy around 92.34%, the MLP 97.66%, and the convolution network around 99.20%. Convolution layers have been widely considered a great invention for image processing. ## 应用模型
## Application 可以使用训练好的模型对手写体数字图片进行分类，下面程序展示了如何使用paddle.infer接口进行推断。
After training is done, user can use the trained model to classify images. The following code shows how to inference MNIST images through `paddle.infer` interface.
```python ```python
from PIL import Image from PIL import Image
...@@ -381,17 +377,11 @@ lab = np.argsort(-probs) # probs and lab are the results of one batch data ...@@ -381,17 +377,11 @@ lab = np.argsort(-probs) # probs and lab are the results of one batch data
print "Label of image/infer_3.png is: %d" % lab[0][0] print "Label of image/infer_3.png is: %d" % lab[0][0]
``` ```
## 总结
## Conclusion 本教程的softmax回归、多层感知器和卷积神经网络是最基础的深度学习模型，后续章节中复杂的神经网络都是从它们衍生出来的，因此这几个模型对之后的学习大有裨益。同时，我们也观察到从最简单的softmax回归变换到稍复杂的卷积神经网络的时候，MNIST数据集上的识别准确率有了大幅度的提升，原因是卷积层具有局部连接和共享权重的特性。在之后学习新模型的时候，希望大家也要深入到新模型相比原模型带来效果提升的关键之处。此外，本教程还介绍了PaddlePaddle模型搭建的基本流程，从dataprovider的编写、网络层的构建，到最后的训练和预测。对这个流程熟悉以后，大家就可以用自己的数据，定义自己的网络模型，并完成自己的训练和预测任务了。
This tutorial describes a few common deep learning models using **Softmax regression**, **Multilayer Perceptron Network**, and **Convolutional Neural Network**. Understanding these models is crucial for future learning; the subsequent tutorials derive more sophisticated networks by building on top of them.
When our model evolves from a simple softmax regression to a slightly complex Convolutional Neural Network, the recognition accuracy on the MNIST data set achieves a large improvement in accuracy. This is due to the Convolutional layers' local connections and parameter sharing. While learning new models in the future, we encourage the readers to understand the key ideas that lead a new model to improve the results of an old one.
Moreover, this tutorial introduces the basic flow of PaddlePaddle model design, which starts with a *dataprovider*, a model layer construction, and finally training and prediction. Motivated readers can leverage the flow used in this MNIST handwritten digit classification example and experiment with different data and network architectures to train models for classification tasks of their choice.
## References ## 参考文献
1. LeCun, Yann, Léon Bottou, Yoshua Bengio, and Patrick Haffner. ["Gradient-based learning applied to document recognition."](http://ieeexplore.ieee.org/abstract/document/726791/) Proceedings of the IEEE 86, no. 11 (1998): 2278-2324. 1. LeCun, Yann, Léon Bottou, Yoshua Bengio, and Patrick Haffner. ["Gradient-based learning applied to document recognition."](http://ieeexplore.ieee.org/abstract/document/726791/) Proceedings of the IEEE 86, no. 11 (1998): 2278-2324.
2. Wejéus, Samuel. ["A Neural Network Approach to Arbitrary SymbolRecognition on Modern Smartphones."](http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A753279&dswid=-434) (2014). 2. Wejéus, Samuel. ["A Neural Network Approach to Arbitrary SymbolRecognition on Modern Smartphones."](http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A753279&dswid=-434) (2014).
...@@ -405,7 +395,7 @@ Moreover, this tutorial introduces the basic flow of PaddlePaddle model design, ...@@ -405,7 +395,7 @@ Moreover, this tutorial introduces the basic flow of PaddlePaddle model design,
10. Bishop, Christopher M. ["Pattern recognition."](http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf) Machine Learning 128 (2006): 1-58. 10. Bishop, Christopher M. ["Pattern recognition."](http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf) Machine Learning 128 (2006): 1-58.
<br/> <br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>. <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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Image Classification # 图像分类
=======================
The source code for this chapter is at [book/image_classification](https://github.com/PaddlePaddle/book/tree/develop/03.image_classification). First-time users, please refer to PaddlePaddle [Installation Tutorial](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book) for installation instructions. 本教程源代码目录在[book/image_classification](https://github.com/PaddlePaddle/book/tree/develop/03.image_classification)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## Background ## 背景介绍
Compared to words, images provide much more vivid and easier to understand information with an artistic sense. They are an important source for people to express and exchange ideas. In this chapter, we focus on one of the essential problems in image recognition -- image classification. 图像相比文字能够提供更加生动、容易理解及更具艺术感的信息，是人们转递与交换信息的重要来源。在本教程中，我们专注于图像识别领域的一个重要问题，即图像分类。
Image classification is the task of distinguishing images in different categories based on their semantic meaning. It is a core problem in computer vision and is also the foundation of other higher level computer vision tasks such as object detection, image segmentation, object tracking, action recognition, etc. Image classification has applications in many areas such as face recognition, intelligent video analysis in security systems, traffic scene recognition in transportation systems, content-based image retrieval and automatic photo indexing in web services, image classification in medicine, etc. 图像分类是根据图像的语义信息将不同类别图像区分开来，是计算机视觉中重要的基本问题，也是图像检测、图像分割、物体跟踪、行为分析等其他高层视觉任务的基础。图像分类在很多领域有广泛应用，包括安防领域的人脸识别和智能视频分析等，交通领域的交通场景识别，互联网领域基于内容的图像检索和相册自动归类，医学领域的图像识别等。
To classify an image we first encode the entire image using handcrafted or learned features and then determine the category using a classifier. Thus, feature extraction plays an important role in image classification. Prior to deep learning the BoW(Bag of Words) model was the most widely used method for classifying an image as well as an object. The BoW technique was introduced in Natural Language Processing where a training sentence is represented as a bag of words. In the context of image classification, the BoW model requires constructing a dictionary. The simplest BoW framework can be designed with three steps: **feature extraction**, **feature encoding** and **classifier design**.
Using Deep learning, image classification can be framed as a supervised or unsupervised learning problem that uses hierarchical features automatically without any need for manually crafted features from the image. In recent years, Convolutional Neural Networks (CNNs) have made significant progress in image classification. CNNs use raw image pixels as input, extract low-level and high-level abstract features through convolution operations, and directly output the classification results from the model. This style of end-to-end learning has lead to not only increased performance but also wider adoption various applications. 一般来说，图像分类通过手工特征或特征学习方法对整个图像进行全部描述，然后使用分类器判别物体类别，因此如何提取图像的特征至关重要。在深度学习算法之前使用较多的是基于词袋(Bag of Words)模型的物体分类方法。词袋方法从自然语言处理中引入，即一句话可以用一个装了词的袋子表示其特征，袋子中的词为句子中的单词、短语或字。对于图像而言，词袋方法需要构建字典。最简单的词袋模型框架可以设计为**底层特征抽取**、**特征编码**、**分类器设计**三个过程。
In this chapter, we introduce deep-learning-based image classification methods and explain how to train a CNN model using PaddlePaddle. 而基于深度学习的图像分类方法，可以通过有监督或无监督的方式**学习**层次化的特征描述，从而取代了手工设计或选择图像特征的工作。深度学习模型中的卷积神经网络(Convolution Neural Network, CNN)近年来在图像领域取得了惊人的成绩，CNN直接利用图像像素信息作为输入，最大程度上保留了输入图像的所有信息，通过卷积操作进行特征的提取和高层抽象，模型输出直接是图像识别的结果。这种基于"输入-输出"直接端到端的学习方法取得了非常好的效果，得到了广泛的应用。
## Demonstration 本教程主要介绍图像分类的深度学习模型，以及如何使用PaddlePaddle训练CNN模型。
An image can be classified by a general as well as fine-grained image classifier. ## 效果展示
图像分类包括通用图像分类、细粒度图像分类等。图1展示了通用图像分类效果，即模型可以正确识别图像上的主要物体。
Figure 1 shows the results of a general image classifier -- the trained model can correctly recognize the main objects in the images.
<p align="center"> <p align="center">
<img src="image/dog_cat.png " width="350" ><br/> <img src="image/dog_cat.png " width="350" ><br/>
Figure 1. General image classification 图1. 通用图像分类展示
</p> </p>
Figure 2 shows the results of a fine-grained image classifier. This task of flower recognition requires correctly recognizing of the flower's categories. 图2展示了细粒度图像分类-花卉识别的效果，要求模型可以正确识别花的类别。
<p align="center"> <p align="center">
<img src="image/flowers.png" width="400" ><br/> <img src="image/flowers.png" width="400" ><br/>
Figure 2. Fine-grained image classification 图2. 细粒度图像分类展示
</p> </p>
A good model should recognize objects of different categories correctly. The results of such a model should not vary due to viewpoint variation, illumination conditions, object distortion or occlusion. 一个好的模型既要对不同类别识别正确，同时也应该能够对不同视角、光照、背景、变形或部分遮挡的图像正确识别(这里我们统一称作图像扰动)。图3展示了一些图像的扰动，较好的模型会像聪明的人类一样能够正确识别。
Figure 3 shows some images with various disturbances. A good model should classify these images correctly like humans.
<p align="center"> <p align="center">
<img src="image/variations_en.png" width="550" ><br/> <img src="image/variations.png" width="550" ><br/>
Figure 3. Disturbed images [22] 图3. 扰动图片展示[22]
</p> </p>
## Model Overview ## 模型概览
A large amount of research in image classification is built upon public datasets such as [PASCAL VOC](http://host.robots.ox.ac.uk/pascal/VOC/), [ImageNet](http://image-net.org/) etc. Many image classification algorithms are usually evaluated and compared on these datasets. PASCAL VOC is a computer vision competition started in 2005, and ImageNet is a dataset for Large Scale Visual Recognition Challenge (ILSVRC) started in 2010. In this chapter, we introduce some image classification models from the submissions to these competitions.
Before 2012, traditional image classification was accomplished with the three steps described in the background section. A complete model construction usually involves the following stages: low-level feature extraction, feature encoding, spatial constraint or feature clustering, classifier design, model ensemble.
1). **Low-level feature extraction**: This step extracts large amounts of local features according to fixed strides and scales. Popular local features include Scale-Invariant Feature Transform (SIFT)[1], Histogram of Oriented Gradient(HOG)[2], Local Binary Pattern(LBP)[3], etc. A common practice is to employ multiple feature descriptors in order to avoid missing a lot of information. 图像识别领域大量的研究成果都是建立在[PASCAL VOC](http://host.robots.ox.ac.uk/pascal/VOC/)、[ImageNet](http://image-net.org/)等公开的数据集上，很多图像识别算法通常在这些数据集上进行测试和比较。PASCAL VOC是2005年发起的一个视觉挑战赛，ImageNet是2010年发起的大规模视觉识别竞赛(ILSVRC)的数据集，在本章中我们基于这些竞赛的一些论文介绍图像分类模型。
2). **Feature encoding**: Low-level features contain a large amount of redundancy and noise. In order to improve the robustness of features, it is necessary to employ a feature transformation to encode low-level features. This is called feature encoding. Common feature encoding methods include vector quantization [4], sparse coding [5], locality-constrained linear coding [6], Fisher vector encoding [7], etc. 在2012年之前的传统图像分类方法可以用背景描述中提到的三步完成，但通常完整建立图像识别模型一般包括底层特征学习、特征编码、空间约束、分类器设计、模型融合等几个阶段。
1). **底层特征提取**: 通常从图像中按照固定步长、尺度提取大量局部特征描述。常用的局部特征包括SIFT(Scale-Invariant Feature Transform, 尺度不变特征转换) \[[1](#参考文献)\]、HOG(Histogram of Oriented Gradient, 方向梯度直方图) \[[2](#参考文献)\]、LBP(Local Bianray Pattern, 局部二值模式) \[[3](#参考文献)\] 等，一般也采用多种特征描述子，防止丢失过多的有用信息。
2). **特征编码**: 底层特征中包含了大量冗余与噪声，为了提高特征表达的鲁棒性，需要使用一种特征变换算法对底层特征进行编码，称作特征编码。常用的特征编码包括向量量化编码 \[[4](#参考文献)\]、稀疏编码 \[[5](#参考文献)\]、局部线性约束编码 \[[6](#参考文献)\]、Fisher向量编码 \[[7](#参考文献)\] 等。
3). **空间特征约束**: 特征编码之后一般会经过空间特征约束，也称作**特征汇聚**。特征汇聚是指在一个空间范围内，对每一维特征取最大值或者平均值，可以获得一定特征不变形的特征表达。金字塔特征匹配是一种常用的特征聚会方法，这种方法提出将图像均匀分块，在分块内做特征汇聚。
4). **通过分类器分类**: 经过前面步骤之后一张图像可以用一个固定维度的向量进行描述，接下来就是经过分类器对图像进行分类。通常使用的分类器包括SVM(Support Vector Machine, 支持向量机)、随机森林等。而使用核方法的SVM是最为广泛的分类器，在传统图像分类任务上性能很好。
3). **Spatial constraint**: Spatial constraint or feature clustering is usually adopted after feature encoding for extracting the maximum or average of each dimension in the spatial domain. Pyramid feature matching--a popular feature clustering method--divides an image uniformly into patches and performs feature clustering in each patch. 这种方法在PASCAL VOC竞赛中的图像分类算法中被广泛使用 \[[18](#参考文献)\]。[NEC实验室](http://www.nec-labs.com/)在ILSVRC2010中采用SIFT和LBP特征，两个非线性编码器以及SVM分类器获得图像分类的冠军 \[[8](#参考文献)\]。
4). **Classification**: In the above steps an image can be described by a vector of fixed dimension. Then a classifier can be used to classify the image into categories. Common classifiers include Support Vector Machine(SVM), random forest etc. Kernel SVM is the most popular classifier and has achieved very good performance in traditional image classification tasks. Alex Krizhevsky在2012年ILSVRC提出的CNN模型 \[[9](#参考文献)\] 取得了历史性的突破，效果大幅度超越传统方法，获得了ILSVRC2012冠军，该模型被称作AlexNet。这也是首次将深度学习用于大规模图像分类中。从AlexNet之后，涌现了一系列CNN模型，不断地在ImageNet上刷新成绩，如图4展示。随着模型变得越来越深以及精妙的结构设计，Top-5的错误率也越来越低，降到了3.5%附近。而在同样的ImageNet数据集上，人眼的辨识错误率大概在5.1%，也就是目前的深度学习模型的识别能力已经超过了人眼。
This method has been used widely as image classification algorithm in PASCAL VOC [18]. NEC Labs(http://www.nec-labs.com/) won the championship by employing SIFT and LBP features, two non-linear encoders and SVM in ILSVRC 2010 [8].
The CNN model--AlexNet proposed by Alex Krizhevsky et al.[9], made a breakthrough in ILSVRC 2012. It dramatically outperformed traditional methods and won the ILSVRC championship in 2012. This was also the first time that a deep learning method was used for large-scale image classification. Since AlexNet, a series of CNN models have been proposed that have advanced the state of the art steadily on Imagenet as shown in Figure 4. With deeper and more sophisticated architectures, Top-5 error rate is getting lower and lower (to around 3.5%). The error rate of human raters on the same Imagenet dataset is 5.1%, which means that the image classification capability of a deep learning model has surpassed human raters.
<p align="center"> <p align="center">
<img src="image/ilsvrc.png" width="500" ><br/> <img src="image/ilsvrc.png" width="500" ><br/>
Figure 4. Top-5 error rates on ILSVRC image classification 图4. ILSVRC图像分类Top-5错误率
</p> </p>
### CNN ### CNN
Traditional CNNs consist of convolutional and fully-connected layers and use the softmax multi-category classifier with the cross-entropy loss function. Figure 5 shows a typical CNN. We first introduce the common components of a CNN. 传统CNN包含卷积层、全连接层等组件，并采用softmax多类别分类器和多类交叉熵损失函数，一个典型的卷积神经网络如图5所示，我们先介绍用来构造CNN的常见组件。
<p align="center"> <p align="center">
<img src="image/lenet_en.png"><br/> <img src="image/lenet.png"><br/>
Figure 5. A CNN example [20] 图5. CNN网络示例[20]
</p> </p>
- convolutional layer: this layer uses the convolution operation to extract (low-level and high-level) features and to discover local correlation and spatial invariance. - 卷积层(convolution layer): 执行卷积操作提取底层到高层的特征，发掘出图片局部关联性质和空间不变性质。
- 池化层(pooling layer): 执行降采样操作。通过取卷积输出特征图中局部区块的最大值(max-pooling)或者均值(avg-pooling)。降采样也是图像处理中常见的一种操作，可以过滤掉一些不重要的高频信息。
- pooling layer: this layer down samples feature maps by extracting local max (max-pooling) or average (avg-pooling) value of each patch in the feature map. Down-sampling is a common operation in image processing and is used to filter out high-frequency information. - 全连接层(fully-connected layer，或者fc layer): 输入层到隐藏层的神经元是全部连接的。
- 非线性变化: 卷积层、全连接层后面一般都会接非线性变化层，例如Sigmoid、Tanh、ReLu等来增强网络的表达能力，在CNN里最常使用的为ReLu激活函数。
- Dropout \[[10](#参考文献)\] : 在模型训练阶段随机让一些隐层节点权重不工作，提高网络的泛化能力，一定程度上防止过拟合。
- fully-connected layer: this layer fully connects neurons between two adjacent layers. 另外，在训练过程中由于每层参数不断更新，会导致下一次输入分布发生变化，这样导致训练过程需要精心设计超参数。如2015年Sergey Ioffe和Christian Szegedy提出了Batch Normalization (BN)算法 \[[14](#参考文献)\] 中，每个batch对网络中的每一层特征都做归一化，使得每层分布相对稳定。BN算法不仅起到一定的正则作用，而且弱化了一些超参数的设计。经过实验证明，BN算法加速了模型收敛过程，在后来较深的模型中被广泛使用。
- non-linear activation: Convolutional and fully-connected layers are usually followed by some non-linear activation layers. Non-linearities enhance the expression capability of the network. Some examples of non-linear activation functions are Sigmoid, Tanh and ReLU. ReLU is the most commonly used activation function in CNN. 接下来我们主要介绍VGG，GoogleNet和ResNet网络结构。
- Dropout [10]: At each training stage, individual nodes are dropped out of the network with a certain probability. This improves the network's ability to generalize and avoids overfitting.
Parameter updates at each layer during training causes input layer distributions to change and in turn requires hyper-parameters to be careful tuned. In 2015, Sergey Ioffe and Christian Szegedy proposed a Batch Normalization (BN) algorithm [14], which normalizes the features of each batch in a layer, and enables relatively stable distribution in each layer. Not only does BN algorithm act as a regularizer, but also reduces the need for careful hyper-parameter design. Experiments demonstrate that BN algorithm accelerates the training convergence and has been widely used in later deeper models.
In the following sections, we will introduce the following network architectures - VGG, GoogleNet and ResNets.
### VGG ### VGG
The Oxford Visual Geometry Group (VGG) proposed the VGG network in ILSVRC 2014 [11]. This model is deeper and wider than previous neural architectures. It consists of five main groups of convolution operations. Adjacent convolution groups are connected via max-pooling layers. Each group contains a series of 3x3 convolutional layers (i.e. kernels). The number of convolution kernels stays the same within the group and increases from 64 in the first group to 512 in the last one. The total number of learnable layers could be 11, 13, 16, or 19 depending on the number of convolutional layers in each group. Figure 6 illustrates a 16-layer VGG. The neural architecture of VGG is relatively simple and has been adopted by many papers such as the first one that surpassed human-level performance on ImageNet [19]. 牛津大学VGG(Visual Geometry Group)组在2014年ILSVRC提出的模型被称作VGG模型 \[[11](#参考文献)\] 。该模型相比以往模型进一步加宽和加深了网络结构，它的核心是五组卷积操作，每两组之间做Max-Pooling空间降维。同一组内采用多次连续的3X3卷积，卷积核的数目由较浅组的64增多到最深组的512，同一组内的卷积核数目是一样的。卷积之后接两层全连接层，之后是分类层。由于每组内卷积层的不同，有11、13、16、19层这几种模型，下图展示一个16层的网络结构。VGG模型结构相对简洁，提出之后也有很多文章基于此模型进行研究，如在ImageNet上首次公开超过人眼识别的模型\[[19](#参考文献)\]就是借鉴VGG模型的结构。
<p align="center"> <p align="center">
<img src="image/vgg16.png" width="750" ><br/> <img src="image/vgg16.png" width="750" ><br/>
Figure 6. VGG16 model for ImageNet 图6. 基于ImageNet的VGG16模型
</p> </p>
### GoogleNet ### GoogleNet
GoogleNet [12] won the ILSVRC championship in 2014. GoogleNet borrowed some ideas from the Network in Network(NIN) model [13] and is built on the Inception blocks. Let us first familiarize ourselves with these first. GoogleNet \[[12](#参考文献)\] 在2014年ILSVRC的获得了冠军，在介绍该模型之前我们先来了解NIN(Network in Network)模型 \[[13](#参考文献)\] 和Inception模块，因为GoogleNet模型由多组Inception模块组成，模型设计借鉴了NIN的一些思想。
The two main characteristics of the NIN model are:
1) A single-layer convolutional network is replaced with a Multi-Layer Perceptron Convolution (MLPconv). MLPconv is a tiny multi-layer convolutional network. It enhances non-linearity by adding several 1x1 convolutional layers after linear ones. NIN模型主要有两个特点：1) 引入了多层感知卷积网络(Multi-Layer Perceptron Convolution, MLPconv)代替一层线性卷积网络。MLPconv是一个微小的多层卷积网络，即在线性卷积后面增加若干层1x1的卷积，这样可以提取出高度非线性特征。2) 传统的CNN最后几层一般都是全连接层，参数较多。而NIN模型设计最后一层卷积层包含类别维度大小的特征图，然后采用全局均值池化(Avg-Pooling)替代全连接层，得到类别维度大小的向量，再进行分类。这种替代全连接层的方式有利于减少参数。
2) In traditional CNNs, the last fewer layers are usually fully-connected with a large number of parameters. In contrast, NIN replaces all fully-connected layers with convolutional layers with feature maps of the same size as the category dimension and a global average pooling. This replacement of fully-connected layers significantly reduces the number of parameters. Inception模块如下图7所示，图(a)是最简单的设计，输出是3个卷积层和一个池化层的特征拼接。这种设计的缺点是池化层不会改变特征通道数，拼接后会导致特征的通道数较大，经过几层这样的模块堆积后，通道数会越来越大，导致参数和计算量也随之增大。为了改善这个缺点，图(b)引入3个1x1卷积层进行降维，所谓的降维就是减少通道数，同时如NIN模型中提到的1x1卷积也可以修正线性特征。
Figure 7 depicts two Inception blocks. Figure 7(a) is the simplest design. The output is a concatenation of features from three convolutional layers and one pooling layer. The disadvantage of this design is that the pooling layer does not change the number of filters and leads to an increase in the number of outputs. After several of such blocks, the number of outputs and parameters become larger and larger and lead to higher computation complexity. To overcome this drawback, the Inception block in Figure 7(b) employs three 1x1 convolutional layers. These reduce dimensions or the number of channels but improve the non-linearity of the network.
<p align="center"> <p align="center">
<img src="image/inception_en.png" width="800" ><br/> <img src="image/inception.png" width="800" ><br/>
Figure 7. Inception block 图7. Inception模块
</p> </p>
GoogleNet consists of multiple stacked Inception blocks followed by an avg-pooling layer as in NIN instead of traditional fully connected layers. The difference between GoogleNet and NIN is that GoogleNet adds a fully connected layer after avg-pooling layer to output a vector of category size. Besides these two characteristics, the features from middle layers of a GoogleNet are also very discriminative. Therefore, GoogeleNet inserts two auxiliary classifiers in the model for enhancing gradient and regularization when doing backpropagation. The loss function of the whole network is the weighted sum of these three classifiers. GoogleNet由多组Inception模块堆积而成。另外，在网络最后也没有采用传统的多层全连接层，而是像NIN网络一样采用了均值池化层；但与NIN不同的是，池化层后面接了一层到类别数映射的全连接层。除了这两个特点之外，由于网络中间层特征也很有判别性，GoogleNet在中间层添加了两个辅助分类器，在后向传播中增强梯度并且增强正则化，而整个网络的损失函数是这个三个分类器的损失加权求和。
Figure 8 illustrates the neural architecture of a GoogleNet which consists of 22 layers: it starts with three regular convolutional layers followed by three groups of sub-networks -- the first group contains two Inception blocks, the second one five, and the third one two. It ends up with an average pooling and a fully-connected layer. GoogleNet整体网络结构如图8所示，总共22层网络：开始由3层普通的卷积组成；接下来由三组子网络组成，第一组子网络包含2个Inception模块，第二组包含5个Inception模块，第三组包含2个Inception模块；然后接均值池化层、全连接层。
<p align="center"> <p align="center">
<img src="image/googlenet.jpeg" ><br/> <img src="image/googlenet.jpeg" ><br/>
Figure 8. GoogleNet[12] 图8. GoogleNet[12]
</p> </p>
The above model is the first version of GoogleNet or GoogelNet-v1. GoogleNet-v2 [14] introduced BN layer; GoogleNet-v3 [16] further split some convolutional layers, which increases non-linearity and network depth; GoogelNet-v4 [17] leads to the design idea of ResNet which will be introduced in the next section. The evolution from v1 to v4 improved the accuracy rate consistently. We will not go into details of the neural architectures of v2 to v4.
上面介绍的是GoogleNet第一版模型(称作GoogleNet-v1)。GoogleNet-v2 \[[14](#参考文献)\] 引入BN层；GoogleNet-v3 \[[16](#参考文献)\] 对一些卷积层做了分解，进一步提高网络非线性能力和加深网络；GoogleNet-v4 \[[17](#参考文献)\] 引入下面要讲的ResNet设计思路。从v1到v4每一版的改进都会带来准确度的提升，介于篇幅，这里不再详细介绍v2到v4的结构。
### ResNet ### ResNet
Residual Network(ResNet)[15] won the 2015 championship on three ImageNet competitions -- image classification, object localization, and object detection. The main challenge in training deeper networks is that accuracy degrades with network depth. The authors of ResNet proposed a residual learning approach to ease the difficulty of training deeper networks. Based on the design ideas of BN, small convolutional kernels, full convolutional network, ResNets reformulate the layers as residual blocks, with each block containing two branches, one directly connecting input to the output, the other performing two to three convolutions and calculating the residual function with reference to the layer inputs. The outputs of these two branches are then added up. ResNet(Residual Network) \[[15](#参考文献)\] 是2015年ImageNet图像分类、图像物体定位和图像物体检测比赛的冠军。针对训练卷积神经网络时加深网络导致准确度下降的问题，ResNet提出了采用残差学习。在已有设计思路(BN, 小卷积核，全卷积网络)的基础上，引入了残差模块。每个残差模块包含两条路径，其中一条路径是输入特征的直连通路，另一条路径对该特征做两到三次卷积操作得到该特征的残差，最后再将两条路径上的特征相加。
Figure 9 illustrates the ResNet architecture. To the left is the basic building block, it consists of two 3x3 convolutional layers of the same channels. To the right is a Bottleneck block. The bottleneck is a 1x1 convolutional layer used to reduce dimension from 256 to 64. The other 1x1 convolutional layer is used to increase dimension from 64 to 256. Thus, the number of input and output channels of the middle 3x3 convolutional layer is 64, which is relatively small. 残差模块如图9所示，左边是基本模块连接方式，由两个输出通道数相同的3x3卷积组成。右边是瓶颈模块(Bottleneck)连接方式，之所以称为瓶颈，是因为上面的1x1卷积用来降维(图示例即256->64)，下面的1x1卷积用来升维(图示例即64->256)，这样中间3x3卷积的输入和输出通道数都较小(图示例即64->64)。
<p align="center"> <p align="center">
<img src="image/resnet_block.jpg" width="400"><br/> <img src="image/resnet_block.jpg" width="400"><br/>
Figure 9. Residual block 图9. 残差模块
</p> </p>
Figure 10 illustrates ResNets with 50, 101, 152 layers, respectively. All three networks use bottleneck blocks of different numbers of repetitions. ResNet converges very fast and can be trained with hundreds or thousands of layers. 图10展示了50、101、152层网络连接示意图，使用的是瓶颈模块。这三个模型的区别在于每组中残差模块的重复次数不同(见图右上角)。ResNet训练收敛较快，成功的训练了上百乃至近千层的卷积神经网络。
<p align="center"> <p align="center">
<img src="image/resnet.png"><br/> <img src="image/resnet.png"><br/>
Figure 10. ResNet model for ImageNet 图10. 基于ImageNet的ResNet模型
</p> </p>
## Dataset ## 数据准备
Commonly used public datasets for image classification are [CIFAR](https://www.cs.toronto.edu/~kriz/cifar.html), [ImageNet](http://image-net.org/), [COCO](http://mscoco.org/), etc. Those used for fine-grained image classification are [CUB-200-2011](http://www.vision.caltech.edu/visipedia/CUB-200-2011.html), [Stanford Dog](http://vision.stanford.edu/aditya86/ImageNetDogs/), [Oxford-flowers](http://www.robots.ox.ac.uk/~vgg/data/flowers/), etc. Among these, the ImageNet dataset is the largest. Most research results are reported on ImageNet as mentioned in the Model Overview section. Since 2010, the ImageNet dataset has gone through some changes. The commonly used ImageNet-2012 dataset contains 1000 categories. There are 1,281,167 training images, ranging from 732 to 1200 images per category, and 50,000 validation images with 50 images per category in average. 通用图像分类公开的标准数据集常用的有[CIFAR](https://www.cs.toronto.edu/~kriz/cifar.html)、[ImageNet](http://image-net.org/)、[COCO](http://mscoco.org/)等，常用的细粒度图像分类数据集包括[CUB-200-2011](http://www.vision.caltech.edu/visipedia/CUB-200-2011.html)、[Stanford Dog](http://vision.stanford.edu/aditya86/ImageNetDogs/)、[Oxford-flowers](http://www.robots.ox.ac.uk/~vgg/data/flowers/)等。其中ImageNet数据集规模相对较大，如[模型概览](#模型概览)一章所讲，大量研究成果基于ImageNet。ImageNet数据从2010年来稍有变化，常用的是ImageNet-2012数据集，该数据集包含1000个类别：训练集包含1,281,167张图片，每个类别数据732至1300张不等，验证集包含50,000张图片，平均每个类别50张图片。
Since ImageNet is too large to be downloaded and trained efficiently, we use [CIFAR-10](https://www.cs.toronto.edu/~kriz/cifar.html) in this tutorial. The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. Figure 11 shows all the classes in CIFAR-10 as well as 10 images randomly sampled from each category. 由于ImageNet数据集较大，下载和训练较慢，为了方便大家学习，我们使用[CIFAR10](<https://www.cs.toronto.edu/~kriz/cifar.html>)数据集。CIFAR10数据集包含60,000张32x32的彩色图片，10个类别，每个类包含6,000张。其中50,000张图片作为训练集，10000张作为测试集。图11从每个类别中随机抽取了10张图片，展示了所有的类别。
<p align="center"> <p align="center">
<img src="image/cifar.png" width="350"><br/> <img src="image/cifar.png" width="350"><br/>
Figure 11. CIFAR10 dataset[21] 图11. CIFAR10数据集[21]
</p> </p>
`paddle.datasets` package encapsulates multiple public datasets, including `cifar`, `imdb`, `mnist`, `moivelens` and `wmt14`, etc. There's no need to manually download and preprocess CIFAR-10. Paddle API提供了自动加载cifar数据集模块 `paddle.dataset.cifar`。
After issuing a command `python train.py`, training will start immediately. The following sections describe the details: 通过输入`python train.py`，就可以开始训练模型了，以下小节将详细介绍`train.py`的相关内容。
## Model Structure ### 模型结构
### Initialize PaddlePaddle #### Paddle 初始化
We must import and initialize PaddlePaddle (enable/disable GPU, set the number of trainers, etc). 通过 `paddle.init`，初始化Paddle是否使用GPU，trainer的数目等等。
```python ```python
import sys import sys
...@@ -220,29 +207,30 @@ from resnet import resnet_cifar10 ...@@ -220,29 +207,30 @@ from resnet import resnet_cifar10
paddle.init(use_gpu=False, trainer_count=1) paddle.init(use_gpu=False, trainer_count=1)
``` ```
As mentioned in section [Model Overview](#model-overview), here we provide the implementations of the VGG and ResNet models. 本教程中我们提供了VGG和ResNet两个模型的配置。
### VGG #### VGG
First, we use a VGG network. Since the image size and amount of CIFAR10 are relatively small comparing to ImageNet, we use a small version of VGG network for CIFAR10. Convolution groups incorporate BN and dropout operations. 首先介绍VGG模型结构，由于CIFAR10图片大小和数量相比ImageNet数据小很多，因此这里的模型针对CIFAR10数据做了一定的适配。卷积部分引入了BN和Dropout操作。
1. Define input data and its dimension 1. 定义数据输入及其维度
The input to the network is defined as `paddle.layer.data`, or image pixels in the context of image classification. The images in CIFAR10 are 32x32 color images of three channels. Therefore, the size of the input data is 3072 (3x32x32), and the number of categories is 10. 网络输入定义为 `data_layer` (数据层)，在图像分类中即为图像像素信息。CIFRAR10是RGB 3通道32x32大小的彩色图，因此输入数据大小为3072(3x32x32)，类别大小为10，即10分类。
```python ```python
datadim = 3 * 32 * 32 datadim = 3 * 32 * 32
classdim = 10 classdim = 10
image = paddle.layer.data( image = paddle.layer.data(
name="image", type=paddle.data_type.dense_vector(datadim)) name="image", type=paddle.data_type.dense_vector(datadim))
``` ```
2. Define VGG main module 2. 定义VGG网络核心模块
```python ```python
net = vgg_bn_drop(image) net = vgg_bn_drop(image)
``` ```
The input to VGG main module is from the data layer. `vgg_bn_drop` defines a 16-layer VGG network, with each convolutional layer followed by BN and dropout layers. Here is the definition in detail: VGG核心模块的输入是数据层，`vgg_bn_drop` 定义了16层VGG结构，每层卷积后面引入BN层和Dropout层，详细的定义如下：
```python ```python
def vgg_bn_drop(input): def vgg_bn_drop(input):
...@@ -275,15 +263,15 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela ...@@ -275,15 +263,15 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela
return fc2 return fc2
``` ```
2.1. First, define a convolution block or conv_block. The default convolution kernel is 3x3, and the default pooling size is 2x2 with stride 2. Dropout specifies the probability in dropout operation. Function `img_conv_group` is defined in `paddle.networks` consisting of a series of `Conv->BN->ReLu->Dropout` and a `Pooling`. 2.1. 首先定义了一组卷积网络，即conv_block。卷积核大小为3x3，池化窗口大小为2x2，窗口滑动大小为2，groups决定每组VGG模块是几次连续的卷积操作，dropouts指定Dropout操作的概率。所使用的`img_conv_group`是在`paddle.networks`中预定义的模块，由若干组 Conv->BN->ReLu->Dropout 和 一组 Pooling 组成。
2.2. Five groups of convolutions. The first two groups perform two convolutions, while the last three groups perform three convolutions. The dropout rate of the last convolution in each group is set to 0, which means there is no dropout for this layer. 2.2. 五组卷积操作，即 5个conv_block。 第一、二组采用两次连续的卷积操作。第三、四、五组采用三次连续的卷积操作。每组最后一个卷积后面Dropout概率为0，即不使用Dropout操作。
2.3. The last two layers are fully-connected layers of dimension 512. 2.3. 最后接两层512维的全连接。
3. Define Classifier 3. 定义分类器
The above VGG network extracts high-level features and maps them to a vector of the same size as the categories. Softmax function or classifier is then used for calculating the probability of the image belonging to each category. 通过上面VGG网络提取高层特征，然后经过全连接层映射到类别维度大小的向量，再通过Softmax归一化得到每个类别的概率，也可称作分类器。
```python ```python
out = paddle.layer.fc(input=net, out = paddle.layer.fc(input=net,
...@@ -291,9 +279,9 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela ...@@ -291,9 +279,9 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela
act=paddle.activation.Softmax()) act=paddle.activation.Softmax())
``` ```
4. Define Loss Function and Outputs 4. 定义损失函数和网络输出
In the context of supervised learning, labels of training images are defined in `paddle.layer.data` as well. During training, the cross-entropy loss function is used and the loss is the output of the network. During testing, the outputs are the probabilities calculated in the classifier. 在有监督训练中需要输入图像对应的类别信息，同样通过`paddle.layer.data`来定义。训练中采用多类交叉熵作为损失函数，并作为网络的输出，预测阶段定义网络的输出为分类器得到的概率信息。
```python ```python
lbl = paddle.layer.data( lbl = paddle.layer.data(
...@@ -303,20 +291,19 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela ...@@ -303,20 +291,19 @@ First, we use a VGG network. Since the image size and amount of CIFAR10 are rela
### ResNet ### ResNet
The first, third and fourth steps of a ResNet are the same as a VGG. The second one is the main module. ResNet模型的第1、3、4步和VGG模型相同，这里不再介绍。主要介绍第2步即CIFAR10数据集上ResNet核心模块。
```python ```python
net = resnet_cifar10(image, depth=56) net = resnet_cifar10(image, depth=56)
``` ```
Here are some basic functions used in `resnet_cifar10`: 先介绍`resnet_cifar10`中的一些基本函数，再介绍网络连接过程。
- `conv_bn_layer` : convolutional layer followed by BN. - `conv_bn_layer` : 带BN的卷积层。
- `shortcut` : the shortcut branch in a residual block. There are two kinds of shortcuts: 1x1 convolution used when the number of channels between input and output is different; direct connection used otherwise. - `shortcut` : 残差模块的"直连"路径，"直连"实际分两种形式：残差模块输入和输出特征通道数不等时，采用1x1卷积的升维操作；残差模块输入和输出通道相等时，采用直连操作。
- `basicblock` : 一个基础残差模块，即图9左边所示，由两组3x3卷积组成的路径和一条"直连"路径组成。
- `basicblock` : a basic residual module as shown in the left of Figure 9, it consists of two sequential 3x3 convolutions and one "shortcut" branch. - `bottleneck` : 一个瓶颈残差模块，即图9右边所示，由上下1x1卷积和中间3x3卷积组成的路径和一条"直连"路径组成。
- `bottleneck` : a bottleneck module as shown in the right of Figure 9, it consists of two 1x1 convolutions with one 3x3 convolution in between branch and a "shortcut" branch. - `layer_warp` : 一组残差模块，由若干个残差模块堆积而成。每组中第一个残差模块滑动窗口大小与其他可以不同，以用来减少特征图在垂直和水平方向的大小。
- `layer_warp` : a group of residual modules consisting of several stacking blocks. In each group, the sliding window size of the first residual block could be different from the rest of blocks, in order to reduce the size of feature maps along horizontal and vertical directions.
```python ```python
def conv_bn_layer(input, def conv_bn_layer(input,
...@@ -358,13 +345,13 @@ def layer_warp(block_func, ipt, features, count, stride): ...@@ -358,13 +345,13 @@ def layer_warp(block_func, ipt, features, count, stride):
return tmp return tmp
``` ```
The following are the components of `resnet_cifar10`: `resnet_cifar10` 的连接结构主要有以下几个过程。
1. The lowest level is `conv_bn_layer`. 1. 底层输入连接一层 `conv_bn_layer`，即带BN的卷积层。
2. The middle level consists of three `layer_warp`, each of which uses the left residual block in Figure 9. 2. 然后连接3组残差模块即下面配置3组 `layer_warp` ，每组采用图 10 左边残差模块组成。
3. The last level is average pooling layer. 3. 最后对网络做均值池化并返回该层。
Note: besides the first convolutional layer and the last fully-connected layer, the total number of layers in three `layer_warp` should be dividable by 6, that is the depth of `resnet_cifar10` should satisfy $(depth - 2) % 6 == 0$. 注意：除过第一层卷积层和最后一层全连接层之外，要求三组 `layer_warp` 总的含参层数能够被6整除，即 `resnet_cifar10` 的 depth 要满足 $(depth - 2) % 6 == 0$ 。
```python ```python
def resnet_cifar10(ipt, depth=32): def resnet_cifar10(ipt, depth=32):
...@@ -382,21 +369,26 @@ def resnet_cifar10(ipt, depth=32): ...@@ -382,21 +369,26 @@ def resnet_cifar10(ipt, depth=32):
return pool return pool
``` ```
## Model Training ## 训练模型
### Define Parameters ### 定义参数
First, we create the model parameters according to the previous model configuration `cost`. 首先依据模型配置的`cost`定义模型参数。
```python ```python
# Create parameters # Create parameters
parameters = paddle.parameters.create(cost) parameters = paddle.parameters.create(cost)
``` ```
### Create Trainer 可以打印参数名字，如果在网络配置中没有指定名字，则默认生成。
```python
print parameters.keys()
```
### 构造训练(Trainer)
Before creating a training module, it is necessary to set the algorithm. 根据网络拓扑结构和模型参数来构造出trainer用来训练，在构造时还需指定优化方法，这里使用最基本的Momentum方法，同时设定了学习率、正则等。
Here we specify `Momentum` optimization algorithm via `paddle.optimizer`.
```python ```python
# Create optimizer # Create optimizer
...@@ -414,13 +406,14 @@ trainer = paddle.trainer.SGD(cost=cost, ...@@ -414,13 +406,14 @@ trainer = paddle.trainer.SGD(cost=cost,
update_equation=momentum_optimizer) update_equation=momentum_optimizer)
``` ```
The learning rate adjustment policy can be defined with variables `learning_rate_decay_a`($a$), `learning_rate_decay_b`($b$) and `learning_rate_schedule`. In this example, discrete exponential method is used for adjusting learning rate. The formula is as follows, 通过 `learning_rate_decay_a` (简写$a$） 、`learning_rate_decay_b` (简写$b$) 和 `learning_rate_schedule` 指定学习率调整策略，这里采用离散指数的方式调节学习率，计算公式如下， $n$ 代表已经处理过的累计总样本数，$lr_{0}$ 即为 `settings` 里设置的 `learning_rate`。
$$ lr = lr_{0} * a^ {\lfloor \frac{n}{ b}\rfloor} $$ $$ lr = lr_{0} * a^ {\lfloor \frac{n}{ b}\rfloor} $$
where $n$ is the number of processed samples, $lr_{0}$ is the learning_rate.
### Training
`cifar.train10()` will yield records during each pass, after shuffling, a batch input is generated for training. ### 训练
cifar.train10()每次产生一条样本，在完成shuffle和batch之后，作为训练的输入。
```python ```python
reader=paddle.batch( reader=paddle.batch(
...@@ -429,17 +422,16 @@ reader=paddle.batch( ...@@ -429,17 +422,16 @@ reader=paddle.batch(
batch_size=128) batch_size=128)
``` ```
`feeding` is devoted to specifying the correspondence between each yield record and `paddle.layer.data`. For instance, 通过`feeding`来指定每一个数据和`paddle.layer.data`的对应关系。例如: `cifar.train10()`产生数据的第0列对应image层的特征。
the first column of data generated by `cifar.train10()` corresponds to image layer's feature.
```python ```python
feeding={'image': 0, feeding={'image': 0,
'label': 1} 'label': 1}
``` ```
Callback function `event_handler` will be called during training when a pre-defined event happens. 可以使用`event_handler`回调函数来观察训练过程，或进行测试等, 该回调函数是`trainer.train`函数里设定。
`event_handler_plot`is used to plot a figure like below： `event_handler_plot`可以用来利用回调数据来打点画图:
![png](./image/train_and_test.png) ![png](./image/train_and_test.png)
...@@ -459,6 +451,7 @@ def event_handler_plot(event): ...@@ -459,6 +451,7 @@ def event_handler_plot(event):
cost_ploter.plot() cost_ploter.plot()
step += 1 step += 1
if isinstance(event, paddle.event.EndPass): if isinstance(event, paddle.event.EndPass):
result = trainer.test( result = trainer.test(
reader=paddle.batch( reader=paddle.batch(
paddle.dataset.cifar.test10(), batch_size=128), paddle.dataset.cifar.test10(), batch_size=128),
...@@ -466,10 +459,10 @@ def event_handler_plot(event): ...@@ -466,10 +459,10 @@ def event_handler_plot(event):
cost_ploter.append(test_title, step, result.cost) cost_ploter.append(test_title, step, result.cost)
``` ```
`event_handler` is used to plot some text data when training. `event_handler` 用来在训练过程中输出文本日志
```python ```python
# event handler to track training and testing process # End batch and end pass event handler
def event_handler(event): def event_handler(event):
if isinstance(event, paddle.event.EndIteration): if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0: if event.batch_id % 100 == 0:
...@@ -490,7 +483,7 @@ def event_handler(event): ...@@ -490,7 +483,7 @@ def event_handler(event):
print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics) print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics)
``` ```
Finally, we can invoke `trainer.train` to start training: 通过`trainer.train`函数训练:
```python ```python
trainer.train( trainer.train(
...@@ -500,7 +493,7 @@ trainer.train( ...@@ -500,7 +493,7 @@ trainer.train(
feeding=feeding) feeding=feeding)
``` ```
Here is an example log after training for one pass. The average error rates are 0.6875 on the training set and 0.8852 on the validation set. 一轮训练log示例如下所示，经过1个pass， 训练集上平均error为0.6875 ，测试集上平均error为0.8852 。
```text ```text
Pass 0, Batch 0, Cost 2.473182, {'classification_error_evaluator': 0.9140625} Pass 0, Batch 0, Cost 2.473182, {'classification_error_evaluator': 0.9140625}
...@@ -514,17 +507,16 @@ Pass 0, Batch 300, Cost 1.668833, {'classification_error_evaluator': 0.6875} ...@@ -514,17 +507,16 @@ Pass 0, Batch 300, Cost 1.668833, {'classification_error_evaluator': 0.6875}
Test with Pass 0, {'classification_error_evaluator': 0.885200023651123} Test with Pass 0, {'classification_error_evaluator': 0.885200023651123}
``` ```
Figure 12 shows the curve of training error rate, which indicates it converges at Pass 200 with error rate 8.54%. 图12是训练的分类错误率曲线图，运行到第200个pass后基本收敛，最终得到测试集上分类错误率为8.54%。
<p align="center"> <p align="center">
<img src="image/plot_en.png" width="400" ><br/> <img src="image/plot.png" width="400" ><br/>
Figure 12. The error rate of VGG model on CIFAR10 图12. CIFAR10数据集上VGG模型的分类错误率
</p> </p>
## 应用模型
可以使用训练好的模型对图片进行分类，下面程序展示了如何使用`paddle.infer`接口进行推断，可以打开注释，更改加载的模型。
## Application
After training is done, users can use the trained model to classify images. The following code shows how to infer through `paddle.infer` interface. You can remove the comments to change the model name.
```python ```python
from PIL import Image from PIL import Image
...@@ -534,22 +526,20 @@ def load_image(file): ...@@ -534,22 +526,20 @@ def load_image(file):
im = Image.open(file) im = Image.open(file)
im = im.resize((32, 32), Image.ANTIALIAS) im = im.resize((32, 32), Image.ANTIALIAS)
im = np.array(im).astype(np.float32) im = np.array(im).astype(np.float32)
# The storage order of the loaded image is W(widht), # PIL打开图片存储顺序为H(高度)，W(宽度)，C(通道)。
# H(height), C(channel). PaddlePaddle requires # PaddlePaddle要求数据顺序为CHW，所以需要转换顺序。
# the CHW order, so transpose them.
im = im.transpose((2, 0, 1)) # CHW im = im.transpose((2, 0, 1)) # CHW
# In the training phase, the channel order of CIFAR # CIFAR训练图片通道顺序为B(蓝),G(绿),R(红),
# image is B(Blue), G(green), R(Red). But PIL open # 而PIL打开图片默认通道顺序为RGB,因为需要交换通道。
# image in RGB mode. It must swap the channel order.
im = im[(2, 1, 0),:,:] # BGR im = im[(2, 1, 0),:,:] # BGR
im = im.flatten() im = im.flatten()
im = im / 255.0 im = im / 255.0
return im return im
test_data = [] test_data = []
cur_dir = os.path.dirname(os.path.realpath(__file__)) cur_dir = os.path.dirname(os.path.realpath(__file__))
test_data.append((load_image(cur_dir + '/image/dog.png'),) test_data.append((load_image(cur_dir + '/image/dog.png'),)
# users can remove the comments and change the model name
# with gzip.open('params_pass_50.tar.gz', 'r') as f: # with gzip.open('params_pass_50.tar.gz', 'r') as f:
# parameters = paddle.parameters.Parameters.from_tar(f) # parameters = paddle.parameters.Parameters.from_tar(f)
...@@ -560,12 +550,12 @@ print "Label of image/dog.png is: %d" % lab[0][0] ...@@ -560,12 +550,12 @@ print "Label of image/dog.png is: %d" % lab[0][0]
``` ```
## Conclusion ## 总结
Traditional image classification methods have complicated frameworks that involve multiple stages of processing. In contrast, CNN models can be trained end-to-end with a significant increase in classification accuracy. In this chapter, we introduced three models -- VGG, GoogleNet, ResNet and provided PaddlePaddle config files for training VGG and ResNet on CIFAR10. We also explained how to perform prediction and feature extraction using the PaddlePaddle API. For other datasets such as ImageNet, the procedure for config and training are the same and you are welcome to give it a try. 传统图像分类方法由多个阶段构成，框架较为复杂，而端到端的CNN模型结构可一步到位，而且大幅度提升了分类准确率。本文我们首先介绍VGG、GoogleNet、ResNet三个经典的模型；然后基于CIFAR10数据集，介绍如何使用PaddlePaddle配置和训练CNN模型，尤其是VGG和ResNet模型；最后介绍如何使用PaddlePaddle的API接口对图片进行预测和特征提取。对于其他数据集比如ImageNet，配置和训练流程是同样的，大家可以自行进行实验。
## Reference ## 参考文献
[1] D. G. Lowe, [Distinctive image features from scale-invariant keypoints](http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf). IJCV, 60(2):91-110, 2004. [1] D. G. Lowe, [Distinctive image features from scale-invariant keypoints](http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf). IJCV, 60(2):91-110, 2004.
...@@ -612,7 +602,7 @@ Traditional image classification methods have complicated frameworks that involv ...@@ -612,7 +602,7 @@ Traditional image classification methods have complicated frameworks that involv
[22] http://cs231n.github.io/classification/ [22] http://cs231n.github.io/classification/
<br/> <br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>. <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
</div> </div>
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<div id="markdown" style='display:none'> <div id="markdown" style='display:none'>
# Word2Vec
This is intended as a reference tutorial. The source code of this tutorial lives on [book/word2vec](https://github.com/PaddlePaddle/book/tree/develop/04.word2vec). # 词向量
For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book). 本教程源代码目录在[book/word2vec](https://github.com/PaddlePaddle/book/tree/develop/04.word2vec)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## Background Introduction ## 背景介绍
This section introduces the concept of **word embedding**, which is a vector representation of words. It is a popular technique used in natural language processing. Word embeddings support many Internet services, including search engines, advertising systems, and recommendation systems. 本章我们介绍词的向量表征，也称为word embedding。词向量是自然语言处理中常见的一个操作，是搜索引擎、广告系统、推荐系统等互联网服务背后常见的基础技术。
### One-Hot Vectors 在这些互联网服务里，我们经常要比较两个词或者两段文本之间的相关性。为了做这样的比较，我们往往先要把词表示成计算机适合处理的方式。最自然的方式恐怕莫过于向量空间模型(vector space model)。
在这种方式里，每个词被表示成一个实数向量（one-hot vector），其长度为字典大小，每个维度对应一个字典里的每个词，除了这个词对应维度上的值是1，其他元素都是0。
Building these services requires us to quantify the similarity between two words or paragraphs. This calls for a new representation of all the words to make them more suitable for computation. An obvious way to achieve this is through the vector space model, where every word is represented as an **one-hot vector**. One-hot vector虽然自然，但是用处有限。比如，在互联网广告系统里，如果用户输入的query是“母亲节”，而有一个广告的关键词是“康乃馨”。虽然按照常理，我们知道这两个词之间是有联系的——母亲节通常应该送给母亲一束康乃馨；但是这两个词对应的one-hot vectors之间的距离度量，无论是欧氏距离还是余弦相似度(cosine similarity)，由于其向量正交，都认为这两个词毫无相关性。 得出这种与我们相悖的结论的根本原因是：每个词本身的信息量都太小。所以，仅仅给定两个词，不足以让我们准确判别它们是否相关。要想精确计算相关性，我们还需要更多的信息——从大量数据里通过机器学习方法归纳出来的知识。
For each word, its vector representation has the corresponding entry in the vector as 1, and all other entries as 0. The lengths of one-hot vectors match the size of the dictionary. Each entry of a vector corresponds to the presence (or absence) of a word in the dictionary. 在机器学习领域里，各种“知识”被各种模型表示，词向量模型(word embedding model)就是其中的一类。通过词向量模型可将一个 one-hot vector映射到一个维度更低的实数向量（embedding vector），如$embedding(母亲节) = [0.3, 4.2, -1.5, ...], embedding(康乃馨) = [0.2, 5.6, -2.3, ...]$。在这个映射到的实数向量表示中，希望两个语义（或用法）上相似的词对应的词向量“更像”，这样如“母亲节”和“康乃馨”的对应词向量的余弦相似度就不再为零了。
One-hot vectors are intuitive, yet they have limited usefulness. Take the example of an Internet advertising system: Suppose a customer enters the query "Mother's Day", while an ad bids for the keyword carnations". Because the one-hot vectors of these two words are perpendicular, the metric distance (either Euclidean or cosine similarity) between them would indicate little relevance. However, *we* know that these two queries are connected semantically, since people often gift their mothers bundles of carnation flowers on Mother's Day. This discrepancy is due to the low information capacity in each vector. That is, comparing the vector representations of two words does not assess their relevance sufficiently. To calculate their similarity accurately, we need more information, which could be learned from large amounts of data through machine learning methods. 词向量模型可以是概率模型、共生矩阵(co-occurrence matrix)模型或神经元网络模型。在用神经网络求词向量之前，传统做法是统计一个词语的共生矩阵$X$。$X$是一个$|V| \times |V|$ 大小的矩阵，$X_{ij}$表示在所有语料中，词汇表`V`(vocabulary)中第i个词和第j个词同时出现的词数，$|V|$为词汇表的大小。对$X$做矩阵分解（如奇异值分解，Singular Value Decomposition \[[5](#参考文献)\]），得到的$U$即视为所有词的词向量：
Like many machine learning models, word embeddings can represent knowledge in various ways. Another model may project an one-hot vector to an embedding vector of lower dimension e.g. $embedding(mother's day) = [0.3, 4.2, -1.5, ...], embedding(carnations) = [0.2, 5.6, -2.3, ...]$. Mapping one-hot vectors onto an embedded vector space has the potential to bring the embedding vectors of similar words (either semantically or usage-wise) closer to each other, so that the cosine similarity between the corresponding vectors for words like "Mother's Day" and "carnations" are no longer zero.
A word embedding model could be a probabilistic model, a co-occurrence matrix model, or a neural network. Before people started using neural networks to generate word embedding, the traditional method was to calculate a co-occurrence matrix $X$ of words. Here, $X$ is a $|V| \times |V|$ matrix, where $X_{ij}$ represents the co-occurrence times of the $i$th and $j$th words in the vocabulary `V` within all corpus, and $|V|$ is the size of the vocabulary. By performing matrix decomposition on $X$ e.g. Singular Value Decomposition \[[5](#References)\]
$$X = USV^T$$ $$X = USV^T$$
the resulting $U$ can be seen as the word embedding of all the words. 但这样的传统做法有很多问题：<br/>
1) 由于很多词没有出现，导致矩阵极其稀疏，因此需要对词频做额外处理来达到好的矩阵分解效果；<br/>
2) 矩阵非常大，维度太高(通常达到$10^6*10^6$的数量级)；<br/>
3) 需要手动去掉停用词（如although, a,...），不然这些频繁出现的词也会影响矩阵分解的效果。
However, this method suffers from many drawbacks:
1) Since many pairs of words don't co-occur, the co-occurrence matrix is sparse. To achieve good performance of matrix factorization, further treatment on word frequency is needed;
2) The matrix is large, frequently on the order of $10^6*10^6$;
3) We need to manually filter out stop words (like "although", "a", ...), otherwise these frequent words will affect the performance of matrix factorization.
The neural network based model does not require storing huge hash tables of statistics on all of the corpus. It obtains the word embedding by learning from semantic information, hence could avoid the aforementioned problems in the traditional method. In this chapter, we will introduce the details of neural network word embedding model and how to train such model in PaddlePaddle. 基于神经网络的模型不需要计算存储一个在全语料上统计的大表，而是通过学习语义信息得到词向量，因此能很好地解决以上问题。在本章里，我们将展示基于神经网络训练词向量的细节，以及如何用PaddlePaddle训练一个词向量模型。
## Results Demonstration
In this section, after training the word embedding model, we could use the data visualization algorithm $t-$SNE\[[4](#reference)\] to draw the word embedding vectors after projecting them onto a two-dimensional space (see figure below). From the figure we could see that the semantically relevant words -- *a*, *the*, and *these* or *big* and *huge* -- are close to each other in the projected space, while irrelevant words -- *say* and *business* or *decision* and *japan* -- are far from each other. ## 效果展示
本章中，当词向量训练好后，我们可以用数据可视化算法t-SNE\[[4](#参考文献)\]画出词语特征在二维上的投影（如下图所示）。从图中可以看出，语义相关的词语（如a, the, these; big, huge）在投影上距离很近，语意无关的词（如say, business; decision, japan）在投影上的距离很远。
<p align="center"> <p align="center">
<img src = "image/2d_similarity.png" width=400><br/> <img src = "image/2d_similarity.png" width=400><br/>
Figure 1. Two dimension projection of word embeddings 图1. 词向量的二维投影
</p> </p>
### Cosine Similarity 另一方面，我们知道两个向量的余弦值在$[-1,1]$的区间内：两个完全相同的向量余弦值为1, 两个相互垂直的向量之间余弦值为0，两个方向完全相反的向量余弦值为-1，即相关性和余弦值大小成正比。因此我们还可以计算两个词向量的余弦相似度:
On the other hand, we know that the cosine similarity between two vectors falls between $[-1,1]$. Specifically, the cosine similarity is 1 when the vectors are identical, 0 when the vectors are perpendicular, -1 when the are of opposite directions. That is, the cosine similarity between two vectors scales with their relevance. So we can calculate the cosine similarity of two word embedding vectors to represent their relevance:
``` ```
please input two words: big huge
similarity: 0.899180685161 similarity: 0.899180685161
please input two words: big huge
please input two words: from company please input two words: from company
similarity: -0.0997506977351 similarity: -0.0997506977351
``` ```
The above results could be obtained by running `calculate_dis.py`, which loads the words in the dictionary and their corresponding trained word embeddings. For detailed instruction, see section [Model Application](#Model Application). 以上结果可以通过运行`calculate_dis.py`, 加载字典里的单词和对应训练特征结果得到，我们将在[应用模型](#应用模型)中详细描述用法。
## Model Overview
In this section, we will introduce three word embedding models: N-gram model, CBOW, and Skip-gram, which all output the frequency of each word given its immediate context. ## 模型概览
For N-gram model, we will first introduce the concept of language model, and implement it using PaddlePaddle in section [Model Training](#Model Training). 在这里我们介绍三个训练词向量的模型：N-gram模型，CBOW模型和Skip-gram模型，它们的中心思想都是通过上下文得到一个词出现的概率。对于N-gram模型，我们会先介绍语言模型的概念，并在之后的[训练模型](#训练模型)中，带大家用PaddlePaddle实现它。而后两个模型，是近年来最有名的神经元词向量模型，由 Tomas Mikolov 在Google 研发\[[3](#参考文献)\]，虽然它们很浅很简单，但训练效果很好。
The latter two models, which became popular recently, are neural word embedding model developed by Tomas Mikolov at Google \[[3](#reference)\]. Despite their apparent simplicity, these models train very well. ### 语言模型
### Language Model 在介绍词向量模型之前，我们先来引入一个概念：语言模型。
语言模型旨在为语句的联合概率函数$P(w_1, ..., w_T)$建模, 其中$w_i$表示句子中的第i个词。语言模型的目标是，希望模型对有意义的句子赋予大概率，对没意义的句子赋予小概率。
这样的模型可以应用于很多领域，如机器翻译、语音识别、信息检索、词性标注、手写识别等，它们都希望能得到一个连续序列的概率。 以信息检索为例，当你在搜索“how long is a football bame”时（bame是一个医学名词），搜索引擎会提示你是否希望搜索"how long is a football game", 这是因为根据语言模型计算出“how long is a football bame”的概率很低，而与bame近似的，可能引起错误的词中，game会使该句生成的概率最大。
Before diving into word embedding models, we will first introduce the concept of **language model**. Language models build the joint probability function $P(w_1, ..., w_T)$ of a sentence, where $w_i$ is the i-th word in the sentence. The goal is to give higher probabilities to meaningful sentences, and lower probabilities to meaningless constructions. 对语言模型的目标概率$P(w_1, ..., w_T)$，如果假设文本中每个词都是相互独立的，则整句话的联合概率可以表示为其中所有词语条件概率的乘积，即：
In general, models that generate the probability of a sequence can be applied to many fields, like machine translation, speech recognition, information retrieval, part-of-speech tagging, and handwriting recognition. Take information retrieval, for example. If you were to search for "how long is a football bame" (where bame is a medical noun), the search engine would have asked if you had meant "how long is a football game" instead. This is because the probability of "how long is a football bame" is very low according to the language model; in addition, among all of the words easily confused with "bame", "game" would build the most probable sentence.
#### Target Probability
For language model's target probability $P(w_1, ..., w_T)$, if the words in the sentence were to be independent, the joint probability of the whole sentence would be the product of each word's probability:
$$P(w_1, ..., w_T) = \prod_{t=1}^TP(w_t)$$ $$P(w_1, ..., w_T) = \prod_{t=1}^TP(w_t)$$
However, the frequency of words in a sentence typically relates to the words before them, so canonical language models are constructed using conditional probability in its target probability: 然而我们知道语句中的每个词出现的概率都与其前面的词紧密相关, 所以实际上通常用条件概率表示语言模型：
$$P(w_1, ..., w_T) = \prod_{t=1}^TP(w_t | w_1, ... , w_{t-1})$$ $$P(w_1, ..., w_T) = \prod_{t=1}^TP(w_t | w_1, ... , w_{t-1})$$
### N-gram neural model ### N-gram neural model
In computational linguistics, n-gram is an important method to represent text. An n-gram represents a contiguous sequence of n consecutive items given a text. Based on the desired application scenario, each item could be a letter, a syllable or a word. The N-gram model is also an important method in statistical language modeling. When training language models with n-grams, the first (n-1) words of an n-gram are used to predict the *n*th word. 在计算语言学中，n-gram是一种重要的文本表示方法，表示一个文本中连续的n个项。基于具体的应用场景，每一项可以是一个字母、单词或者音节。 n-gram模型也是统计语言模型中的一种重要方法，用n-gram训练语言模型时，一般用每个n-gram的历史n-1个词语组成的内容来预测第n个词。
Yoshua Bengio and other scientists describe how to train a word embedding model using neural network in the famous paper of Neural Probabilistic Language Models \[[1](#reference)\] published in 2003. The Neural Network Language Model (NNLM) described in the paper learns the language model and word embedding simultaneously through a linear transformation and a non-linear hidden connection. That is, after training on large amounts of corpus, the model learns the word embedding; then, it computes the probability of the whole sentence, using the embedding. This type of language model can overcome the **curse of dimensionality** i.e. model inaccuracy caused by the difference in dimensionality between training and testing data. Note that the term *neural network language model* is ill-defined, so we will not use the name NNLM but only refer to it as *N-gram neural model* in this section. Yoshua Bengio等科学家就于2003年在著名论文 Neural Probabilistic Language Models \[[1](#参考文献)\] 中介绍如何学习一个神经元网络表示的词向量模型。文中的神经概率语言模型（Neural Network Language Model，NNLM）通过一个线性映射和一个非线性隐层连接，同时学习了语言模型和词向量，即通过学习大量语料得到词语的向量表达，通过这些向量得到整个句子的概率。用这种方法学习语言模型可以克服维度灾难（curse of dimensionality）,即训练和测试数据不同导致的模型不准。注意：由于“神经概率语言模型”说法较为泛泛，我们在这里不用其NNLM的本名，考虑到其具体做法，本文中称该模型为N-gram neural model。
We have previously described language model using conditional probability, where the probability of the *t*-th word in a sentence depends on all $t-1$ words before it. Furthermore, since words further prior have less impact on a word, and every word within an n-gram is only effected by its previous n-1 words, we have: 我们在上文中已经讲到用条件概率建模语言模型，即一句话中第$t$个词的概率和该句话的前$t-1$个词相关。可实际上越远的词语其实对该词的影响越小，那么如果考虑一个n-gram, 每个词都只受其前面`n-1`个词的影响，则有：
$$P(w_1, ..., w_T) = \prod_{t=n}^TP(w_t|w_{t-1}, w_{t-2}, ..., w_{t-n+1})$$ $$P(w_1, ..., w_T) = \prod_{t=n}^TP(w_t|w_{t-1}, w_{t-2}, ..., w_{t-n+1})$$
Given some real corpus in which all sentences are meaningful, the n-gram model should maximize the following objective function: 给定一些真实语料，这些语料中都是有意义的句子，N-gram模型的优化目标则是最大化目标函数:
$$\frac{1}{T}\sum_t f(w_t, w_{t-1}, ..., w_{t-n+1};\theta) + R(\theta)$$ $$\frac{1}{T}\sum_t f(w_t, w_{t-1}, ..., w_{t-n+1};\theta) + R(\theta)$$
where $f(w_t, w_{t-1}, ..., w_{t-n+1})$ represents the conditional probability of the current word $w_t$ given its previous $n-1$ words, and $R(\theta)$ represents parameter regularization term. 其中$f(w_t, w_{t-1}, ..., w_{t-n+1})$表示根据历史n-1个词得到当前词$w_t$的条件概率，$R(\theta)$表示参数正则项。
<p align="center"> <p align="center">
<img src="image/nnlm_en.png" width=500><br/> <img src="image/nnlm.png" width=500><br/>
Figure 2. N-gram neural network model 图2. N-gram神经网络模型
</p> </p>
图2展示了N-gram神经网络模型，从下往上看，该模型分为以下几个部分：
- 对于每个样本，模型输入$w_{t-n+1},...w_{t-1}$, 输出句子第t个词为字典中`|V|`个词的概率。
Figure 2 shows the N-gram neural network model. From the bottom up, the model has the following components: 每个输入词$w_{t-n+1},...w_{t-1}$首先通过映射矩阵映射到词向量$C(w_{t-n+1}),...C(w_{t-1})$。
- For each sample, the model gets input $w_{t-n+1},...w_{t-1}$, and outputs the probability that the t-th word is one of `|V|` in the dictionary.
Every input word $w_{t-n+1},...w_{t-1}$ first gets transformed into word embedding $C(w_{t-n+1}),...C(w_{t-1})$ through a transformation matrix. - 然后所有词语的词向量连接成一个大向量，并经过一个非线性映射得到历史词语的隐层表示：
- All the word embeddings concatenate into a single vector, which is mapped (nonlinearly) into the $t$-th word hidden representation:
$$g=Utanh(\theta^Tx + b_1) + Wx + b_2$$ $$g=Utanh(\theta^Tx + b_1) + Wx + b_2$$
where $x$ is the large vector concatenated from all the word embeddings representing the context; $\theta$, $U$, $b_1$, $b_2$ and $W$ are parameters connecting word embedding layers to the hidden layers. $g$ represents the unnormalized probability of the output word, $g_i$ represents the unnormalized probability of the output word being the i-th word in the dictionary. 其中，$x$为所有词语的词向量连接成的大向量，表示文本历史特征；$\theta$、$U$、$b_1$、$b_2$和$W$分别为词向量层到隐层连接的参数。$g$表示未经归一化的所有输出单词概率，$g_i$表示未经归一化的字典中第$i$个单词的输出概率。
- Based on the definition of softmax, using normalized $g_i$, the probability that the output word is $w_t$ is represented as: - 根据softmax的定义，通过归一化$g_i$, 生成目标词$w_t$的概率为：
$$P(w_t | w_1, ..., w_{t-n+1}) = \frac{e^{g_{w_t}}}{\sum_i^{|V|} e^{g_i}}$$ $$P(w_t | w_1, ..., w_{t-n+1}) = \frac{e^{g_{w_t}}}{\sum_i^{|V|} e^{g_i}}$$
- The cost of the entire network is a multi-class cross-entropy and can be described by the following loss function - 整个网络的损失值(cost)为多类分类交叉熵，用公式表示为
$$J(\theta) = -\sum_{i=1}^N\sum_{c=1}^{|V|}y_k^{i}log(softmax(g_k^i))$$ $$J(\theta) = -\sum_{i=1}^N\sum_{c=1}^{|V|}y_k^{i}log(softmax(g_k^i))$$
where $y_k^i$ represents the true label for the $k$-th class in the $i$-th sample ($0$ or $1$), $softmax(g_k^i)$ represents the softmax probability for the $k$-th class in the $i$-th sample. 其中$y_k^i$表示第$i$个样本第$k$类的真实标签(0或1)，$softmax(g_k^i)$表示第i个样本第k类softmax输出的概率。
### Continuous Bag-of-Words model(CBOW) ### Continuous Bag-of-Words model(CBOW)
CBOW model predicts the current word based on the N words both before and after it. When $N=2$, the model is as the figure below: CBOW模型通过一个词的上下文（各N个词）预测当前词。当N=2时，模型如下图所示：
<p align="center"> <p align="center">
<img src="image/cbow_en.png" width=250><br/> <img src="image/cbow.png" width=250><br/>
Figure 3. CBOW model 图3. CBOW模型
</p> </p>
Specifically, by ignoring the order of words in the sequence, CBOW uses the average value of the word embedding of the context to predict the current word: 具体来说，不考虑上下文的词语输入顺序，CBOW是用上下文词语的词向量的均值来预测当前词。即：
$$\text{context} = \frac{x_{t-1} + x_{t-2} + x_{t+1} + x_{t+2}}{4}$$ $$context = \frac{x_{t-1} + x_{t-2} + x_{t+1} + x_{t+2}}{4}$$
where $x_t$ is the word embedding of the t-th word, classification score vector is $z=U*\text{context}$, the final classification $y$ uses softmax and the loss function uses multi-class cross-entropy. 其中$x_t$为第$t$个词的词向量，分类分数（score）向量 $z=U*context$，最终的分类$y$采用softmax，损失函数采用多类分类交叉熵。
### Skip-gram model ### Skip-gram model
The advantages of CBOW is that it smooths over the word embeddings of the context and reduces noise, so it is very effective on small dataset. Skip-gram uses a word to predict its context and get multiple context for the given word, so it can be used in larger datasets. CBOW的好处是对上下文词语的分布在词向量上进行了平滑，去掉了噪声，因此在小数据集上很有效。而Skip-gram的方法中，用一个词预测其上下文，得到了当前词上下文的很多样本，因此可用于更大的数据集。
<p align="center"> <p align="center">
<img src="image/skipgram_en.png" width=250><br/> <img src="image/skipgram.png" width=250><br/>
Figure 4. Skip-gram model 图4. Skip-gram模型
</p> </p>
As illustrated in the figure above, skip-gram model maps the word embedding of the given word onto $2n$ word embeddings (including $n$ words before and $n$ words after the given word), and then combine the classification loss of all those $2n$ words by softmax. 如上图所示，Skip-gram模型的具体做法是，将一个词的词向量映射到$2n$个词的词向量（$2n$表示当前输入词的前后各$n$个词），然后分别通过softmax得到这$2n$个词的分类损失值之和。
## Dataset
We will use Peen Treebank (PTB) (Tomas Mikolov's pre-processed version) dataset. PTB is a small dataset, used in Recurrent Neural Network Language Modeling Toolkit\[[2](#reference)\]. Its statistics are as follows: ## 数据准备
### 数据介绍
本教程使用Penn Treebank （PTB）（经Tomas Mikolov预处理过的版本）数据集。PTB数据集较小，训练速度快，应用于Mikolov的公开语言模型训练工具\[[2](#参考文献)\]中。其统计情况如下：
<p align="center"> <p align="center">
<table> <table>
<tr> <tr>
<td>training set</td> <td>训练数据</td>
<td>validation set</td> <td>验证数据</td>
<td>test set</td> <td>测试数据</td>
</tr> </tr>
<tr> <tr>
<td>ptb.train.txt</td> <td>ptb.train.txt</td>
...@@ -208,27 +201,21 @@ We will use Peen Treebank (PTB) (Tomas Mikolov's pre-processed version) dataset. ...@@ -208,27 +201,21 @@ We will use Peen Treebank (PTB) (Tomas Mikolov's pre-processed version) dataset.
<td>ptb.test.txt</td> <td>ptb.test.txt</td>
</tr> </tr>
<tr> <tr>
<td>42068 lines</td> <td>42068句</td>
<td>3370 lines</td> <td>3370句</td>
<td>3761 lines</td> <td>3761句</td>
</tr> </tr>
</table> </table>
</p> </p>
### Python Dataset Module
We encapsulated the PTB Data Set in our Python module `paddle.dataset.imikolov`. This module can
1. download the dataset to `~/.cache/paddle/dataset/imikolov`, if not yet, and
2. [preprocesses](#preprocessing) the dataset.
### Preprocessing ### 数据预处理
We will be training a 5-gram model. Given five words in a window, we will predict the fifth word given the first four words. 本章训练的是5-gram模型，表示在PaddlePaddle训练时，每条数据的前4个词用来预测第5个词。PaddlePaddle提供了对应PTB数据集的python包`paddle.dataset.imikolov`，自动做数据的下载与预处理，方便大家使用。
Beginning and end of a sentence have a special meaning, so we will add begin token `<s>` in the front of the sentence. And end token `<e>` in the end of the sentence. By moving the five word window in the sentence, data instances are generated. 预处理会把数据集中的每一句话前后加上开始符号`<s>`以及结束符号`<e>`。然后依据窗口大小（本教程中为5），从头到尾每次向右滑动窗口并生成一条数据。
For example, the sentence "I have a dream that one day" generates five data instances: 如"I have a dream that one day" 一句提供了5条数据：
```text ```text
<s> I have a dream <s> I have a dream
...@@ -238,35 +225,33 @@ a dream that one day ...@@ -238,35 +225,33 @@ a dream that one day
dream that one day <e> dream that one day <e>
``` ```
At last, each data instance will be converted into an integer sequence according it's words' index inside the dictionary. 最后，每个输入会按其单词次在字典里的位置，转化成整数的索引序列，作为PaddlePaddle的输入。
## 编程实现
## Training 本配置的模型结构如下图所示：
The neural network that we will be using is illustrated in the graph below:
<p align="center"> <p align="center">
<img src="image/ngram.en.png" width=400><br/> <img src="image/ngram.png" width=400><br/>
Figure 5. N-gram neural network model in model configuration 图5. 模型配置中的N-gram神经网络模型
</p> </p>
`word2vec/train.py` demonstrates training word2vec using PaddlePaddle: 首先，加载所需要的包：
- Import packages.
```python ```python
import math import math
import paddle.v2 as paddle import paddle.v2 as paddle
``` ```
- Configure parameter. 然后，定义参数：
```python ```python
embsize = 32 # word vector dimension embsize = 32 # 词向量维度
hiddensize = 256 # hidden layer dimension hiddensize = 256 # 隐层维度
N = 5 # train 5-gram N = 5 # 训练5-Gram
``` ```
- Map the $n-1$ words $w_{t-n+1},...w_{t-1}$ before $w_t$ to a D-dimensional vector though matrix of dimention $|V|\times D$ (D=32 in this example). 接着，定义网络结构：
- 将$w_t$之前的$n-1$个词 $w_{t-n+1},...w_{t-1}$，通过$|V|\times D$的矩阵映射到D维词向量（本例中取D=32）。
```python ```python
def wordemb(inlayer): def wordemb(inlayer):
...@@ -282,13 +267,13 @@ def wordemb(inlayer): ...@@ -282,13 +267,13 @@ def wordemb(inlayer):
return wordemb return wordemb
``` ```
- Define name and type for input to data layer. - 定义输入层接受的数据类型以及名字。
```python ```python
paddle.init(use_gpu=False, trainer_count=3) paddle.init(use_gpu=False, trainer_count=3) # 初始化PaddlePaddle
word_dict = paddle.dataset.imikolov.build_dict() word_dict = paddle.dataset.imikolov.build_dict()
dict_size = len(word_dict) dict_size = len(word_dict)
# Every layer takes integer value of range [0, dict_size) # 每个输入层都接受整形数据，这些数据的范围是[0, dict_size)
firstword = paddle.layer.data( firstword = paddle.layer.data(
name="firstw", type=paddle.data_type.integer_value(dict_size)) name="firstw", type=paddle.data_type.integer_value(dict_size))
secondword = paddle.layer.data( secondword = paddle.layer.data(
...@@ -306,13 +291,13 @@ Ethird = wordemb(thirdword) ...@@ -306,13 +291,13 @@ Ethird = wordemb(thirdword)
Efourth = wordemb(fourthword) Efourth = wordemb(fourthword)
``` ```
- Concatenate n-1 word embedding vectors into a single feature vector. - 将这n-1个词向量经过concat_layer连接成一个大向量作为历史文本特征。
```python ```python
contextemb = paddle.layer.concat(input=[Efirst, Esecond, Ethird, Efourth]) contextemb = paddle.layer.concat(input=[Efirst, Esecond, Ethird, Efourth])
``` ```
- Feature vector will go through a fully connected layer which outputs a hidden feature vector. - 将历史文本特征经过一个全连接得到文本隐层特征。
```python ```python
hidden1 = paddle.layer.fc(input=contextemb, hidden1 = paddle.layer.fc(input=contextemb,
...@@ -325,7 +310,7 @@ hidden1 = paddle.layer.fc(input=contextemb, ...@@ -325,7 +310,7 @@ hidden1 = paddle.layer.fc(input=contextemb,
learning_rate=1)) learning_rate=1))
``` ```
- Hidden feature vector will go through another fully conected layer, turn into a $|V|$ dimensional vector. At the same time softmax will be applied to get the probability of each word being generated. - 将文本隐层特征，再经过一个全连接，映射成一个$|V|$维向量，同时通过softmax归一化得到这`|V|`个词的生成概率。
```python ```python
predictword = paddle.layer.fc(input=hidden1, predictword = paddle.layer.fc(input=hidden1,
...@@ -334,13 +319,17 @@ predictword = paddle.layer.fc(input=hidden1, ...@@ -334,13 +319,17 @@ predictword = paddle.layer.fc(input=hidden1,
act=paddle.activation.Softmax()) act=paddle.activation.Softmax())
``` ```
- We will use cross-entropy cost function. - 网络的损失函数为多分类交叉熵，可直接调用`classification_cost`函数。
```python ```python
cost = paddle.layer.classification_cost(input=predictword, label=nextword) cost = paddle.layer.classification_cost(input=predictword, label=nextword)
``` ```
- Create parameter, optimizer and trainer. 然后，指定训练相关的参数：
- 训练方法（optimizer)： 代表训练过程在更新权重时采用动量优化器，本教程使用Adam优化器。
- 训练速度（learning_rate）： 迭代的速度，与网络的训练收敛速度有关系。
- 正则化（regularization）： 是防止网络过拟合的一种手段，此处采用L2正则化。
```python ```python
parameters = paddle.parameters.create(cost) parameters = paddle.parameters.create(cost)
...@@ -350,9 +339,9 @@ adagrad = paddle.optimizer.AdaGrad( ...@@ -350,9 +339,9 @@ adagrad = paddle.optimizer.AdaGrad(
trainer = paddle.trainer.SGD(cost, parameters, adagrad) trainer = paddle.trainer.SGD(cost, parameters, adagrad)
``` ```
Next, we will begin the training process. `paddle.dataset.imikolov.train()` and `paddle.dataset.imikolov.test()` is our training set and test set. Both of the function will return a **reader**: In PaddlePaddle, reader is a python function which returns a Python iterator which output a single data instance at a time. 下一步，我们开始训练过程。`paddle.dataset.imikolov.train()`和`paddle.dataset.imikolov.test()`分别做训练和测试数据集。这两个函数各自返回一个reader——PaddlePaddle中的reader是一个Python函数，每次调用的时候返回一个Python generator。
`paddle.batch` takes reader as input, outputs a **batched reader**: In PaddlePaddle, a reader outputs a single data instance at a time but batched reader outputs a minibatch of data instances. `paddle.batch`的输入是一个reader，输出是一个batched reader —— 在PaddlePaddle里，一个reader每次yield一条训练数据，而一个batched reader每次yield一个minbatch。
```python ```python
import gzip import gzip
...@@ -377,7 +366,6 @@ trainer.train( ...@@ -377,7 +366,6 @@ trainer.train(
event_handler=event_handler) event_handler=event_handler)
``` ```
`trainer.train` will start training, the output of `event_handler` will be similar to following:
```text ```text
Pass 0, Batch 0, Cost 7.870579, {'classification_error_evaluator': 1.0}, Testing metrics {'classification_error_evaluator': 0.999591588973999} Pass 0, Batch 0, Cost 7.870579, {'classification_error_evaluator': 1.0}, Testing metrics {'classification_error_evaluator': 0.999591588973999}
Pass 0, Batch 100, Cost 6.136420, {'classification_error_evaluator': 0.84375}, Testing metrics {'classification_error_evaluator': 0.8328699469566345} Pass 0, Batch 100, Cost 6.136420, {'classification_error_evaluator': 0.84375}, Testing metrics {'classification_error_evaluator': 0.8328699469566345}
...@@ -385,16 +373,19 @@ Pass 0, Batch 200, Cost 5.786797, {'classification_error_evaluator': 0.8125}, Te ...@@ -385,16 +373,19 @@ Pass 0, Batch 200, Cost 5.786797, {'classification_error_evaluator': 0.8125}, Te
... ...
``` ```
After 30 passes, we can get average error rate around 0.735611. 训练过程是完全自动的，event_handler里打印的日志类似如上所示：
经过30个pass，我们将得到平均错误率为classification_error_evaluator=0.735611。
## 应用模型
训练模型后，我们可以加载模型参数，用训练出来的词向量初始化其他模型，也可以将模型查看参数用来做后续应用。
## Model Application
After the model is trained, we can load saved model parameters and uses it for other models. We can also use the parameters in applications. ### 查看词向量
### Viewing Word Vector PaddlePaddle训练出来的参数可以直接使用`parameters.get()`获取出来。例如查看单词`apple`的词向量，即为
Parameters trained by PaddlePaddle can be viewed by `parameters.get()`. For example, we can check the word vector for word `apple`.
```python ```python
embeddings = parameters.get("_proj").reshape(len(word_dict), embsize) embeddings = parameters.get("_proj").reshape(len(word_dict), embsize)
...@@ -411,9 +402,10 @@ print embeddings[word_dict['apple']] ...@@ -411,9 +402,10 @@ print embeddings[word_dict['apple']]
0.19072419 -0.24286366] 0.19072419 -0.24286366]
``` ```
### Modifying Word Vector
Word vectors (`embeddings`) that we get is a numpy array. We can modify this array and set it back to `parameters`. ### 修改词向量
获得到的embedding为一个标准的numpy矩阵。我们可以对这个numpy矩阵进行修改，然后赋值回去。
```python ```python
...@@ -425,9 +417,10 @@ modify_embedding(embeddings) ...@@ -425,9 +417,10 @@ modify_embedding(embeddings)
parameters.set("_proj", embeddings) parameters.set("_proj", embeddings)
``` ```
### Calculating Cosine Similarity ### 计算词语之间的余弦距离
Cosine similarity is one way of quantifying the similarity between two vectors. The range of result is $[-1, 1]$. The bigger the value, the similar two vectors are: 两个向量之间的距离可以用余弦值来表示，余弦值在$[-1,1]$的区间内，向量间余弦值越大，其距离越近。这里我们在`calculate_dis.py`中实现不同词语的距离度量。
用法如下：
```python ```python
...@@ -443,14 +436,11 @@ print spatial.distance.cosine(emb_1, emb_2) ...@@ -443,14 +436,11 @@ print spatial.distance.cosine(emb_1, emb_2)
0.99375076448 0.99375076448
``` ```
## Conclusion ## 总结
本章中，我们介绍了词向量、语言模型和词向量的关系、以及如何通过训练神经网络模型获得词向量。在信息检索中，我们可以根据向量间的余弦夹角，来判断query和文档关键词这二者间的相关性。在句法分析和语义分析中，训练好的词向量可以用来初始化模型，以得到更好的效果。在文档分类中，有了词向量之后，可以用聚类的方法将文档中同义词进行分组。希望大家在本章后能够自行运用词向量进行相关领域的研究。
This chapter introduces word embedding, the relationship between language model and word embedding, and how to train neural networks to learn word embedding.
In information retrieval, the relevance between the query and document keyword can be computed through the cosine similarity of their word embeddings. In grammar analysis and semantic analysis, a previously trained word embedding can initialize models for better performance. In document classification, clustering the word embedding can group synonyms in the documents. We hope that readers can use word embedding models in their work after reading this chapter.
## Referenes ## 参考文献
1. Bengio Y, Ducharme R, Vincent P, et al. [A neural probabilistic language model](http://www.jmlr.org/papers/volume3/bengio03a/bengio03a.pdf)[J]. journal of machine learning research, 2003, 3(Feb): 1137-1155. 1. Bengio Y, Ducharme R, Vincent P, et al. [A neural probabilistic language model](http://www.jmlr.org/papers/volume3/bengio03a/bengio03a.pdf)[J]. journal of machine learning research, 2003, 3(Feb): 1137-1155.
2. Mikolov T, Kombrink S, Deoras A, et al. [Rnnlm-recurrent neural network language modeling toolkit](http://www.fit.vutbr.cz/~imikolov/rnnlm/rnnlm-demo.pdf)[C]//Proc. of the 2011 ASRU Workshop. 2011: 196-201. 2. Mikolov T, Kombrink S, Deoras A, et al. [Rnnlm-recurrent neural network language modeling toolkit](http://www.fit.vutbr.cz/~imikolov/rnnlm/rnnlm-demo.pdf)[C]//Proc. of the 2011 ASRU Workshop. 2011: 196-201.
3. Mikolov T, Chen K, Corrado G, et al. [Efficient estimation of word representations in vector space](https://arxiv.org/pdf/1301.3781.pdf)[J]. arXiv preprint arXiv:1301.3781, 2013. 3. Mikolov T, Chen K, Corrado G, et al. [Efficient estimation of word representations in vector space](https://arxiv.org/pdf/1301.3781.pdf)[J]. arXiv preprint arXiv:1301.3781, 2013.
...@@ -458,7 +448,7 @@ In information retrieval, the relevance between the query and document keyword c ...@@ -458,7 +448,7 @@ In information retrieval, the relevance between the query and document keyword c
5. https://en.wikipedia.org/wiki/Singular_value_decomposition 5. https://en.wikipedia.org/wiki/Singular_value_decomposition
<br/> <br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>. <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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# 个性化推荐
本教程源代码目录在[book/recommender_system](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## 背景介绍
在网络技术不断发展和电子商务规模不断扩大的背景下，商品数量和种类快速增长，用户需要花费大量时间才能找到自己想买的商品，这就是信息超载问题。为了解决这个难题，推荐系统（Recommender System）应运而生。
个性化推荐系统是信息过滤系统（Information Filtering System）的子集，它可以用在很多领域，如电影、音乐、电商和 Feed 流推荐等。推荐系统通过分析、挖掘用户行为，发现用户的个性化需求与兴趣特点，将用户可能感兴趣的信息或商品推荐给用户。与搜索引擎不同，推荐系统不需要用户准确地描述出自己的需求，而是根据分析历史行为建模，主动提供满足用户兴趣和需求的信息。
传统的推荐系统方法主要有：
- 协同过滤推荐（Collaborative Filtering Recommendation）：该方法收集分析用户历史行为、活动、偏好，计算一个用户与其他用户的相似度，利用目标用户的相似用户对商品评价的加权评价值，来预测目标用户对特定商品的喜好程度。优点是可以给用户推荐未浏览过的新产品；缺点是对于没有任何行为的新用户存在冷启动的问题，同时也存在用户与商品之间的交互数据不够多造成的稀疏问题，会导致模型难以找到相近用户。
- 基于内容过滤推荐[[1](#参考文献)]（Content-based Filtering Recommendation）：该方法利用商品的内容描述，抽象出有意义的特征，通过计算用户的兴趣和商品描述之间的相似度，来给用户做推荐。优点是简单直接，不需要依据其他用户对商品的评价，而是通过商品属性进行商品相似度度量，从而推荐给用户所感兴趣商品的相似商品；缺点是对于没有任何行为的新用户同样存在冷启动的问题。
- 组合推荐[[2](#参考文献)]（Hybrid Recommendation）：运用不同的输入和技术共同进行推荐，以弥补各自推荐技术的缺点。
其中协同过滤是应用最广泛的技术之一，它又可以分为多个子类：基于用户 （User-Based）的推荐[[3](#参考文献)] 、基于物品（Item-Based）的推荐[[4](#参考文献)]、基于社交网络关系（Social-Based）的推荐[[5](#参考文献)]、基于模型（Model-based）的推荐等。1994年明尼苏达大学推出的GroupLens系统[[3](#参考文献)]一般被认为是推荐系统成为一个相对独立的研究方向的标志。该系统首次提出了基于协同过滤来完成推荐任务的思想，此后，基于该模型的协同过滤推荐引领了推荐系统十几年的发展方向。
深度学习具有优秀的自动提取特征的能力，能够学习多层次的抽象特征表示，并对异质或跨域的内容信息进行学习，可以一定程度上处理推荐系统冷启动问题[[6](#参考文献)]。本教程主要介绍个性化推荐的深度学习模型，以及如何使用PaddlePaddle实现模型。
## 效果展示
我们使用包含用户信息、电影信息与电影评分的数据集作为个性化推荐的应用场景。当我们训练好模型后，只需要输入对应的用户ID和电影ID，就可以得出一个匹配的分数（范围[0,5]，分数越高视为兴趣越大），然后根据所有电影的推荐得分排序，推荐给用户可能感兴趣的电影。
```
Input movie_id: 1962
Input user_id: 1
Prediction Score is 4.25
```
## 模型概览
本章中，我们首先介绍YouTube的视频推荐系统[[7](#参考文献)]，然后介绍我们实现的融合推荐模型。
### YouTube的深度神经网络推荐系统
YouTube是世界上最大的视频上传、分享和发现网站，YouTube推荐系统为超过10亿用户从不断增长的视频库中推荐个性化的内容。整个系统由两个神经网络组成：候选生成网络和排序网络。候选生成网络从百万量级的视频库中生成上百个候选，排序网络对候选进行打分排序，输出排名最高的数十个结果。系统结构如图1所示：
<p align="center">
<img src="image/YouTube_Overview.png" width="70%" ><br/>
图1. YouTube 推荐系统结构
</p>
#### 候选生成网络（Candidate Generation Network）
候选生成网络将推荐问题建模为一个类别数极大的多类分类问题：对于一个Youtube用户，使用其观看历史（视频ID）、搜索词记录（search tokens）、人口学信息（如地理位置、用户登录设备）、二值特征（如性别，是否登录）和连续特征（如用户年龄）等，对视频库中所有视频进行多分类，得到每一类别的分类结果（即每一个视频的推荐概率），最终输出概率较高的几百个视频。
首先，将观看历史及搜索词记录这类历史信息，映射为向量后取平均值得到定长表示；同时，输入人口学特征以优化新用户的推荐效果，并将二值特征和连续特征归一化处理到[0, 1]范围。接下来，将所有特征表示拼接为一个向量，并输入给非线形多层感知器（MLP，详见[识别数字](https://github.com/PaddlePaddle/book/blob/develop/02.recognize_digits/README.md)教程）处理。最后，训练时将MLP的输出给softmax做分类，预测时计算用户的综合特征（MLP的输出）与所有视频的相似度，取得分最高的$k$个作为候选生成网络的筛选结果。图2显示了候选生成网络结构。
<p align="center">
<img src="image/Deep_candidate_generation_model_architecture.png" width="70%" ><br/>
图2. 候选生成网络结构
</p>
对于一个用户$U$，预测此刻用户要观看的视频$\omega$为视频$i$的概率公式为：
$$P(\omega=i|u)=\frac{e^{v_{i}u}}{\sum_{j \in V}e^{v_{j}u}}$$
其中$u$为用户$U$的特征表示，$V$为视频库集合，$v_i$为视频库中第$i$个视频的特征表示。$u$和$v_i$为长度相等的向量，两者点积可以通过全连接层实现。
考虑到softmax分类的类别数非常多，为了保证一定的计算效率：1）训练阶段，使用负样本类别采样将实际计算的类别数缩小至数千；2）推荐（预测）阶段，忽略softmax的归一化计算（不影响结果），将类别打分问题简化为点积（dot product）空间中的最近邻（nearest neighbor）搜索问题，取与$u$最近的$k$个视频作为生成的候选。
#### 排序网络（Ranking Network）
排序网络的结构类似于候选生成网络，但是它的目标是对候选进行更细致的打分排序。和传统广告排序中的特征抽取方法类似，这里也构造了大量的用于视频排序的相关特征（如视频 ID、上次观看时间等）。这些特征的处理方式和候选生成网络类似，不同之处是排序网络的顶部是一个加权逻辑回归（weighted logistic regression），它对所有候选视频进行打分，从高到底排序后将分数较高的一些视频返回给用户。
### 融合推荐模型
本节会使卷积神经网络（Convolutional Neural Networks）来学习电影名称的表示。下面会依次介绍文本卷积神经网络以及融合推荐模型。
#### 文本卷积神经网络（CNN）
卷积神经网络经常用来处理具有类似网格拓扑结构（grid-like topology）的数据。例如，图像可以视为二维网格的像素点，自然语言可以视为一维的词序列。卷积神经网络可以提取多种局部特征，并对其进行组合抽象得到更高级的特征表示。实验表明，卷积神经网络能高效地对图像及文本问题进行建模处理。
卷积神经网络主要由卷积（convolution）和池化（pooling）操作构成，其应用及组合方式灵活多变，种类繁多。本小结我们以如图3所示的网络进行讲解：
<p align="center">
<img src="image/text_cnn.png" width = "80%" align="center"/><br/>
图3. 卷积神经网络文本分类模型
</p>
假设待处理句子的长度为$n$，其中第$i$个词的词向量（word embedding）为$x_i\in\mathbb{R}^k$，$k$为维度大小。
首先，进行词向量的拼接操作：将每$h$个词拼接起来形成一个大小为$h$的词窗口，记为$x_{i:i+h-1}$，它表示词序列$x_{i},x_{i+1},\ldots,x_{i+h-1}$的拼接，其中，$i$表示词窗口中第一个词在整个句子中的位置，取值范围从$1$到$n-h+1$，$x_{i:i+h-1}\in\mathbb{R}^{hk}$。
其次，进行卷积操作：把卷积核(kernel)$w\in\mathbb{R}^{hk}$应用于包含$h$个词的窗口$x_{i:i+h-1}$，得到特征$c_i=f(w\cdot x_{i:i+h-1}+b)$，其中$b\in\mathbb{R}$为偏置项（bias），$f$为非线性激活函数，如$sigmoid$。将卷积核应用于句子中所有的词窗口${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$，产生一个特征图（feature map）：
$$c=[c_1,c_2,\ldots,c_{n-h+1}], c \in \mathbb{R}^{n-h+1}$$
接下来，对特征图采用时间维度上的最大池化（max pooling over time）操作得到此卷积核对应的整句话的特征$\hat c$，它是特征图中所有元素的最大值：
$$\hat c=max(c)$$
#### 模型概览
在融合推荐模型的电影推荐系统中：
1. 首先，使用用户特征和电影特征作为神经网络的输入，其中：
- 用户特征融合了四个属性信息，分别是用户ID、性别、职业和年龄。
- 电影特征融合了三个属性信息，分别是电影ID、电影类型ID和电影名称。
2. 对用户特征，将用户ID映射为维度大小为256的向量表示，输入全连接层，并对其他三个属性也做类似的处理。然后将四个属性的特征表示分别全连接并相加。
3. 对电影特征，将电影ID以类似用户ID的方式进行处理，电影类型ID以向量的形式直接输入全连接层，电影名称用文本卷积神经网络得到其定长向量表示。然后将三个属性的特征表示分别全连接并相加。
4. 得到用户和电影的向量表示后，计算二者的余弦相似度作为推荐系统的打分。最后，用该相似度打分和用户真实打分的差异的平方作为该回归模型的损失函数。
<p align="center">
<img src="image/rec_regression_network.png" width="90%" ><br/>
图4. 融合推荐模型
</p>
## 数据准备
### 数据介绍与下载
我们以 [MovieLens 百万数据集（ml-1m）](http://files.grouplens.org/datasets/movielens/ml-1m.zip)为例进行介绍。ml-1m 数据集包含了 6,000 位用户对 4,000 部电影的 1,000,000 条评价（评分范围 1~5 分，均为整数），由 GroupLens Research 实验室搜集整理。
Paddle在API中提供了自动加载数据的模块。数据模块为 `paddle.dataset.movielens`
```python
import paddle.v2 as paddle
paddle.init(use_gpu=False)
```
```python
# Run this block to show dataset's documentation
# help(paddle.dataset.movielens)
```
在原始数据中包含电影的特征数据，用户的特征数据，和用户对电影的评分。
例如，其中某一个电影特征为:
```python
movie_info = paddle.dataset.movielens.movie_info()
print movie_info.values()[0]
```
<MovieInfo id(1), title(Toy Story ), categories(['Animation', "Children's", 'Comedy'])>
这表示，电影的id是1，标题是《Toy Story》，该电影被分为到三个类别中。这三个类别是动画，儿童，喜剧。
```python
user_info = paddle.dataset.movielens.user_info()
print user_info.values()[0]
```
<UserInfo id(1), gender(F), age(1), job(10)>
这表示，该用户ID是1，女性，年龄比18岁还年轻。职业ID是10。
其中，年龄使用下列分布
* 1: "Under 18"
* 18: "18-24"
* 25: "25-34"
* 35: "35-44"
* 45: "45-49"
* 50: "50-55"
* 56: "56+"
职业是从下面几种选项里面选则得出:
* 0: "other" or not specified
* 1: "academic/educator"
* 2: "artist"
* 3: "clerical/admin"
* 4: "college/grad student"
* 5: "customer service"
* 6: "doctor/health care"
* 7: "executive/managerial"
* 8: "farmer"
* 9: "homemaker"
* 10: "K-12 student"
* 11: "lawyer"
* 12: "programmer"
* 13: "retired"
* 14: "sales/marketing"
* 15: "scientist"
* 16: "self-employed"
* 17: "technician/engineer"
* 18: "tradesman/craftsman"
* 19: "unemployed"
* 20: "writer"
而对于每一条训练/测试数据，均为 <用户特征> + <电影特征> + 评分。
例如，我们获得第一条训练数据:
```python
train_set_creator = paddle.dataset.movielens.train()
train_sample = next(train_set_creator())
uid = train_sample[0]
mov_id = train_sample[len(user_info[uid].value())]
print "User %s rates Movie %s with Score %s"%(user_info[uid], movie_info[mov_id], train_sample[-1])
```
User <UserInfo id(1), gender(F), age(1), job(10)> rates Movie <MovieInfo id(1193), title(One Flew Over the Cuckoo's Nest ), categories(['Drama'])> with Score [5.0]
即用户1对电影1193的评价为5分。
## 模型配置说明
下面我们开始根据输入数据的形式配置模型。
```python
uid = paddle.layer.data(
name='user_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_user_id() + 1))
usr_emb = paddle.layer.embedding(input=uid, size=32)
usr_fc = paddle.layer.fc(input=usr_emb, size=32)
usr_gender_id = paddle.layer.data(
name='gender_id', type=paddle.data_type.integer_value(2))
usr_gender_emb = paddle.layer.embedding(input=usr_gender_id, size=16)
usr_gender_fc = paddle.layer.fc(input=usr_gender_emb, size=16)
usr_age_id = paddle.layer.data(
name='age_id',
type=paddle.data_type.integer_value(
len(paddle.dataset.movielens.age_table)))
usr_age_emb = paddle.layer.embedding(input=usr_age_id, size=16)
usr_age_fc = paddle.layer.fc(input=usr_age_emb, size=16)
usr_job_id = paddle.layer.data(
name='job_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_job_id() + 1))
usr_job_emb = paddle.layer.embedding(input=usr_job_id, size=16)
usr_job_fc = paddle.layer.fc(input=usr_job_emb, size=16)
```
如上述代码所示，对于每个用户，我们输入4维特征。其中包括`user_id`,`gender_id`,`age_id`,`job_id`。这几维特征均是简单的整数值。为了后续神经网络处理这些特征方便，我们借鉴NLP中的语言模型，将这几维离散的整数值，变换成embedding取出。分别形成`usr_emb`, `usr_gender_emb`, `usr_age_emb`, `usr_job_emb`。
```python
usr_combined_features = paddle.layer.fc(
input=[usr_fc, usr_gender_fc, usr_age_fc, usr_job_fc],
size=200,
act=paddle.activation.Tanh())
```
然后，我们对于所有的用户特征，均输入到一个全连接层(fc)中。将所有特征融合为一个200维度的特征。
进而，我们对每一个电影特征做类似的变换，网络配置为:
```python
mov_id = paddle.layer.data(
name='movie_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_movie_id() + 1))
mov_emb = paddle.layer.embedding(input=mov_id, size=32)
mov_fc = paddle.layer.fc(input=mov_emb, size=32)
mov_categories = paddle.layer.data(
name='category_id',
type=paddle.data_type.sparse_binary_vector(
len(paddle.dataset.movielens.movie_categories())))
mov_categories_hidden = paddle.layer.fc(input=mov_categories, size=32)
movie_title_dict = paddle.dataset.movielens.get_movie_title_dict()
mov_title_id = paddle.layer.data(
name='movie_title',
type=paddle.data_type.integer_value_sequence(len(movie_title_dict)))
mov_title_emb = paddle.layer.embedding(input=mov_title_id, size=32)
mov_title_conv = paddle.networks.sequence_conv_pool(
input=mov_title_emb, hidden_size=32, context_len=3)
mov_combined_features = paddle.layer.fc(
input=[mov_fc, mov_categories_hidden, mov_title_conv],
size=200,
act=paddle.activation.Tanh())
```
电影ID和电影类型分别映射到其对应的特征隐层。对于电影标题名称(title)，一个ID序列表示的词语序列，在输入卷积层后，将得到每个时间窗口的特征（序列特征），然后通过在时间维度降采样得到固定维度的特征，整个过程在sequence_conv_pool实现。
最后再将电影的特征融合进`mov_combined_features`中。
```python
inference = paddle.layer.cos_sim(a=usr_combined_features, b=mov_combined_features, size=1, scale=5)
```
进而，我们使用余弦相似度计算用户特征与电影特征的相似性。并将这个相似性拟合(回归)到用户评分上。
```python
cost = paddle.layer.mse_cost(
input=inference,
label=paddle.layer.data(
name='score', type=paddle.data_type.dense_vector(1)))
```
至此，我们的优化目标就是这个网络配置中的`cost`了。
## 训练模型
### 定义参数
神经网络的模型，我们可以简单的理解为网络拓朴结构+参数。之前一节，我们定义出了优化目标`cost`。这个`cost`即为网络模型的拓扑结构。我们开始训练模型，需要先定义出参数。定义方法为:
```python
parameters = paddle.parameters.create(cost)
```
[INFO 2017-03-06 17:12:13,284 networks.py:1472] The input order is [user_id, gender_id, age_id, job_id, movie_id, category_id, movie_title, score]
[INFO 2017-03-06 17:12:13,287 networks.py:1478] The output order is [__mse_cost_0__]
`parameters`是模型的所有参数集合。他是一个python的dict。我们可以查看到这个网络中的所有参数名称。因为之前定义模型的时候，我们没有指定参数名称，这里参数名称是自动生成的。当然，我们也可以指定每一个参数名称，方便日后维护。
```python
print parameters.keys()
```
[u'___fc_layer_2__.wbias', u'___fc_layer_2__.w2', u'___embedding_layer_3__.w0', u'___embedding_layer_5__.w0', u'___embedding_layer_2__.w0', u'___embedding_layer_1__.w0', u'___fc_layer_1__.wbias', u'___fc_layer_0__.wbias', u'___fc_layer_1__.w0', u'___fc_layer_0__.w2', u'___fc_layer_0__.w3', u'___fc_layer_0__.w0', u'___fc_layer_0__.w1', u'___fc_layer_2__.w1', u'___fc_layer_2__.w0', u'___embedding_layer_4__.w0', u'___sequence_conv_pool_0___conv_fc.w0', u'___embedding_layer_0__.w0', u'___sequence_conv_pool_0___conv_fc.wbias']
### 构造训练(trainer)
下面，我们根据网络拓扑结构和模型参数来构造出一个本地训练(trainer)。在构造本地训练的时候，我们还需要指定这个训练的优化方法。这里我们使用Adam来作为优化算法。
```python
trainer = paddle.trainer.SGD(cost=cost, parameters=parameters,
update_equation=paddle.optimizer.Adam(learning_rate=1e-4))
```
[INFO 2017-03-06 17:12:13,378 networks.py:1472] The input order is [user_id, gender_id, age_id, job_id, movie_id, category_id, movie_title, score]
[INFO 2017-03-06 17:12:13,379 networks.py:1478] The output order is [__mse_cost_0__]
### 训练
下面我们开始训练过程。
我们直接使用Paddle提供的数据集读取程序。`paddle.dataset.movielens.train()`和`paddle.dataset.movielens.test()`分别做训练和预测数据集。并且通过`feeding`来指定每一个数据和data_layer的对应关系。
例如，这里的feeding表示的是，对于数据层 `user_id`，使用了reader中每一条数据的第0个元素。`gender_id`数据层使用了第1个元素。以此类推。
```python
feeding = {
'user_id': 0,
'gender_id': 1,
'age_id': 2,
'job_id': 3,
'movie_id': 4,
'category_id': 5,
'movie_title': 6,
'score': 7
}
```
训练过程是完全自动的。我们可以使用event_handler与event_handler_plot来观察训练过程，或进行测试等。这里我们在event_handler_plot里面绘制了训练误差曲线和测试误差曲线。并且保存了模型。
```python
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "Pass %d Batch %d Cost %.2f" % (
event.pass_id, event.batch_id, event.cost)
```
```python
from paddle.v2.plot import Ploter
train_title = "Train cost"
test_title = "Test cost"
cost_ploter = Ploter(train_title, test_title)
step = 0
def event_handler_plot(event):
global step
if isinstance(event, paddle.event.EndIteration):
if step % 10 == 0: # every 10 batches, record a train cost
cost_ploter.append(train_title, step, event.cost)
if step % 1000 == 0: # every 1000 batches, record a test cost
result = trainer.test(
reader=paddle.batch(
paddle.dataset.movielens.test(), batch_size=256),
feeding=feeding)
cost_ploter.append(test_title, step, result.cost)
if step % 100 == 0: # every 100 batches, update cost plot
cost_ploter.plot()
step += 1
```
```python
trainer.train(
reader=paddle.batch(
paddle.reader.shuffle(
paddle.dataset.movielens.train(), buf_size=8192),
batch_size=256),
event_handler=event_handler_plot,
feeding=feeding,
num_passes=2)
```
![png](./image/output_32_0.png)
## 应用模型
在训练了几轮以后，您可以对模型进行推断。我们可以使用任意一个用户ID和电影ID，来预测该用户对该电影的评分。示例程序为:
```python
import copy
user_id = 234
movie_id = 345
user = user_info[user_id]
movie = movie_info[movie_id]
feature = user.value() + movie.value()
infer_dict = copy.copy(feeding)
del infer_dict['score']
prediction = paddle.infer(inference, parameters=parameters, input=[feature], feeding=infer_dict)
score = (prediction[0][0] + 5.0) / 2
print "[Predict] User %d Rating Movie %d With Score %.2f"%(user_id, movie_id, score)
```
[INFO 2017-03-06 17:17:08,132 networks.py:1472] The input order is [user_id, gender_id, age_id, job_id, movie_id, category_id, movie_title]
[INFO 2017-03-06 17:17:08,134 networks.py:1478] The output order is [__cos_sim_0__]
[Predict] User 234 Rating Movie 345 With Score 4.16
## 总结
本章介绍了传统的推荐系统方法和YouTube的深度神经网络推荐系统，并以电影推荐为例，使用PaddlePaddle训练了一个个性化推荐神经网络模型。推荐系统几乎涵盖了电商系统、社交网络、广告推荐、搜索引擎等领域的方方面面，而在图像处理、自然语言处理等领域已经发挥重要作用的深度学习技术，也将会在推荐系统领域大放异彩。
## 参考文献
1. [Peter Brusilovsky](https://en.wikipedia.org/wiki/Peter_Brusilovsky) (2007). *The Adaptive Web*. p. 325.
2. Robin Burke , [Hybrid Web Recommender Systems](http://www.dcs.warwick.ac.uk/~acristea/courses/CS411/2010/Book%20-%20The%20Adaptive%20Web/HybridWebRecommenderSystems.pdf), pp. 377-408, The Adaptive Web, Peter Brusilovsky, Alfred Kobsa, Wolfgang Nejdl (Ed.), Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Lecture Notes in Computer Science, Vol. 4321, May 2007, 978-3-540-72078-2.
3. P. Resnick, N. Iacovou, etc. “[GroupLens: An Open Architecture for Collaborative Filtering of Netnews](http://ccs.mit.edu/papers/CCSWP165.html)”, Proceedings of ACM Conference on Computer Supported Cooperative Work, CSCW 1994. pp.175-186.
4. Sarwar, Badrul, et al. "[Item-based collaborative filtering recommendation algorithms.](http://files.grouplens.org/papers/www10_sarwar.pdf)" *Proceedings of the 10th international conference on World Wide Web*. ACM, 2001.
5. Kautz, Henry, Bart Selman, and Mehul Shah. "[Referral Web: combining social networks and collaborative filtering.](http://www.cs.cornell.edu/selman/papers/pdf/97.cacm.refweb.pdf)" Communications of the ACM 40.3 (1997): 63-65. APA
6. Yuan, Jianbo, et al. ["Solving Cold-Start Problem in Large-scale Recommendation Engines: A Deep Learning Approach."](https://arxiv.org/pdf/1611.05480v1.pdf) *arXiv preprint arXiv:1611.05480* (2016).
7. Covington P, Adams J, Sargin E. [Deep neural networks for youtube recommendations](https://static.googleusercontent.com/media/research.google.com/zh-CN//pubs/archive/45530.pdf)[C]//Proceedings of the 10th ACM Conference on Recommender Systems. ACM, 2016: 191-198.
<br/>
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# Personalized Recommendation
The source code of this tutorial is in [book/recommender_system](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system).
For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book).
## Background
With the fast growth of e-commerce, online videos, and online reading business, users have to rely on recommender systems to avoid manually browsing tremendous volume of choices. Recommender systems understand users' interest by mining user behavior and other properties of users and products.
Some well know approaches include:
- User behavior-based approach. A well-known method is collaborative filtering. The underlying assumption is that if a person A has the same opinion as a person B on an issue, A is more likely to have B's opinion on a different issue than that of a randomly chosen person.
- Content-based recommendation[[1](#reference)]. This approach infers feature vectors that represent products from their descriptions. It also infers feature vectors that represent users' interests. Then it measures the relevance of users and products by some distances between these feature vectors.
- Hybrid approach[[2](#reference)]: This approach uses the content-based information to help address the cold start problem[[6](#reference)] in behavior-based approach.
Among these options, collaborative filtering might be the most studied one. Some of its variants include user-based[[3](#reference)], item-based [[4](#reference)], social network based[[5](#reference)], and model-based.
This tutorial explains a deep learning based approach and how to implement it using PaddlePaddle. We will train a model using a dataset that includes user information, movie information, and ratings. Once we train the model, we will be able to get a predicted rating given a pair of user and movie IDs.
## Model Overview
To know more about deep learning based recommendation, let us start from going over the Youtube recommender system[[7](#reference)] before introducing our hybrid model.
### YouTube's Deep Learning Recommendation Model
YouTube is a video-sharing Web site with one of the largest user base in the world. Its recommender system serves more than a billion users. This system is composed of two major parts: candidate generation and ranking. The former selects few hundreds of candidates from millions of videos, and the latter ranks and outputs the top 10.
<p align="center">
<img src="image/YouTube_Overview.en.png" width="70%" ><br/>
Figure 1. YouTube recommender system overview.
</p>
#### Candidate Generation Network
Youtube models candidate generation as a multiclass classification problem with a huge number of classes equal to the number of videos. The architecture of the model is as follows:
<p align="center">
<img src="image/Deep_candidate_generation_model_architecture.en.png" width="70%" ><br/>
Figure 2. Deep candidate generation model.
</p>
The first stage of this model maps watching history and search queries into fixed-length representative features. Then, an MLP (multi-layer perceptron, as described in the [Recognize Digits](https://github.com/PaddlePaddle/book/blob/develop/recognize_digits/README.md) tutorial) takes the concatenation of all representative vectors. The output of the MLP represents the user' *intrinsic interests*. At training time, it is used together with a softmax output layer for minimizing the classification error. At serving time, it is used to compute the relevance of the user with all movies.
For a user $U$, the predicted watching probability of video $i$ is
$$P(\omega=i|u)=\frac{e^{v_{i}u}}{\sum_{j \in V}e^{v_{j}u}}$$
where $u$ is the representative vector of user $U$, $V$ is the corpus of all videos, $v_i$ is the representative vector of the $i$-th video. $u$ and $v_i$ are vectors of the same length, so we can compute their dot product using a fully connected layer.
This model could have a performance issue as the softmax output covers millions of classification labels. To optimize performance, at the training time, the authors down-sample negative samples, so the actual number of classes is reduced to thousands. At serving time, the authors ignore the normalization of the softmax outputs, because the results are just for ranking.
#### Ranking Network
The architecture of the ranking network is similar to that of the candidate generation network. Similar to ranking models widely used in online advertising, it uses rich features like video ID, last watching time, etc. The output layer of the ranking network is a weighted logistic regression, which rates all candidate videos.
### Hybrid Model
In the section, let us introduce our movie recommendation system. Especially, we feed moives titles into a text convolution network to get a fixed-length representative feature vector. Accordingly we will introduce the convolutional neural network for texts and the hybrid recommendation model respectively.
#### Convolutional Neural Networks for Texts (CNN)
**Convolutional Neural Networks** are frequently applied to data with grid-like topology such as two-dimensional images and one-dimensional texts. A CNN can extract multiple local features, combine them, and produce high-level abstractions, which correspond to semantic understanding. Empirically, CNN is shown to be efficient for image and text modeling.
CNN mainly contains convolution and pooling operation, with versatile combinations in various applications. Here, we briefly describe a CNN as shown in Figure 3.
<p align="center">
<img src="image/text_cnn_en.png" width = "80%" align="center"/><br/>
Figure 3. CNN for text modeling.
</p>
Let $n$ be the length of the sentence to process, and the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
First, we concatenate the words by piecing together every $h$ words, each as a window of length $h$. This window is denoted as $x_{i:i+h-1}$, consisting of $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $x_i$ is the first word in the window and $i$ takes value ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
Next, we apply the convolution operation: we apply the kernel $w\in\mathbb{R}^{hk}$ in each window, extracting features $c_i=f(w\cdot x_{i:i+h-1}+b)$, where $b\in\mathbb{R}$ is the bias and $f$ is a non-linear activation function such as $sigmoid$. Convolving by the kernel at every window ${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$ produces a feature map in the following form:
$$c=[c_1,c_2,\ldots,c_{n-h+1}], c \in \mathbb{R}^{n-h+1}$$
Next, we apply *max pooling* over time to represent the whole sentence $\hat c$, which is the maximum element across the feature map:
$$\hat c=max(c)$$
#### Model Structure Of The Hybrid Model
In our network, the input includes features of users and movies. The user feature includes four properties: user ID, gender, occupation, and age. Movie features include their IDs, genres, and titles.
We use fully-connected layers to map user features into representative feature vectors and concatenate them. The process of movie features is similar, except that for movie titles -- we feed titles into a text convolution network as described in the above section to get a fixed-length representative feature vector.
Given the feature vectors of users and movies, we compute the relevance using cosine similarity. We minimize the squared error at training time.
<p align="center">
<img src="image/rec_regression_network_en.png" width="90%" ><br/>
Figure 4. A hybrid recommendation model.
</p>
## Dataset
We use the [MovieLens ml-1m](http://files.grouplens.org/datasets/movielens/ml-1m.zip) to train our model. This dataset includes 10,000 ratings of 4,000 movies from 6,000 users to 4,000 movies. Each rate is in the range of 1~5. Thanks to GroupLens Research for collecting, processing and publishing the dataset.
`paddle.v2.datasets` package encapsulates multiple public datasets, including `cifar`, `imdb`, `mnist`, `moivelens` and `wmt14`, etc. There's no need for us to manually download and preprocess `MovieLens` dataset.
The raw `MoiveLens` contains movie ratings, relevant features from both movies and users.
For instance, one movie's feature could be:
```python
import paddle.v2 as paddle
movie_info = paddle.dataset.movielens.movie_info()
print movie_info.values()[0]
```
```text
<MovieInfo id(1), title(Toy Story), categories(['Animation', "Children's", 'Comedy'])>
```
One user's feature could be:
```python
user_info = paddle.dataset.movielens.user_info()
print user_info.values()[0]
```
```text
<UserInfo id(1), gender(F), age(1), job(10)>
```
In this dateset, the distribution of age is shown as follows:
```text
1: "Under 18"
18: "18-24"
25: "25-34"
35: "35-44"
45: "45-49"
50: "50-55"
56: "56+"
```
User's occupation is selected from the following options:
```text
0: "other" or not specified
1: "academic/educator"
2: "artist"
3: "clerical/admin"
4: "college/grad student"
5: "customer service"
6: "doctor/health care"
7: "executive/managerial"
8: "farmer"
9: "homemaker"
10: "K-12 student"
11: "lawyer"
12: "programmer"
13: "retired"
14: "sales/marketing"
15: "scientist"
16: "self-employed"
17: "technician/engineer"
18: "tradesman/craftsman"
19: "unemployed"
20: "writer"
```
Each record consists of three main components: user features, movie features and movie ratings.
Likewise, as a simple example, consider the following:
```python
train_set_creator = paddle.dataset.movielens.train()
train_sample = next(train_set_creator())
uid = train_sample[0]
mov_id = train_sample[len(user_info[uid].value())]
print "User %s rates Movie %s with Score %s"%(user_info[uid], movie_info[mov_id], train_sample[-1])
```
```text
User <UserInfo id(1), gender(F), age(1), job(10)> rates Movie <MovieInfo id(1193), title(One Flew Over the Cuckoo's Nest), categories(['Drama'])> with Score [5.0]
```
The output shows that user 1 gave movie `1193` a rating of 5.
After issuing a command `python train.py`, training will start immediately. The details will be unpacked by the following sessions to see how it works.
## Model Architecture
### Initialize PaddlePaddle
First, we must import and initialize PaddlePaddle (enable/disable GPU, set the number of trainers, etc).
```python
import paddle.v2 as paddle
paddle.init(use_gpu=False)
```
### Model Configuration
```python
uid = paddle.layer.data(
name='user_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_user_id() + 1))
usr_emb = paddle.layer.embedding(input=uid, size=32)
usr_fc = paddle.layer.fc(input=usr_emb, size=32)
usr_gender_id = paddle.layer.data(
name='gender_id', type=paddle.data_type.integer_value(2))
usr_gender_emb = paddle.layer.embedding(input=usr_gender_id, size=16)
usr_gender_fc = paddle.layer.fc(input=usr_gender_emb, size=16)
usr_age_id = paddle.layer.data(
name='age_id',
type=paddle.data_type.integer_value(
len(paddle.dataset.movielens.age_table)))
usr_age_emb = paddle.layer.embedding(input=usr_age_id, size=16)
usr_age_fc = paddle.layer.fc(input=usr_age_emb, size=16)
usr_job_id = paddle.layer.data(
name='job_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_job_id() + 1))
usr_job_emb = paddle.layer.embedding(input=usr_job_id, size=16)
usr_job_fc = paddle.layer.fc(input=usr_job_emb, size=16)
```
As shown in the above code, the input is four dimension integers for each user, that is, `user_id`,`gender_id`, `age_id` and `job_id`. In order to deal with these features conveniently, we use the language model in NLP to transform these discrete values into embedding vaules `usr_emb`, `usr_gender_emb`, `usr_age_emb` and `usr_job_emb`.
```python
usr_combined_features = paddle.layer.fc(
input=[usr_fc, usr_gender_fc, usr_age_fc, usr_job_fc],
size=200,
act=paddle.activation.Tanh())
```
Then, employing user features as input, directly connecting to a fully-connected layer, which is used to reduce dimension to 200.
Furthermore, we do a similar transformation for each movie feature. The model configuration is:
```python
mov_id = paddle.layer.data(
name='movie_id',
type=paddle.data_type.integer_value(
paddle.dataset.movielens.max_movie_id() + 1))
mov_emb = paddle.layer.embedding(input=mov_id, size=32)
mov_fc = paddle.layer.fc(input=mov_emb, size=32)
mov_categories = paddle.layer.data(
name='category_id',
type=paddle.data_type.sparse_binary_vector(
len(paddle.dataset.movielens.movie_categories())))
mov_categories_hidden = paddle.layer.fc(input=mov_categories, size=32)
movie_title_dict = paddle.dataset.movielens.get_movie_title_dict()
mov_title_id = paddle.layer.data(
name='movie_title',
type=paddle.data_type.integer_value_sequence(len(movie_title_dict)))
mov_title_emb = paddle.layer.embedding(input=mov_title_id, size=32)
mov_title_conv = paddle.networks.sequence_conv_pool(
input=mov_title_emb, hidden_size=32, context_len=3)
mov_combined_features = paddle.layer.fc(
input=[mov_fc, mov_categories_hidden, mov_title_conv],
size=200,
act=paddle.activation.Tanh())
```
Movie title, a sequence of words represented by an integer word index sequence, will be feed into a `sequence_conv_pool` layer, which will apply convolution and pooling on time dimension. Because pooling is done on time dimension, the output will be a fixed-length vector regardless the length of the input sequence.
Finally, we can use cosine similarity to calculate the similarity between user characteristics and movie features.
```python
inference = paddle.layer.cos_sim(a=usr_combined_features, b=mov_combined_features, size=1, scale=5)
cost = paddle.layer.mse_cost(
input=inference,
label=paddle.layer.data(
name='score', type=paddle.data_type.dense_vector(1)))
```
## Model Training
### Define Parameters
First, we define the model parameters according to the previous model configuration `cost`.
```python
# Create parameters
parameters = paddle.parameters.create(cost)
```
### Create Trainer
Before jumping into creating a training module, algorithm setting is also necessary. Here we specified Adam optimization algorithm via `paddle.optimizer`.
```python
trainer = paddle.trainer.SGD(cost=cost, parameters=parameters,
update_equation=paddle.optimizer.Adam(learning_rate=1e-4))
```
```text
[INFO 2017-03-06 17:12:13,378 networks.py:1472] The input order is [user_id, gender_id, age_id, job_id, movie_id, category_id, movie_title, score]
[INFO 2017-03-06 17:12:13,379 networks.py:1478] The output order is [__mse_cost_0__]
```
### Training
`paddle.dataset.movielens.train` will yield records during each pass, after shuffling, a batch input is generated for training.
```python
reader=paddle.batch(
paddle.reader.shuffle(
paddle.dataset.movielens.train(), buf_size=8192),
batch_size=256)
```
`feeding` is devoted to specifying the correspondence between each yield record and `paddle.layer.data`. For instance, the first column of data generated by `movielens.train` corresponds to `user_id` feature.
```python
feeding = {
'user_id': 0,
'gender_id': 1,
'age_id': 2,
'job_id': 3,
'movie_id': 4,
'category_id': 5,
'movie_title': 6,
'score': 7
}
```
Callback function `event_handler` and `event_handler_plot` will be called during training when a pre-defined event happens.
```python
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "Pass %d Batch %d Cost %.2f" % (
event.pass_id, event.batch_id, event.cost)
```
```python
from paddle.v2.plot import Ploter
train_title = "Train cost"
test_title = "Test cost"
cost_ploter = Ploter(train_title, test_title)
step = 0
def event_handler_plot(event):
global step
if isinstance(event, paddle.event.EndIteration):
if step % 10 == 0: # every 10 batches, record a train cost
cost_ploter.append(train_title, step, event.cost)
if step % 1000 == 0: # every 1000 batches, record a test cost
result = trainer.test(
reader=paddle.batch(
paddle.dataset.movielens.test(), batch_size=256),
feeding=feeding)
cost_ploter.append(test_title, step, result.cost)
if step % 100 == 0: # every 100 batches, update cost plot
cost_ploter.plot()
step += 1
```
Finally, we can invoke `trainer.train` to start training:
```python
trainer.train(
reader=reader,
event_handler=event_handler_plot,
feeding=feeding,
num_passes=2)
```
## Conclusion
This tutorial goes over traditional approaches in recommender system and a deep learning based approach. We also show that how to train and use the model with PaddlePaddle. Deep learning has been well used in computer vision and NLP, we look forward to its new successes in recommender systems.
## Reference
1. [Peter Brusilovsky](https://en.wikipedia.org/wiki/Peter_Brusilovsky) (2007). *The Adaptive Web*. p. 325.
2. Robin Burke , [Hybrid Web Recommender Systems](http://www.dcs.warwick.ac.uk/~acristea/courses/CS411/2010/Book%20-%20The%20Adaptive%20Web/HybridWebRecommenderSystems.pdf), pp. 377-408, The Adaptive Web, Peter Brusilovsky, Alfred Kobsa, Wolfgang Nejdl (Ed.), Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Lecture Notes in Computer Science, Vol. 4321, May 2007, 978-3-540-72078-2.
3. P. Resnick, N. Iacovou, etc. “[GroupLens: An Open Architecture for Collaborative Filtering of Netnews](http://ccs.mit.edu/papers/CCSWP165.html)”, Proceedings of ACM Conference on Computer Supported Cooperative Work, CSCW 1994. pp.175-186.
4. Sarwar, Badrul, et al. "[Item-based collaborative filtering recommendation algorithms.](http://files.grouplens.org/papers/www10_sarwar.pdf)" *Proceedings of the 10th International Conference on World Wide Web*. ACM, 2001.
5. Kautz, Henry, Bart Selman, and Mehul Shah. "[Referral Web: Combining Social networks and collaborative filtering.](http://www.cs.cornell.edu/selman/papers/pdf/97.cacm.refweb.pdf)" Communications of the ACM 40.3 (1997): 63-65. APA
6. Yuan, Jianbo, et al. ["Solving Cold-Start Problem in Large-scale Recommendation Engines: A Deep Learning Approach."](https://arxiv.org/pdf/1611.05480v1.pdf) *arXiv preprint arXiv:1611.05480* (2016).
7. Covington P, Adams J, Sargin E. [Deep neural networks for youtube recommendations](https://static.googleusercontent.com/media/research.google.com/zh-CN//pubs/archive/45530.pdf)[C]//Proceedings of the 10th ACM Conference on Recommender Systems. ACM, 2016: 191-198.
<br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.
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# 情感分析
本教程源代码目录在[book/understand_sentiment](https://github.com/PaddlePaddle/book/tree/develop/06.understand_sentiment)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## 背景介绍
在自然语言处理中，情感分析一般是指判断一段文本所表达的情绪状态。其中，一段文本可以是一个句子，一个段落或一个文档。情绪状态可以是两类，如（正面，负面），（高兴，悲伤）；也可以是三类，如（积极，消极，中性）等等。情感分析的应用场景十分广泛，如把用户在购物网站（亚马逊、天猫、淘宝等）、旅游网站、电影评论网站上发表的评论分成正面评论和负面评论；或为了分析用户对于某一产品的整体使用感受，抓取产品的用户评论并进行情感分析等等。表格1展示了对电影评论进行情感分析的例子：
| 电影评论 | 类别 |
| -------- | ----- |
| 在冯小刚这几年的电影里，算最好的一部的了| 正面 |
| 很不好看，好像一个地方台的电视剧 | 负面 |
| 圆方镜头全程炫技，色调背景美则美矣，但剧情拖沓，口音不伦不类，一直努力却始终无法入戏| 负面|
|剧情四星。但是圆镜视角加上婺源的风景整个非常有中国写意山水画的感觉，看得实在太舒服了。。|正面|
<p align="center">表格 1 电影评论情感分析</p>
在自然语言处理中，情感分析属于典型的**文本分类**问题，即把需要进行情感分析的文本划分为其所属类别。文本分类涉及文本表示和分类方法两个问题。在深度学习的方法出现之前，主流的文本表示方法为词袋模型BOW(bag of words)，话题模型等等；分类方法有SVM(support vector machine), LR(logistic regression)等等。
对于一段文本，BOW表示会忽略其词顺序、语法和句法，将这段文本仅仅看做是一个词集合，因此BOW方法并不能充分表示文本的语义信息。例如，句子“这部电影糟糕透了”和“一个乏味，空洞，没有内涵的作品”在情感分析中具有很高的语义相似度，但是它们的BOW表示的相似度为0。又如，句子“一个空洞，没有内涵的作品”和“一个不空洞而且有内涵的作品”的BOW相似度很高，但实际上它们的意思很不一样。
本章我们所要介绍的深度学习模型克服了BOW表示的上述缺陷，它在考虑词顺序的基础上把文本映射到低维度的语义空间，并且以端对端（end to end）的方式进行文本表示及分类，其性能相对于传统方法有显著的提升\[[1](#参考文献)\]。
## 模型概览
本章所使用的文本表示模型为卷积神经网络（Convolutional Neural Networks）和循环神经网络(Recurrent Neural Networks)及其扩展。下面依次介绍这几个模型。
### 文本卷积神经网络简介（CNN）
我们在[推荐系统](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system)一节介绍过应用于文本数据的卷及神经网络模型的计算过程，这里进行一个简单的回顾。
对卷积神经网络来说，首先使用卷积处理输入的词向量序列，产生一个特征图（feature map），对特征图采用时间维度上的最大池化（max pooling over time）操作得到此卷积核对应的整句话的特征，最后，将所有卷积核得到的特征拼接起来即为文本的定长向量表示，对于文本分类问题，将其连接至softmax即构建出完整的模型。在实际应用中，我们会使用多个卷积核来处理句子，窗口大小相同的卷积核堆叠起来形成一个矩阵，这样可以更高效的完成运算。另外，我们也可使用窗口大小不同的卷积核来处理句子，[推荐系统](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system)一节的图3作为示意画了四个卷积核，不同颜色表示不同大小的卷积核操作。
对于一般的短文本分类问题，上文所述的简单的文本卷积网络即可达到很高的正确率\[[1](#参考文献)\]。若想得到更抽象更高级的文本特征表示，可以构建深层文本卷积神经网络\[[2](#参考文献),[3](#参考文献)\]。
### 循环神经网络（RNN）
循环神经网络是一种能对序列数据进行精确建模的有力工具。实际上，循环神经网络的理论计算能力是图灵完备的\[[4](#参考文献)\]。自然语言是一种典型的序列数据（词序列），近年来，循环神经网络及其变体（如long short term memory\[[5](#参考文献)\]等）在自然语言处理的多个领域，如语言模型、句法解析、语义角色标注（或一般的序列标注）、语义表示、图文生成、对话、机器翻译等任务上均表现优异甚至成为目前效果最好的方法。
<p align="center">
<img src="image/rnn.png" width = "60%" align="center"/><br/>
图1. 循环神经网络按时间展开的示意图
</p>
循环神经网络按时间展开后如图1所示：在第$t$时刻，网络读入第$t$个输入$x_t$（向量表示）及前一时刻隐层的状态值$h_{t-1}$（向量表示，$h_0$一般初始化为$0$向量），计算得出本时刻隐层的状态值$h_t$，重复这一步骤直至读完所有输入。如果将循环神经网络所表示的函数记为$f$，则其公式可表示为：
$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{h-1}+b_h)$$
其中$W_{xh}$是输入到隐层的矩阵参数，$W_{hh}$是隐层到隐层的矩阵参数，$b_h$为隐层的偏置向量（bias）参数，$\sigma$为$sigmoid$函数。
在处理自然语言时，一般会先将词（one-hot表示）映射为其词向量（word embedding）表示，然后再作为循环神经网络每一时刻的输入$x_t$。此外，可以根据实际需要的不同在循环神经网络的隐层上连接其它层。如，可以把一个循环神经网络的隐层输出连接至下一个循环神经网络的输入构建深层（deep or stacked）循环神经网络，或者提取最后一个时刻的隐层状态作为句子表示进而使用分类模型等等。
### 长短期记忆网络（LSTM）
对于较长的序列数据，循环神经网络的训练过程中容易出现梯度消失或爆炸现象\[[6](#参考文献)\]。为了解决这一问题，Hochreiter S, Schmidhuber J. (1997)提出了LSTM(long short term memory\[[5](#参考文献)\])。
相比于简单的循环神经网络，LSTM增加了记忆单元$c$、输入门$i$、遗忘门$f$及输出门$o$。这些门及记忆单元组合起来大大提升了循环神经网络处理长序列数据的能力。若将基于LSTM的循环神经网络表示的函数记为$F$，则其公式为：
$$ h_t=F(x_t,h_{t-1})$$
$F$由下列公式组合而成\[[7](#参考文献)\]：
\begin{align}
i_t & = \sigma(W_{xi}x_t+W_{hi}h_{h-1}+W_{ci}c_{t-1}+b_i)\\\\
f_t & = \sigma(W_{xf}x_t+W_{hf}h_{h-1}+W_{cf}c_{t-1}+b_f)\\\\
c_t & = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
o_t & = \sigma(W_{xo}x_t+W_{ho}h_{h-1}+W_{co}c_{t}+b_o)\\\\
h_t & = o_t\odot tanh(c_t)\\\\
\end{align}
其中，$i_t, f_t, c_t, o_t$分别表示输入门，遗忘门，记忆单元及输出门的向量值，带角标的$W$及$b$为模型参数，$tanh$为双曲正切函数，$\odot$表示逐元素（elementwise）的乘法操作。输入门控制着新输入进入记忆单元$c$的强度，遗忘门控制着记忆单元维持上一时刻值的强度，输出门控制着输出记忆单元的强度。三种门的计算方式类似，但有着完全不同的参数，它们各自以不同的方式控制着记忆单元$c$，如图2所示：
<p align="center">
<img src="image/lstm.png" width = "65%" align="center"/><br/>
图2. 时刻$t$的LSTM [7]
</p>
LSTM通过给简单的循环神经网络增加记忆及控制门的方式，增强了其处理远距离依赖问题的能力。类似原理的改进还有Gated Recurrent Unit (GRU)\[[8](#参考文献)\]，其设计更为简洁一些。**这些改进虽然各有不同，但是它们的宏观描述却与简单的循环神经网络一样（如图2所示），即隐状态依据当前输入及前一时刻的隐状态来改变，不断地循环这一过程直至输入处理完毕：**
$$ h_t=Recrurent(x_t,h_{t-1})$$
其中，$Recrurent$可以表示简单的循环神经网络、GRU或LSTM。
### 栈式双向LSTM（Stacked Bidirectional LSTM）
对于正常顺序的循环神经网络，$h_t$包含了$t$时刻之前的输入信息，也就是上文信息。同样，为了得到下文信息，我们可以使用反方向（将输入逆序处理）的循环神经网络。结合构建深层循环神经网络的方法（深层神经网络往往能得到更抽象和高级的特征表示），我们可以通过构建更加强有力的基于LSTM的栈式双向循环神经网络\[[9](#参考文献)\]，来对时序数据进行建模。
如图3所示（以三层为例），奇数层LSTM正向，偶数层LSTM反向，高一层的LSTM使用低一层LSTM及之前所有层的信息作为输入，对最高层LSTM序列使用时间维度上的最大池化即可得到文本的定长向量表示（这一表示充分融合了文本的上下文信息，并且对文本进行了深层次抽象），最后我们将文本表示连接至softmax构建分类模型。
<p align="center">
<img src="image/stacked_lstm.jpg" width=450><br/>
图3. 栈式双向LSTM用于文本分类
</p>
## 示例程序
### 数据集介绍
我们以[IMDB情感分析数据集](http://ai.stanford.edu/%7Eamaas/data/sentiment/)为例进行介绍。IMDB数据集的训练集和测试集分别包含25000个已标注过的电影评论。其中，负面评论的得分小于等于4，正面评论的得分大于等于7，满分10分。
```text
aclImdb
|- test
|-- neg
|-- pos
|- train
|-- neg
|-- pos
```
Paddle在`dataset/imdb.py`中提实现了imdb数据集的自动下载和读取，并提供了读取字典、训练数据、测试数据等API。
```python
import sys
import paddle.v2 as paddle
```
## 配置模型
在该示例中，我们实现了两种文本分类算法，分别基于[推荐系统](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system)一节介绍过的文本卷积神经网络，以及[栈式双向LSTM](#栈式双向LSTM（Stacked Bidirectional LSTM）)。
### 文本卷积神经网络
```python
def convolution_net(input_dim,
class_dim=2,
emb_dim=128,
hid_dim=128,
is_predict=False):
data = paddle.layer.data("word",
paddle.data_type.integer_value_sequence(input_dim))
emb = paddle.layer.embedding(input=data, size=emb_dim)
conv_3 = paddle.networks.sequence_conv_pool(
input=emb, context_len=3, hidden_size=hid_dim)
conv_4 = paddle.networks.sequence_conv_pool(
input=emb, context_len=4, hidden_size=hid_dim)
output = paddle.layer.fc(input=[conv_3, conv_4],
size=class_dim,
act=paddle.activation.Softmax())
if not is_predict:
lbl = paddle.layer.data("label", paddle.data_type.integer_value(2))
cost = paddle.layer.classification_cost(input=output, label=lbl)
return cost
else:
return output
```
网络的输入`input_dim`表示的是词典的大小，`class_dim`表示类别数。这里，我们使用[`sequence_conv_pool`](https://github.com/PaddlePaddle/Paddle/blob/develop/python/paddle/trainer_config_helpers/networks.py) API实现了卷积和池化操作。
### 栈式双向LSTM
```python
def stacked_lstm_net(input_dim,
class_dim=2,
emb_dim=128,
hid_dim=512,
stacked_num=3,
is_predict=False):
"""
A Wrapper for sentiment classification task.
This network uses bi-directional recurrent network,
consisting three LSTM layers. This configure is referred to
the paper as following url, but use fewer layrs.
http://www.aclweb.org/anthology/P15-1109
input_dim: here is word dictionary dimension.
class_dim: number of categories.
emb_dim: dimension of word embedding.
hid_dim: dimension of hidden layer.
stacked_num: number of stacked lstm-hidden layer.
"""
assert stacked_num % 2 == 1
layer_attr = paddle.attr.Extra(drop_rate=0.5)
fc_para_attr = paddle.attr.Param(learning_rate=1e-3)
lstm_para_attr = paddle.attr.Param(initial_std=0., learning_rate=1.)
para_attr = [fc_para_attr, lstm_para_attr]
bias_attr = paddle.attr.Param(initial_std=0., l2_rate=0.)
relu = paddle.activation.Relu()
linear = paddle.activation.Linear()
data = paddle.layer.data("word",
paddle.data_type.integer_value_sequence(input_dim))
emb = paddle.layer.embedding(input=data, size=emb_dim)
fc1 = paddle.layer.fc(input=emb,
size=hid_dim,
act=linear,
bias_attr=bias_attr)
lstm1 = paddle.layer.lstmemory(
input=fc1, act=relu, bias_attr=bias_attr, layer_attr=layer_attr)
inputs = [fc1, lstm1]
for i in range(2, stacked_num + 1):
fc = paddle.layer.fc(input=inputs,
size=hid_dim,
act=linear,
param_attr=para_attr,
bias_attr=bias_attr)
lstm = paddle.layer.lstmemory(
input=fc,
reverse=(i % 2) == 0,
act=relu,
bias_attr=bias_attr,
layer_attr=layer_attr)
inputs = [fc, lstm]
fc_last = paddle.layer.pooling(input=inputs[0], pooling_type=paddle.pooling.Max())
lstm_last = paddle.layer.pooling(input=inputs[1], pooling_type=paddle.pooling.Max())
output = paddle.layer.fc(input=[fc_last, lstm_last],
size=class_dim,
act=paddle.activation.Softmax(),
bias_attr=bias_attr,
param_attr=para_attr)
if not is_predict:
lbl = paddle.layer.data("label", paddle.data_type.integer_value(2))
cost = paddle.layer.classification_cost(input=output, label=lbl)
return cost
else:
return output
```
网络的输入`stacked_num`表示的是LSTM的层数，需要是奇数，确保最高层LSTM正向。Paddle里面是通过一个fc和一个lstmemory来实现基于LSTM的循环神经网络。
## 训练模型
```python
if __name__ == '__main__':
# init
paddle.init(use_gpu=False)
```
启动paddle程序，use_gpu=False表示用CPU训练，如果系统支持GPU也可以修改成True使用GPU训练。
### 训练数据
使用Paddle提供的数据集`dataset.imdb`中的API来读取训练数据。
```python
print 'load dictionary...'
word_dict = paddle.dataset.imdb.word_dict()
dict_dim = len(word_dict)
class_dim = 2
```
加载数据字典，这里通过`word_dict()`API可以直接构造字典。`class_dim`是指样本类别数，该示例中样本只有正负两类。
```python
train_reader = paddle.batch(
paddle.reader.shuffle(
lambda: paddle.dataset.imdb.train(word_dict), buf_size=1000),
batch_size=100)
test_reader = paddle.batch(
lambda: paddle.dataset.imdb.test(word_dict),
batch_size=100)
```
这里，`dataset.imdb.train()`和`dataset.imdb.test()`分别是`dataset.imdb`中的训练数据和测试数据API。`train_reader`在训练时使用，意义是将读取的训练数据进行shuffle后，组成一个batch数据。同理，`test_reader`是在测试的时候使用，将读取的测试数据组成一个batch。
```python
feeding={'word': 0, 'label': 1}
```
`feeding`用来指定`train_reader`和`test_reader`返回的数据与模型配置中data_layer的对应关系。这里表示reader返回的第0列数据对应`word`层，第1列数据对应`label`层。
### 构造模型
```python
# Please choose the way to build the network
# by uncommenting the corresponding line.
cost = convolution_net(dict_dim, class_dim=class_dim)
# cost = stacked_lstm_net(dict_dim, class_dim=class_dim, stacked_num=3)
```
该示例中默认使用`convolution_net`网络，如果使用`stacked_lstm_net`网络，注释相应的行即可。其中cost是网络的优化目标，同时cost包含了整个网络的拓扑信息。
### 网络参数
```python
# create parameters
parameters = paddle.parameters.create(cost)
```
根据网络的拓扑构造网络参数。这里parameters是整个网络的参数集。
### 优化算法
```python
# create optimizer
adam_optimizer = paddle.optimizer.Adam(
learning_rate=2e-3,
regularization=paddle.optimizer.L2Regularization(rate=8e-4),
model_average=paddle.optimizer.ModelAverage(average_window=0.5))
```
Paddle中提供了一系列优化算法的API，这里使用Adam优化算法。
### 训练
可以通过`paddle.trainer.SGD`构造一个sgd trainer，并调用`trainer.train`来训练模型。另外，通过给train函数传递一个`event_handler`来获取每个batch和每个pass结束的状态。
```python
# End batch and end pass event handler
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "\nPass %d, Batch %d, Cost %f, %s" % (
event.pass_id, event.batch_id, event.cost, event.metrics)
else:
sys.stdout.write('.')
sys.stdout.flush()
if isinstance(event, paddle.event.EndPass):
result = trainer.test(reader=test_reader, feeding=feeding)
print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics)
```
比如，构造如下一个`event_handler`可以在每100个batch结束后输出cost和error；在每个pass结束后调用`trainer.test`计算一遍测试集并获得当前模型在测试集上的error。
```python
from paddle.v2.plot import Ploter
train_title = "Train cost"
cost_ploter = Ploter(train_title)
step = 0
def event_handler_plot(event):
global step
if isinstance(event, paddle.event.EndIteration):
cost_ploter.append(train_title, step, event.cost)
cost_ploter.plot()
step += 1
```
或者构造一个`event_handler_plot`画出cost曲线。
```python
# create trainer
trainer = paddle.trainer.SGD(cost=cost,
parameters=parameters,
update_equation=adam_optimizer)
trainer.train(
reader=train_reader,
event_handler=event_handler,
feeding=feeding,
num_passes=2)
```
程序运行之后的输出如下。
```text
Pass 0, Batch 0, Cost 0.693721, {'classification_error_evaluator': 0.5546875}
...................................................................................................
Pass 0, Batch 100, Cost 0.294321, {'classification_error_evaluator': 0.1015625}
...............................................................................................
Test with Pass 0, {'classification_error_evaluator': 0.11432000249624252}
```
## 应用模型
可以使用训练好的模型对电影评论进行分类，下面程序展示了如何使用`paddle.infer`接口进行推断。
```python
import numpy as np
# Movie Reviews, from imdb test
reviews = [
'Read the book, forget the movie!',
'This is a great movie.'
]
reviews = [c.split() for c in reviews]
UNK = word_dict['<unk>']
input = []
for c in reviews:
input.append([[word_dict.get(words, UNK) for words in c]])
# 0 stands for positive sample, 1 stands for negative sample
label = {0:'pos', 1:'neg'}
# Use the network used by trainer
out = convolution_net(dict_dim, class_dim=class_dim, is_predict=True)
# out = stacked_lstm_net(dict_dim, class_dim=class_dim, stacked_num=3, is_predict=True)
probs = paddle.infer(output_layer=out, parameters=parameters, input=input)
labs = np.argsort(-probs)
for idx, lab in enumerate(labs):
print idx, "predicting probability is", probs[idx], "label is", label[lab[0]]
```
## 总结
本章我们以情感分析为例，介绍了使用深度学习的方法进行端对端的短文本分类，并且使用PaddlePaddle完成了全部相关实验。同时，我们简要介绍了两种文本处理模型：卷积神经网络和循环神经网络。在后续的章节中我们会看到这两种基本的深度学习模型在其它任务上的应用。
## 参考文献
1. Kim Y. [Convolutional neural networks for sentence classification](http://arxiv.org/pdf/1408.5882)[J]. arXiv preprint arXiv:1408.5882, 2014.
2. Kalchbrenner N, Grefenstette E, Blunsom P. [A convolutional neural network for modelling sentences](http://arxiv.org/pdf/1404.2188.pdf?utm_medium=App.net&utm_source=PourOver)[J]. arXiv preprint arXiv:1404.2188, 2014.
3. Yann N. Dauphin, et al. [Language Modeling with Gated Convolutional Networks](https://arxiv.org/pdf/1612.08083v1.pdf)[J] arXiv preprint arXiv:1612.08083, 2016.
4. Siegelmann H T, Sontag E D. [On the computational power of neural nets](http://research.cs.queensu.ca/home/akl/cisc879/papers/SELECTED_PAPERS_FROM_VARIOUS_SOURCES/05070215382317071.pdf)[C]//Proceedings of the fifth annual workshop on Computational learning theory. ACM, 1992: 440-449.
5. Hochreiter S, Schmidhuber J. [Long short-term memory](http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf)[J]. Neural computation, 1997, 9(8): 1735-1780.
6. Bengio Y, Simard P, Frasconi P. [Learning long-term dependencies with gradient descent is difficult](http://www-dsi.ing.unifi.it/~paolo/ps/tnn-94-gradient.pdf)[J]. IEEE transactions on neural networks, 1994, 5(2): 157-166.
7. Graves A. [Generating sequences with recurrent neural networks](http://arxiv.org/pdf/1308.0850)[J]. arXiv preprint arXiv:1308.0850, 2013.
8. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](http://arxiv.org/pdf/1406.1078)[J]. arXiv preprint arXiv:1406.1078, 2014.
9. Zhou J, Xu W. [End-to-end learning of semantic role labeling using recurrent neural networks](http://www.aclweb.org/anthology/P/P15/P15-1109.pdf)[C]//Proceedings of the Annual Meeting of the Association for Computational Linguistics. 2015.
<br/>
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# Sentiment Analysis
The source codes of this section can be located at [book/understand_sentiment](https://github.com/PaddlePaddle/book/tree/develop/06.understand_sentiment). First-time users may refer to PaddlePaddle for [Installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book).
## Background
In natural language processing, sentiment analysis refers to determining the emotion expressed in a piece of text. The text can be a sentence, a paragraph, or a document. Emotion categorization can be binary -- positive/negative or happy/sad -- or in three classes -- positive/neutral/negative. Sentiment analysis is applicable in a wide range of services, such as e-commerce sites like Amazon and Taobao, hospitality services like Airbnb and hotels.com, and movie rating sites like Rotten Tomatoes and IMDB. It can be used to gauge from the reviews how the customers feel about the product. Table 1 illustrates an example of sentiment analysis in movie reviews:
| Movie Review | Category |
| -------- | ----- |
| Best movie of Xiaogang Feng in recent years!| Positive |
| Pretty bad. Feels like a tv-series from a local TV-channel | Negative |
| Politically correct version of Taken ... and boring as Heck| Negative|
|delightful, mesmerizing, and completely unexpected. The plot is nicely designed.|Positive|
<p align="center">Table 1 Sentiment Analysis in Movie Reviews</p>
In natural language processing, sentiment analysis can be categorized as a **Text Classification problem**, i.e., to categorize a piece of text to a specific class. It involves two related tasks: text representation and classification. Before the emergence of deep learning techniques, the mainstream methods for text representation include BOW (*bag of words*) and topic modeling, while the latter contain SVM (*support vector machine*) and LR (*logistic regression*).
The BOW model does not capture all the information in a piece of text, as it ignores syntax and grammar and just treats the text as a set of words. For example, “this movie is extremely bad“ and “boring, dull, and empty work” describe very similar semantic meaning, yet their BOW representations have with little similarity. Furthermore, “the movie is bad“ and “the movie is not bad“ have high similarity with BOW features, but they express completely opposite semantics.
This chapter introduces a deep learning model that handles these issues in BOW. Our model embeds texts into a low-dimensional space and takes word order into consideration. It is an end-to-end framework and it has large performance improvement over traditional methods \[[1](#Reference)\].
## Model Overview
The model we used in this chapter uses **Convolutional Neural Networks** (**CNNs**) and **Recurrent Neural Networks** (**RNNs**) with some specific extensions.
### Revisit to the Convolutional Neural Networks for Texts (CNN)
The convolutional neural network for texts is introduced in chapter [recommender_system](https://github.com/PaddlePaddle/book/tree/develop/05.recommender_system), here we make a brief overview.
CNN mainly contains convolution and pooling operation, with versatile combinations in various applications. We first apply the convolution operation: we apply the kernel in each window, extracting features. Convolving by the kernel at every window produces a feature map. Next, we apply *max pooling* over time to represent the whole sentence, which is the maximum element across the feature map. In real applications, we will apply multiple CNN kernels on the sentences. It can be implemented efficiently by concatenating the kernels together as a matrix. Also, we can use CNN kernels with different kernel size. Finally, concatenating the resulting features produces a fixed-length representation, which can be combined with a softmax to form the model for the sentiment analysis problem.
For short texts, the aforementioned CNN model can achieve very high accuracy \[[1](#Reference)\]. If we want to extract more abstract representations, we may apply a deeper CNN model \[[2](#Reference),[3](#Reference)\].
### Recurrent Neural Network (RNN)
RNN is an effective model for sequential data. In terms of computability, the RNN is Turing-complete \[[4](#Reference)\]. Since NLP is a classical problem on sequential data, the RNN, especially its variant LSTM\[[5](#Reference)\]), achieves state-of-the-art performance on various NLP tasks, such as language modeling, syntax parsing, POS-tagging, image captioning, dialog, machine translation, and so forth.
<p align="center">
<img src="image/rnn.png" width = "60%" align="center"/><br/>
Figure 1. An illustration of an unfolded RNN in time.
</p>
As shown in Figure 1, we unfold an RNN: at the $t$-th time step, the network takes two inputs: the $t$-th input vector $\vec{x_t}$ and the latent state from the last time-step $\vec{h_{t-1}}$. From those, it computes the latent state of the current step $\vec{h_t}$. This process is repeated until all inputs are consumed. Denoting the RNN as function $f$, it can be formulated as follows:
$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{h-1}}+\vec{b_h})$$
where $W_{xh}$ is the weight matrix to feed into the latent layer; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$ function.
In NLP, words are often represented as a one-hot vectors and then mapped to an embedding. The embedded feature goes through an RNN as input $x_t$ at every time step. Moreover, we can add other layers on top of RNN, such as a deep or stacked RNN. Finally, the last latent state may be used as a feature for sentence classification.
### Long-Short Term Memory (LSTM)
Training an RNN on long sequential data sometimes leads to the gradient vanishing or exploding\[[6](#)\]. To solve this problem Hochreiter S, Schmidhuber J. (1997) proposed **Long Short Term Memory** (LSTM)\[[5](#Reference)\]).
Compared to the structure of a simple RNN, an LSTM includes memory cell $c$, input gate $i$, forget gate $f$ and output gate $o$. These gates and memory cells dramatically improve the ability for the network to handle long sequences. We can formulate the **LSTM-RNN**, denoted as a function $F$, as follows：
$$ h_t=F(x_t,h_{t-1})$$
$F$ contains following formulations\[[7](#Reference)\]：
\begin{align}
i_t & = \sigma(W_{xi}x_t+W_{hi}h_{h-1}+W_{ci}c_{t-1}+b_i)\\\\
f_t & = \sigma(W_{xf}x_t+W_{hf}h_{h-1}+W_{cf}c_{t-1}+b_f)\\\\
c_t & = f_t\odot c_{t-1}+i_t\odot \tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
o_t & = \sigma(W_{xo}x_t+W_{ho}h_{h-1}+W_{co}c_{t}+b_o)\\\\
h_t & = o_t\odot \tanh(c_t)\\\\
\end{align}
In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate, respectively. $W$ and $b$ are model parameters, $\tanh$ is a hyperbolic tangent, and $\odot$ denotes an element-wise product operation. The input gate controls the magnitude of the new input into the memory cell $c$; the forget gate controls the memory propagated from the last time step; the output gate controls the magnitutde of the output. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 2:
<p align="center">
<img src="image/lstm_en.png" width = "65%" align="center"/><br/>
Figure 2. LSTM at time step $t$ [7].
</p>
LSTM enhances the ability of considering long-term reliance, with the help of memory cell and gate. Similar structures are also proposed in Gated Recurrent Unit (GRU)\[[8](Reference)\] with simpler design. **The structures are still similar to RNN, though with some modifications (As shown in Figure 2), i.e., latent status depends on input as well as the latent status of last time-step, and the process goes on recurrently until all input are consumed:**
$$ h_t=Recrurent(x_t,h_{t-1})$$
where $Recrurent$ is a simple RNN, GRU or LSTM.
### Stacked Bidirectional LSTM
For vanilla LSTM, $h_t$ contains input information from previous time-step $1..t-1$ context. We can also apply an RNN with reverse-direction to take successive context $t+1…n$ into consideration. Combining constructing deep RNN (deeper RNN can contain more abstract and higher level semantic), we can design structures with deep stacked bidirectional LSTM to model sequential data\[[9](#Reference)\].
As shown in Figure 3 (3-layer RNN), odd/even layers are forward/reverse LSTM. Higher layers of LSTM take lower-layers LSTM as input, and the top-layer LSTM produces a fixed length vector by max-pooling (this representation considers contexts from previous and successive words for higher-level abstractions). Finally, we concatenate the output to a softmax layer for classification.
<p align="center">
<img src="image/stacked_lstm_en.png" width=450><br/>
Figure 3. Stacked Bidirectional LSTM for NLP modeling.
</p>
## Dataset
We use [IMDB](http://ai.stanford.edu/%7Eamaas/data/sentiment/) dataset for sentiment analysis in this tutorial, which consists of 50,000 movie reviews split evenly into 25k train and 25k test sets. In the labeled train/test sets, a negative review has a score <= 4 out of 10, and a positive review has a score >= 7 out of 10.
`paddle.datasets` package encapsulates multiple public datasets, including `cifar`, `imdb`, `mnist`, `moivelens`, and `wmt14`, etc. There's no need for us to manually download and preprocess IMDB.
After issuing a command `python train.py`, training will start immediately. The details will be unpacked by the following sessions to see how it works.
## Model Structure
### Initialize PaddlePaddle
We must import and initialize PaddlePaddle (enable/disable GPU, set the number of trainers, etc).
```python
import sys
import paddle.v2 as paddle
# PaddlePaddle init
paddle.init(use_gpu=False, trainer_count=1)
```
As alluded to in section [Model Overview](#model-overview), here we provide the implementations of both Text CNN and Stacked-bidirectional LSTM models.
### Text Convolution Neural Network (Text CNN)
We create a neural network `convolution_net` as the following snippet code.
Note: `paddle.networks.sequence_conv_pool` includes both convolution and pooling layer operations.
```python
def convolution_net(input_dim, class_dim=2, emb_dim=128, hid_dim=128):
data = paddle.layer.data("word",
paddle.data_type.integer_value_sequence(input_dim))
emb = paddle.layer.embedding(input=data, size=emb_dim)
conv_3 = paddle.networks.sequence_conv_pool(
input=emb, context_len=3, hidden_size=hid_dim)
conv_4 = paddle.networks.sequence_conv_pool(
input=emb, context_len=4, hidden_size=hid_dim)
output = paddle.layer.fc(input=[conv_3, conv_4],
size=class_dim,
act=paddle.activation.Softmax())
lbl = paddle.layer.data("label", paddle.data_type.integer_value(2))
cost = paddle.layer.classification_cost(input=output, label=lbl)
return cost
```
1. Define input data and its dimension
Parameter `input_dim` denotes the dictionary size, and `class_dim` is the number of categories. In `convolution_net`, the input to the network is defined in `paddle.layer.data`.
1. Define Classifier
The above Text CNN network extracts high-level features and maps them to a vector of the same size as the categories. `paddle.activation.Softmax` function or classifier is then used for calculating the probability of the sentence belonging to each category.
1. Define Loss Function
In the context of supervised learning, labels of the training set are defined in `paddle.layer.data`, too. During training, cross-entropy is used as loss function in `paddle.layer.classification_cost` and as the output of the network; During testing, the outputs are the probabilities calculated in the classifier.
#### Stacked bidirectional LSTM
We create a neural network `stacked_lstm_net` as below.
```python
def stacked_lstm_net(input_dim,
class_dim=2,
emb_dim=128,
hid_dim=512,
stacked_num=3):
"""
A Wrapper for sentiment classification task.
This network uses bi-directional recurrent network,
consisting three LSTM layers. This configure is referred to
the paper as following url, but use fewer layrs.
http://www.aclweb.org/anthology/P15-1109
input_dim: here is word dictionary dimension.
class_dim: number of categories.
emb_dim: dimension of word embedding.
hid_dim: dimension of hidden layer.
stacked_num: number of stacked lstm-hidden layer.
"""
assert stacked_num % 2 == 1
layer_attr = paddle.attr.Extra(drop_rate=0.5)
fc_para_attr = paddle.attr.Param(learning_rate=1e-3)
lstm_para_attr = paddle.attr.Param(initial_std=0., learning_rate=1.)
para_attr = [fc_para_attr, lstm_para_attr]
bias_attr = paddle.attr.Param(initial_std=0., l2_rate=0.)
relu = paddle.activation.Relu()
linear = paddle.activation.Linear()
data = paddle.layer.data("word",
paddle.data_type.integer_value_sequence(input_dim))
emb = paddle.layer.embedding(input=data, size=emb_dim)
fc1 = paddle.layer.fc(input=emb,
size=hid_dim,
act=linear,
bias_attr=bias_attr)
lstm1 = paddle.layer.lstmemory(
input=fc1, act=relu, bias_attr=bias_attr, layer_attr=layer_attr)
inputs = [fc1, lstm1]
for i in range(2, stacked_num + 1):
fc = paddle.layer.fc(input=inputs,
size=hid_dim,
act=linear,
param_attr=para_attr,
bias_attr=bias_attr)
lstm = paddle.layer.lstmemory(
input=fc,
reverse=(i % 2) == 0,
act=relu,
bias_attr=bias_attr,
layer_attr=layer_attr)
inputs = [fc, lstm]
fc_last = paddle.layer.pooling(
input=inputs[0], pooling_type=paddle.pooling.Max())
lstm_last = paddle.layer.pooling(
input=inputs[1], pooling_type=paddle.pooling.Max())
output = paddle.layer.fc(input=[fc_last, lstm_last],
size=class_dim,
act=paddle.activation.Softmax(),
bias_attr=bias_attr,
param_attr=para_attr)
lbl = paddle.layer.data("label", paddle.data_type.integer_value(2))
cost = paddle.layer.classification_cost(input=output, label=lbl)
return cost
```
1. Define input data and its dimension
Parameter `input_dim` denotes the dictionary size, and `class_dim` is the number of categories. In `stacked_lstm_net`, the input to the network is defined in `paddle.layer.data`.
1. Define Classifier
The above stacked bidirectional LSTM network extracts high-level features and maps them to a vector of the same size as the categories. `paddle.activation.Softmax` function or classifier is then used for calculating the probability of the sentence belonging to each category.
1. Define Loss Function
In the context of supervised learning, labels of the training set are defined in `paddle.layer.data`, too. During training, cross-entropy is used as loss function in `paddle.layer.classification_cost` and as the output of the network; During testing, the outputs are the probabilities calculated in the classifier.
To reiterate, we can either invoke `convolution_net` or `stacked_lstm_net`.
```python
word_dict = paddle.dataset.imdb.word_dict()
dict_dim = len(word_dict)
class_dim = 2
# option 1
cost = convolution_net(dict_dim, class_dim=class_dim)
# option 2
# cost = stacked_lstm_net(dict_dim, class_dim=class_dim, stacked_num=3)
```
## Model Training
### Define Parameters
First, we create the model parameters according to the previous model configuration `cost`.
```python
# create parameters
parameters = paddle.parameters.create(cost)
```
### Create Trainer
Before jumping into creating a training module, algorithm setting is also necessary.
Here we specified `Adam` optimization algorithm via `paddle.optimizer`.
```python
# create optimizer
adam_optimizer = paddle.optimizer.Adam(
learning_rate=2e-3,
regularization=paddle.optimizer.L2Regularization(rate=8e-4),
model_average=paddle.optimizer.ModelAverage(average_window=0.5))
# create trainer
trainer = paddle.trainer.SGD(cost=cost,
parameters=parameters,
update_equation=adam_optimizer)
```
### Training
`paddle.dataset.imdb.train()` will yield records during each pass, after shuffling, a batch input is generated for training.
```python
train_reader = paddle.batch(
paddle.reader.shuffle(
lambda: paddle.dataset.imdb.train(word_dict), buf_size=1000),
batch_size=100)
test_reader = paddle.batch(
lambda: paddle.dataset.imdb.test(word_dict), batch_size=100)
```
`feeding` is devoted to specifying the correspondence between each yield record and `paddle.layer.data`. For instance, the first column of data generated by `paddle.dataset.imdb.train()` corresponds to `word` feature.
```python
feeding = {'word': 0, 'label': 1}
```
Callback function `event_handler` will be invoked to track training progress when a pre-defined event happens.
```python
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "\nPass %d, Batch %d, Cost %f, %s" % (
event.pass_id, event.batch_id, event.cost, event.metrics)
else:
sys.stdout.write('.')
sys.stdout.flush()
if isinstance(event, paddle.event.EndPass):
result = trainer.test(reader=test_reader, feeding=feeding)
print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics)
```
Finally, we can invoke `trainer.train` to start training:
```python
trainer.train(
reader=train_reader,
event_handler=event_handler,
feeding=feeding,
num_passes=10)
```
## Conclusion
In this chapter, we use sentiment analysis as an example to introduce applying deep learning models on end-to-end short text classification, as well as how to use PaddlePaddle to implement the model. Meanwhile, we briefly introduce two models for text processing: CNN and RNN. In following chapters, we will see how these models can be applied in other tasks.
## Reference
1. Kim Y. [Convolutional neural networks for sentence classification](http://arxiv.org/pdf/1408.5882)[J]. arXiv preprint arXiv:1408.5882, 2014.
2. Kalchbrenner N, Grefenstette E, Blunsom P. [A convolutional neural network for modelling sentences](http://arxiv.org/pdf/1404.2188.pdf?utm_medium=App.net&utm_source=PourOver)[J]. arXiv preprint arXiv:1404.2188, 2014.
3. Yann N. Dauphin, et al. [Language Modeling with Gated Convolutional Networks](https://arxiv.org/pdf/1612.08083v1.pdf)[J] arXiv preprint arXiv:1612.08083, 2016.
4. Siegelmann H T, Sontag E D. [On the computational power of neural nets](http://research.cs.queensu.ca/home/akl/cisc879/papers/SELECTED_PAPERS_FROM_VARIOUS_SOURCES/05070215382317071.pdf)[C]//Proceedings of the fifth annual workshop on Computational learning theory. ACM, 1992: 440-449.
5. Hochreiter S, Schmidhuber J. [Long short-term memory](http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf)[J]. Neural computation, 1997, 9(8): 1735-1780.
6. Bengio Y, Simard P, Frasconi P. [Learning long-term dependencies with gradient descent is difficult](http://www-dsi.ing.unifi.it/~paolo/ps/tnn-94-gradient.pdf)[J]. IEEE transactions on neural networks, 1994, 5(2): 157-166.
7. Graves A. [Generating sequences with recurrent neural networks](http://arxiv.org/pdf/1308.0850)[J]. arXiv preprint arXiv:1308.0850, 2013.
8. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](http://arxiv.org/pdf/1406.1078)[J]. arXiv preprint arXiv:1406.1078, 2014.
9. Zhou J, Xu W. [End-to-end learning of semantic role labeling using recurrent neural networks](http://www.aclweb.org/anthology/P/P15/P15-1109.pdf)[C]//Proceedings of the Annual Meeting of the Association for Computational Linguistics. 2015.
<br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.
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# Semantic Role Labeling # 语义角色标注
The source code of this chapter is live on [book/label_semantic_roles](https://github.com/PaddlePaddle/book/tree/develop/07.label_semantic_roles). 本教程源代码目录在[book/label_semantic_roles](https://github.com/PaddlePaddle/book/tree/develop/07.label_semantic_roles)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book). ## 背景介绍
## Background 自然语言分析技术大致分为三个层面：词法分析、句法分析和语义分析。语义角色标注是实现浅层语义分析的一种方式。在一个句子中，谓词是对主语的陈述或说明，指出“做什么”、“是什么”或“怎么样，代表了一个事件的核心，跟谓词搭配的名词称为论元。语义角色是指论元在动词所指事件中担任的角色。主要有：施事者（Agent）、受事者（Patient）、客体（Theme）、经验者（Experiencer）、受益者（Beneficiary）、工具（Instrument）、处所（Location）、目标（Goal）和来源（Source）等。
Natural language analysis techniques consist of lexical, syntactic, and semantic analysis. **Semantic Role Labeling (SRL)** is an instance of **Shallow Semantic Analysis**. 请看下面的例子，“遇到” 是谓词（Predicate，通常简写为“Pred”），“小明”是施事者（Agent），“小红”是受事者（Patient），“昨天” 是事件发生的时间（Time），“公园”是事情发生的地点（Location）。
In a sentence, a **predicate** states a property or a characterization of a *subject*, such as what it does and what it is like. The predicate represents the core of an event, whereas the words accompanying the predicate are **arguments**. A **semantic role** refers to the abstract role an argument of a predicate take on in the event, including *agent*, *patient*, *theme*, *experiencer*, *beneficiary*, *instrument*, *location*, *goal*, and *source*. $$\mbox{[小明]}_{\mbox{Agent}}\mbox{[昨天]}_{\mbox{Time}}\mbox{[晚上]}_\mbox{Time}\mbox{在[公园]}_{\mbox{Location}}\mbox{[遇到]}_{\mbox{Predicate}}\mbox{了[小红]}_{\mbox{Patient}}\mbox{。}$$
In the following example of a Chinese sentence, "to encounter" is the predicate (*pred*); "Ming" is the *agent*; "Hong" is the *patient*; "yesterday" and "evening" are the *time*; finally, "the park" is the *location*. 语义角色标注（Semantic Role Labeling，SRL）以句子的谓词为中心，不对句子所包含的语义信息进行深入分析，只分析句子中各成分与谓词之间的关系，即句子的谓词（Predicate）- 论元（Argument）结构，并用语义角色来描述这些结构关系，是许多自然语言理解任务（如信息抽取，篇章分析，深度问答等）的一个重要中间步骤。在研究中一般都假定谓词是给定的，所要做的就是找出给定谓词的各个论元和它们的语义角色。
$$\mbox{[小明 Ming]}_{\mbox{Agent}}\mbox{[昨天 yesterday]}_{\mbox{Time}}\mbox{[晚上 evening]}_\mbox{Time}\mbox{在[公园 a park]}_{\mbox{Location}}\mbox{[遇到 to encounter]}_{\mbox{Predicate}}\mbox{了[小红 Hong]}_{\mbox{Patient}}\mbox{。}$$ 传统的SRL系统大多建立在句法分析基础之上，通常包括5个流程：
Instead of analyzing the semantic information, **Semantic Role Labeling** (**SRL**) identifies the relation between the predicate and the other constituents surrounding it. The predicate-argument structures are labeled as specific semantic roles. A wide range of natural language understanding tasks, including *information extraction*, *discourse analysis*, and *deepQA*. Research usually assumes a predicate of a sentence to be specified; the only task is to identify its arguments and their semantic roles.
Conventional SRL systems mostly build on top of syntactic analysis, usually consisting of five steps:
1. Construct a syntax tree, as shown in Fig. 1
2. Identity the candidate arguments of the given predicate on the tree.
3. Prune the most unlikely candidate arguments.
4. Identify the real arguments, often by a binary classifier.
5. Multi-classify on results from step 4 to label the semantic roles. Steps 2 and 3 usually introduce hand-designed features based on syntactic analysis (step 1).
1. 构建一棵句法分析树，例如，图1是对上面例子进行依存句法分析得到的一棵句法树。
2. 从句法树上识别出给定谓词的候选论元。
3. 候选论元剪除；一个句子中的候选论元可能很多，候选论元剪除就是从大量的候选项中剪除那些最不可能成为论元的候选项。
4. 论元识别：这个过程是从上一步剪除之后的候选中判断哪些是真正的论元，通常当做一个二分类问题来解决。
5. 对第4步的结果，通过多分类得到论元的语义角色标签。可以看到，句法分析是基础，并且后续步骤常常会构造的一些人工特征，这些特征往往也来自句法分析。
<div align="center"> <div align="center">
<img src="image/dependency_parsing_en.png" width = "80%" align=center /><br> <img src="image/dependency_parsing.png" width = "80%" align=center /><br>
Fig 1. Syntax tree 图1. 依存句法分析句法树示例
</div> </div>
然而，完全句法分析需要确定句子所包含的全部句法信息，并确定句子各成分之间的关系，是一个非常困难的任务，目前技术下的句法分析准确率并不高，句法分析的细微错误都会导致SRL的错误。为了降低问题的复杂度，同时获得一定的句法结构信息，“浅层句法分析”的思想应运而生。浅层句法分析也称为部分句法分析（partial parsing）或语块划分（chunking）。和完全句法分析得到一颗完整的句法树不同，浅层句法分析只需要识别句子中某些结构相对简单的独立成分，例如：动词短语，这些被识别出来的结构称为语块。为了回避 “无法获得准确率较高的句法树” 所带来的困难，一些研究\[[1](#参考文献)\]也提出了基于语块（chunk）的SRL方法。基于语块的SRL方法将SRL作为一个序列标注问题来解决。序列标注任务一般都会采用BIO表示方式来定义序列标注的标签集，我们先来介绍这种表示方法。在BIO表示法中，B代表语块的开始，I代表语块的中间，O代表语块结束。通过B、I、O 三种标记将不同的语块赋予不同的标签，例如：对于一个角色为A的论元，将它所包含的第一个语块赋予标签B-A，将它所包含的其它语块赋予标签I-A，不属于任何论元的语块赋予标签O。
However, a complete syntactic analysis requires identifying the relation among all constituents. Thus, the accuracy of SRL is sensitive to the preciseness of the syntactic analysis, making SRL challenging. To reduce its complexity and obtain some information on the syntactic structures, we often use *shallow syntactic analysis* a.k.a. partial parsing or chunking. Unlike complete syntactic analysis, which requires the construction of the complete parsing tree, *Shallow Syntactic Analysis* only requires identifying some independent constituents with relatively simple structures, such as verb phrases (chunk). To avoid difficulties in constructing a syntax tree with high accuracy, some work\[[1](#Reference)\] proposed semantic chunking-based SRL methods, which reduces SRL into a sequence tagging problem. Sequence tagging tasks classify syntactic chunks using **BIO representation**. For syntactic chunks forming role A, its first chunk receives the B-A tag (Begin) and the remaining ones receive the tag I-A (Inside); in the end, the chunks left out receive the tag O. 我们继续以上面的这句话为例，图1展示了BIO表示方法。
The BIO representation of above example is shown in Fig.1.
<div align="center"> <div align="center">
<img src="image/bio_example_en.png" width = "90%" align=center /><br> <img src="image/bio_example.png" width = "90%" align=center /><br>
Fig 2. BIO representation 图2. BIO标注方法示例
</div> </div>
This example illustrates the simplicity of sequence tagging, since 从上面的例子可以看到，根据序列标注结果可以直接得到论元的语义角色标注结果，是一个相对简单的过程。这种简单性体现在：（1）依赖浅层句法分析，降低了句法分析的要求和难度；（2）没有了候选论元剪除这一步骤；（3）论元的识别和论元标注是同时实现的。这种一体化处理论元识别和论元标注的方法，简化了流程，降低了错误累积的风险，往往能够取得更好的结果。
1. It only relies on shallow syntactic analysis, reduces the precision requirement of syntactic analysis;
2. Pruning the candidate arguments is no longer necessary;
3. Arguments are identified and tagged at the same time. Simplifying the workflow reduces the risk of accumulating errors; oftentimes, methods that unify multiple steps boost performance.
In this tutorial, our SRL system is built as an end-to-end system via a neural network. The system takes only text sequences as input, without using any syntactic parsing results or complex hand-designed features. The public dataset [CoNLL-2004 and CoNLL-2005 Shared Tasks](http://www.cs.upc.edu/~srlconll/) is used for the following task: given a sentence with predicates marked, identify the corresponding arguments and their semantic roles through sequence tagging.
## Model 与基于语块的SRL方法类似，在本教程中我们也将SRL看作一个序列标注问题，不同的是，我们只依赖输入文本序列，不依赖任何额外的语法解析结果或是复杂的人造特征，利用深度神经网络构建一个端到端学习的SRL系统。我们以[CoNLL-2004 and CoNLL-2005 Shared Tasks](http://www.cs.upc.edu/~srlconll/)任务中SRL任务的公开数据集为例，实践下面的任务：给定一句话和这句话里的一个谓词，通过序列标注的方式，从句子中找到谓词对应的论元，同时标注它们的语义角色。
**Recurrent Neural Networks** (*RNN*) are important tools for sequence modeling and have been successfully used in some natural language processing tasks. Unlike feed-forward neural networks, RNNs can model the dependencies between elements of sequences. As a variant of RNNs', LSTMs aim model long-term dependency in long sequences. We have introduced this in [understand_sentiment](https://github.com/PaddlePaddle/book/tree/develop/05.understand_sentiment). In this chapter, we continue to use LSTMs to solve SRL problems. ## 模型概览
### Stacked Recurrent Neural Network 循环神经网络（Recurrent Neural Network）是一种对序列建模的重要模型，在自然语言处理任务中有着广泛地应用。不同于前馈神经网络（Feed-forward Neural Network），RNN能够处理输入之间前后关联的问题。LSTM是RNN的一种重要变种，常用来学习长序列中蕴含的长程依赖关系，我们在[情感分析](https://github.com/PaddlePaddle/book/tree/develop/05.understand_sentiment)一篇中已经介绍过，这一篇中我们依然利用LSTM来解决SRL问题。
*Deep Neural Networks* can extract hierarchical representations. The higher layers can form relatively abstract/complex representations, based on primitive features discovered through the lower layers. Unfolding LSTMs through time results in a deep feed-forward neural network. This is because any computational path between the input at time $k < t$ to the output at time $t$ crosses several nonlinear layers. On the other hand, due to parameter sharing over time, LSTMs are also *shallow*; that is, the computation carried out at each time-step is just a linear transformation. Deep LSTM networks are typically constructed by stacking multiple LSTM layers on top of each other and taking the output from lower LSTM layer at time $t$ as the input of upper LSTM layer at time $t$. Deep, hierarchical neural networks can be efficient at representing some functions and modeling varying-length dependencies\[[2](#Reference)\]. ### 栈式循环神经网络（Stacked Recurrent Neural Network）
深层网络有助于形成层次化特征，网络上层在下层已经学习到的初级特征基础上，形成更复杂的高级特征。尽管LSTM沿时间轴展开后等价于一个非常“深”的前馈网络，但由于LSTM各个时间步参数共享，$t-1$时刻状态到$t$时刻的映射，始终只经过了一次非线性映射，也就是说单层LSTM对状态转移的建模是 “浅” 的。堆叠多个LSTM单元，令前一个LSTM$t$时刻的输出，成为下一个LSTM单元$t$时刻的输入，帮助我们构建起一个深层网络，我们把它称为第一个版本的栈式循环神经网络。深层网络提高了模型拟合复杂模式的能力，能够更好地建模跨不同时间步的模式\[[2](#参考文献)\]。
However, in a deep LSTM network, any gradient propagated back in depth needs to traverse a large number of nonlinear steps. As a result, while LSTMs of 4 layers can be trained properly, those with 4-8 have much worse performance. Conventional LSTMs prevent back-propagated errors from vanishing or exploding by introducing shortcut connections to skip the intermediate nonlinear layers. Therefore, deep LSTMs can consider shortcut connections in depth as well. 然而，训练一个深层LSTM网络并非易事。纵向堆叠多个LSTM单元可能遇到梯度在纵向深度上传播受阻的问题。通常，堆叠4层LSTM单元可以正常训练，当层数达到4~8层时，会出现性能衰减，这时必须考虑一些新的结构以保证梯度纵向顺畅传播，这是训练深层LSTM网络必须解决的问题。我们可以借鉴LSTM解决 “梯度消失梯度爆炸” 问题的智慧之一：在记忆单元（Memory Cell）这条信息传播的路线上没有非线性映射，当梯度反向传播时既不会衰减、也不会爆炸。因此，深层LSTM模型也可以在纵向上添加一条保证梯度顺畅传播的路径。
一个LSTM单元完成的运算可以被分为三部分：（1）输入到隐层的映射（input-to-hidden） ：每个时间步输入信息$x$会首先经过一个矩阵映射，再作为遗忘门，输入门，记忆单元，输出门的输入，注意，这一次映射没有引入非线性激活；（2）隐层到隐层的映射（hidden-to-hidden）：这一步是LSTM计算的主体，包括遗忘门，输入门，记忆单元更新，输出门的计算；（3）隐层到输出的映射（hidden-to-output）：通常是简单的对隐层向量进行激活。我们在第一个版本的栈式网络的基础上，加入一条新的路径：除上一层LSTM输出之外，将前层LSTM的输入到隐层的映射作为的一个新的输入，同时加入一个线性映射去学习一个新的变换。
A single LSTM cell has three operations: 图3是最终得到的栈式循环神经网络结构示意图。
1. input-to-hidden: map input $x$ to the input of the forget gates, input gates, memory cells and output gates by linear transformation (i.e., matrix mapping);
2. hidden-to-hidden: calculate forget gates, input gates, output gates and update memory cell, this is the main part of LSTMs;
3. hidden-to-output: this part typically involves an activation operation on hidden states.
Based on the stacked LSTMs, we add shortcut connections: take the input-to-hidden from the previous layer as a new input and learn another linear transformation.
Fig.3 illustrates the final stacked recurrent neural networks.
<p align="center"> <p align="center">
<img src="./image/stacked_lstm_en.png" width = "40%" align=center><br> <img src="./image/stacked_lstm.png" width = "40%" align=center><br>
Fig 3. Stacked Recurrent Neural Networks 图3. 基于LSTM的栈式循环神经网络结构示意图
</p> </p>
### Bidirectional Recurrent Neural Network ### 双向循环神经网络（Bidirectional Recurrent Neural Network）
While LSTMs can summarize the history -- all the previous input seen up until now -- they can not see the future. Because most NLP (natural language processing) tasks provide the entirety of sentences, sequential learning can benefit from having the future encoded as well as the history. 在LSTM中，$t$时刻的隐藏层向量编码了到$t$时刻为止所有输入的信息，但$t$时刻的LSTM可以看到历史，却无法看到未来。在绝大多数自然语言处理任务中，我们几乎总是能拿到整个句子。这种情况下，如果能够像获取历史信息一样，得到未来的信息，对序列学习任务会有很大的帮助。
To address, we can design a bidirectional recurrent neural network by making a minor modification. A higher LSTM layer can process the sequence in reversed direction with regards to its immediate lower LSTM layer, i.e., deep LSTM layers take turns to train on input sequences from left-to-right and right-to-left. Therefore, LSTM layers at time-step $t$ can see both histories and the future, starting from the second layer. Fig. 4 illustrates the bidirectional recurrent neural networks.
为了克服这一缺陷，我们可以设计一种双向循环网络单元，它的思想简单且直接：对上一节的栈式循环神经网络进行一个小小的修改，堆叠多个LSTM单元，让每一层LSTM单元分别以：正向、反向、正向 …… 的顺序学习上一层的输出序列。于是，从第2层开始，$t$时刻我们的LSTM单元便总是可以看到历史和未来的信息。图4是基于LSTM的双向循环神经网络结构示意图。
<p align="center"> <p align="center">
<img src="./image/bidirectional_stacked_lstm_en.png" width = "60%" align=center><br> <img src="./image/bidirectional_stacked_lstm.png" width = "60%" align=center><br>
Fig 4. Bidirectional LSTMs 图4. 基于LSTM的双向循环神经网络结构示意图
</p> </p>
Note that, this bidirectional RNNs is different with the one proposed by Bengio et al. in machine translation tasks \[[3](#Reference), [4](#Reference)\]. We will introduce another bidirectional RNNs in the following tasks [machine translation](https://github.com/PaddlePaddle/book/blob/develop/machine_translation/README.en.md) 需要说明的是，这种双向RNN结构和Bengio等人在机器翻译任务中使用的双向RNN结构\[[3](#参考文献), [4](#参考文献)\] 并不相同，我们会在后续[机器翻译](https://github.com/PaddlePaddle/book/blob/develop/machine_translation/README.md)任务中，介绍另一种双向循环神经网络。
### Conditional Random Field (CRF)
Typically, a neural network's lower layers learn representations while its very top layer learns the final task. These principles can guide our problem-solving approaches. In SRL tasks, a **Conditional Random Field** (*CRF*) is built on top of the network in order to perform the final prediction to tag sequences. It takes as input the representations provided by the last LSTM layer. ### 条件随机场 (Conditional Random Field)
使用神经网络模型解决问题的思路通常是：前层网络学习输入的特征表示，网络的最后一层在特征基础上完成最终的任务。在SRL任务中，深层LSTM网络学习输入的特征表示，条件随机场（Conditional Random Filed， CRF）在特征的基础上完成序列标注，处于整个网络的末端。
The CRF is an undirected probabilistic graph with nodes denoting random variables and edges denoting dependencies between these variables. In essence, CRFs learn the conditional probability $P(Y|X)$, where $X = (x_1, x_2, ... , x_n)$ are sequences of input and $Y = (y_1, y_2, ... , y_n)$ are label sequences; to decode, simply search through $Y$ for a sequence that maximizes the conditional probability $P(Y|X)$, i.e., $Y^* = \mbox{arg max}_{Y} P(Y | X)$。 CRF是一种概率化结构模型，可以看作是一个概率无向图模型，结点表示随机变量，边表示随机变量之间的概率依赖关系。简单来讲，CRF学习条件概率$P(X|Y)$，其中 $X = (x_1, x_2, ... , x_n)$ 是输入序列，$Y = (y_1, y_2, ... , y_n)$ 是标记序列；解码过程是给定 $X$序列求解令$P(Y|X)$最大的$Y$序列，即$Y^* = \mbox{arg max}_{Y} P(Y | X)$。
Sequence tagging tasks do not assume a lot of conditional independence, because they are only concerned with the input and the output being linear sequences. Thus, the graph model of sequence tagging tasks is usually a simple chain or line, which results in a **Linear-Chain Conditional Random Field**, shown in Fig.5. 序列标注任务只需要考虑输入和输出都是一个线性序列，并且由于我们只是将输入序列作为条件，不做任何条件独立假设，因此输入序列的元素之间并不存在图结构。综上，在序列标注任务中使用的是如图5所示的定义在链式图上的CRF，称之为线性链条件随机场（Linear Chain Conditional Random Field）。
<p align="center"> <p align="center">
<img src="./image/linear_chain_crf.png" width = "35%" align=center><br> <img src="./image/linear_chain_crf.png" width = "35%" align=center><br>
Fig 5. Linear Chain Conditional Random Field used in SRL tasks 图5. 序列标注任务中使用的线性链条件随机场
</p> </p>
By the fundamental theorem of random fields \[[5](#Reference)\], the joint distribution over the label sequence $Y$ given $X$ has the form: 根据线性链条件随机场上的因子分解定理\[[5](#参考文献)\]，在给定观测序列$X$时，一个特定标记序列$Y$的概率可以定义为：
$$p(Y | X) = \frac{1}{Z(X)} \text{exp}\left(\sum_{i=1}^{n}\left(\sum_{j}\lambda_{j}t_{j} (y_{i - 1}, y_{i}, X, i) + \sum_{k} \mu_k s_k (y_i, X, i)\right)\right)$$ $$p(Y | X) = \frac{1}{Z(X)} \text{exp}\left(\sum_{i=1}^{n}\left(\sum_{j}\lambda_{j}t_{j} (y_{i - 1}, y_{i}, X, i) + \sum_{k} \mu_k s_k (y_i, X, i)\right)\right)$$
其中$Z(X)$是归一化因子，$t_j$ 是定义在边上的特征函数，依赖于当前和前一个位置，称为转移特征，表示对于输入序列$X$及其标注序列在 $i$及$i - 1$位置上标记的转移概率。$s_k$是定义在结点上的特征函数，称为状态特征，依赖于当前位置，表示对于观察序列$X$及其$i$位置的标记概率。$\lambda_j$ 和 $\mu_k$ 分别是转移特征函数和状态特征函数对应的权值。实际上，$t$和$s$可以用相同的数学形式表示，再对转移特征和状态特在各个位置$i$求和有：$f_{k}(Y, X) = \sum_{i=1}^{n}f_k({y_{i - 1}, y_i, X, i})$，把$f$统称为特征函数，于是$P(Y|X)$可表示为：
where, $Z(X)$ is normalization constant, ${t_j}$ represents the feature functions defined on edges called the *transition feature*, which denotes the transition probabilities from $y_{i-1}$ to $y_i$ given input sequence $X$. ${s_k}$ represents the feature function defined on nodes, called the state feature, denoting the probability of $y_i$ given input sequence $X$. In addition, $\lambda_j$ and $\mu_k$ are weights corresponding to $t_j$ and $s_k$. Alternatively, $t$ and $s$ can be written in the same form that depends on $y_{i - 1}$, $y_i$, $X$, and $i$. Taking its summation over all nodes $i$, we have: $f_{k}(Y, X) = \sum_{i=1}^{n}f_k({y_{i - 1}, y_i, X, i})$, which defines the *feature function* $f$. Thus, $P(Y|X)$ can be written as:
$$p(Y|X, W) = \frac{1}{Z(X)}\text{exp}\sum_{k}\omega_{k}f_{k}(Y, X)$$ $$p(Y|X, W) = \frac{1}{Z(X)}\text{exp}\sum_{k}\omega_{k}f_{k}(Y, X)$$
where $\omega$ are the weights to the feature function that the CRF learns. While training, given input sequences and label sequences $D = \left[(X_1, Y_1), (X_2 , Y_2) , ... , (X_N, Y_N)\right]$, by maximum likelihood estimation (**MLE**), we construct the following objective function: $\omega$是特征函数对应的权值，是CRF模型要学习的参数。训练时，对于给定的输入序列和对应的标记序列集合$D = \left[(X_1, Y_1), (X_2 , Y_2) , ... , (X_N, Y_N)\right]$ ，通过正则化的极大似然估计，求解如下优化目标：
$$\DeclareMathOperator*{\argmax}{arg\,max} L(\lambda, D) = - \text{log}\left(\prod_{m=1}^{N}p(Y_m|X_m, W)\right) + C \frac{1}{2}\lVert W\rVert^{2}$$ $$\DeclareMathOperator*{\argmax}{arg\,max} L(\lambda, D) = - \text{log}\left(\prod_{m=1}^{N}p(Y_m|X_m, W)\right) + C \frac{1}{2}\lVert W\rVert^{2}$$
这个优化目标可以通过反向传播算法和整个神经网络一起求解。解码时，对于给定的输入序列$X$，通过解码算法（通常有：维特比算法、Beam Search）求令出条件概率$\bar{P}(Y|X)$最大的输出序列 $\bar{Y}$。
This objective function can be solved via back-propagation in an end-to-end manner. While decoding, given input sequences $X$, search for sequence $\bar{Y}$ to maximize the conditional probability $\bar{P}(Y|X)$ via decoding methods (such as *Viterbi*, or [Beam Search Algorithm](https://github.com/PaddlePaddle/book/blob/develop/07.machine_translation/README.en.md#Beam%20Search%20Algorithm)). ### 深度双向LSTM（DB-LSTM）SRL模型
### Deep Bidirectional LSTM (DB-LSTM) SRL model
Given predicates and a sentence, SRL tasks aim to identify arguments of the given predicate and their semantic roles. If a sequence has $n$ predicates, we will process this sequence $n$ times. Here is the breakdown of a straight-forward model:
1. Construct inputs; 在SRL任务中，输入是 “谓词” 和 “一句话”，目标是从这句话中找到谓词的论元，并标注论元的语义角色。如果一个句子含有$n$个谓词，这个句子会被处理$n$次。一个最为直接的模型是下面这样：
- input 1: predicate, input 2: sentence
- expand input 1 into a sequence of the same length with input 2's sentence, using one-hot representation;
2. Convert the one-hot sequences from step 1 to vector sequences via a word embedding's lookup table;
3. Learn the representation of input sequences by taking vector sequences from step 2 as inputs;
4. Take the representation from step 3 as input, label sequence as supervisory signal, and realize sequence tagging tasks.
Here, we propose some improvements by introducing two simple but effective features: 1. 构造输入；
- 输入1是谓词，输入2是句子
- 将输入1扩展成和输入2一样长的序列，用one-hot方式表示；
2. one-hot方式的谓词序列和句子序列通过词表，转换为实向量表示的词向量序列；
3. 将步骤2中的2个词向量序列作为双向LSTM的输入，学习输入序列的特征表示；
4. CRF以步骤3中模型学习到的特征为输入，以标记序列为监督信号，实现序列标注；
- predicate context (**ctx-p**): A single predicate word may not describe all the predicate information, especially when the same words appear multiple times in a sentence. With the expanded context, the ambiguity can be largely eliminated. Thus, we extract $n$ words before and after predicate to construct a window chunk. 大家可以尝试上面这种方法。这里，我们提出一些改进，引入两个简单但对提高系统性能非常有效的特征：
- region mark ($m_r$): The binary marker on a word, $m_r$, takes the value of $1$ when the word is in the predicate context region, and $0$ if not. - 谓词上下文：上面的方法中，只用到了谓词的词向量表达谓词相关的所有信息，这种方法始终是非常弱的，特别是如果谓词在句子中出现多次，有可能引起一定的歧义。从经验出发，谓词前后若干个词的一个小片段，能够提供更丰富的信息，帮助消解歧义。于是，我们把这样的经验也添加到模型中，为每个谓词同时抽取一个“谓词上下文” 片段，也就是从这个谓词前后各取$n$个词构成的一个窗口片段；
- 谓词上下文区域标记：为句子中的每一个词引入一个0-1二值变量，表示它们是否在“谓词上下文”片段中；
After these modifications, the model is as follows, as illustrated in Figure 6: 修改后的模型如下（图6是一个深度为4的模型结构示意图）：
1. Construct inputs
- Input 1: word sequence. Input 2: predicate. Input 3: predicate context, extract $n$ words before and after predicate. Input 4: region mark sequence, where an entry is 1 if word is located in the predicate context region, 0 otherwise.
- expand input 2~3 into sequences with the same length with input 1
2. Convert input 1~4 to vector sequences via word embedding lookup tables; While input 1 and 3 shares the same lookup table, input 2 and 4 have separate lookup tables.
3. Take the four vector sequences from step 2 as inputs to bidirectional LSTMs; Train the LSTMs to update representations.
4. Take the representation from step 3 as input to CRF, label sequence as supervisory signal, and complete sequence tagging tasks.
1. 构造输入
- 输入1是句子序列，输入2是谓词序列，输入3是谓词上下文，从句子中抽取这个谓词前后各$n$个词，构成谓词上下文，用one-hot方式表示，输入4是谓词上下文区域标记，标记了句子中每一个词是否在谓词上下文中；
- 将输入2~3均扩展为和输入1一样长的序列；
2. 输入1~4均通过词表取词向量转换为实向量表示的词向量序列；其中输入1、3共享同一个词表，输入2和4各自独有词表；
3. 第2步的4个词向量序列作为双向LSTM模型的输入；LSTM模型学习输入序列的特征表示，得到新的特性表示序列；
4. CRF以第3步中LSTM学习到的特征为输入，以标记序列为监督信号，完成序列标注；
<div align="center"> <div align="center">
<img src="image/db_lstm_network_en.png" width = "60%" align=center /><br> <img src="image/db_lstm_network.png" width = "60%" align=center /><br>
Fig 6. DB-LSTM for SRL tasks 图6. SRL任务上的深层双向LSTM模型
</div> </div>
## Data Preparation
In the tutorial, we use [CoNLL 2005](http://www.cs.upc.edu/~srlconll/) SRL task open dataset as an example. Note that the training set and development set of the CoNLL 2005 SRL task are not free to download after the competition. Currently, only the test set can be obtained, including 23 sections of the Wall Street Journal and three sections of the Brown corpus. In this tutorial, we use the WSJ corpus as the training dataset to explain the model. However, since the training set is small, for a usable neural network SRL system, please consider paying for the full corpus. ## 数据介绍
在此教程中，我们选用[CoNLL 2005](http://www.cs.upc.edu/~srlconll/)SRL任务开放出的数据集作为示例。需要特别说明的是，CoNLL 2005 SRL任务的训练数集和开发集在比赛之后并非免费进行公开，目前，能够获取到的只有测试集，包括Wall Street Journal的23节和Brown语料集中的3节。在本教程中，我们以测试集中的WSJ数据为训练集来讲解模型。但是，由于测试集中样本的数量远远不够，如果希望训练一个可用的神经网络SRL系统，请考虑付费获取全量数据。
The original data includes a variety of information such as POS tagging, naming entity recognition, syntax tree, etc. In this tutorial, we only use the data under `test.wsj/words/` (text sequence) and `test.wsj/props/` (label results). The data directory used in this tutorial is as follows: 原始数据中同时包括了词性标注、命名实体识别、语法解析树等多种信息。本教程中，我们使用test.wsj文件夹中的数据进行训练和测试，并只会用到words文件夹（文本序列）和props文件夹（标注结果）下的数据。本教程使用的数据目录如下：
```text ```text
conll05st-release/ conll05st-release/
...@@ -207,26 +183,27 @@ conll05st-release/ ...@@ -207,26 +183,27 @@ conll05st-release/
└── words # 输入文本序列 └── words # 输入文本序列
``` ```
The annotation information is derived from the results of Penn TreeBank\[[7](#references)\] and PropBank \[[8](# references)\]. The labeling of the PropBank is different from the labeling methods mentioned before, but shares with it the same underlying principle. For descriptions of the labeling, please refer to the paper \[[9](#references)\]. 标注信息源自Penn TreeBank\[[7](#参考文献)\]和PropBank\[[8](#参考文献)\]的标注结果。PropBank标注结果的标签和我们在文章一开始示例中使用的标注结果标签不同，但原理是相同的，关于标注结果标签含义的说明，请参考论文\[[9](#参考文献)\]。
原始数据需要进行数据预处理才能被PaddlePaddle处理，预处理包括下面几个步骤:
The raw data needs to be preprocessed into formats that PaddlePaddle can handle. The preprocessing consists of the following steps: 1. 将文本序列和标记序列其合并到一条记录中；
2. 一个句子如果含有$n$个谓词，这个句子会被处理$n$次，变成$n$条独立的训练样本，每个样本一个不同的谓词；
3. 抽取谓词上下文和构造谓词上下文区域标记；
4. 构造以BIO法表示的标记；
5. 依据词典获取词对应的整数索引。
1. Merge the text sequence and the tag sequence into the same record;
2. If a sentence contains $n$ predicates, the sentence will be processed $n$ times into $n$ separate training samples, each sample with a different predicate;
3. Extract the predicate context and construct the predicate context region marker;
4. Construct the markings in BIO format;
5. Obtain the integer index corresponding to the word according to the dictionary.
```python ```python
# import paddle.v2.dataset.conll05 as conll05 # import paddle.v2.dataset.conll05 as conll05
# conll05.corpus_reader does step 1 and 2 as mentioned above. # conll05.corpus_reader函数完成上面第1步和第2步.
# conll05.reader_creator does step 3 to 5. # conll05.reader_creator函数完成上面第3步到第5步.
# conll05.test gets preprocessed training instances. # conll05.test函数可以获取处理之后的每条样本来供PaddlePaddle训练.
``` ```
After preprocessing, a training sample contains nine features, namely: word sequence, predicate, predicate context (5 columns), region mark sequence, label sequence. The following table is an example of a training sample. 预处理完成之后一条训练样本包含9个特征，分别是：句子序列、谓词、谓词上下文（占 5 列）、谓词上下区域标志、标注序列。下表是一条训练样本的示例。
| word sequence | predicate | predicate context（5 columns） | region mark sequence | label sequence| | 句子序列 | 谓词 | 谓词上下文（窗口 = 5） | 谓词上下文区域标记 | 标注序列 |
|---|---|---|---|---| |---|---|---|---|---|
| A | set | n't been set . × | 0 | B-A1 | | A | set | n't been set . × | 0 | B-A1 |
| record | set | n't been set . × | 0 | I-A1 | | record | set | n't been set . × | 0 | I-A1 |
...@@ -237,18 +214,19 @@ After preprocessing, a training sample contains nine features, namely: word sequ ...@@ -237,18 +214,19 @@ After preprocessing, a training sample contains nine features, namely: word sequ
| set | set | n't been set . × | 1 | B-V | | set | set | n't been set . × | 1 | B-V |
| . | set | n't been set . × | 1 | O | | . | set | n't been set . × | 1 | O |
In addition to the data, we provide following resources:
| filename | explanation | 除数据之外，我们同时提供了以下资源：
| 文件名称 | 说明 |
|---|---| |---|---|
| word_dict | dictionary of input sentences, total 44068 words | | word_dict | 输入句子的词典，共计44068个词 |
| label_dict | dictionary of labels, total 106 labels | | label_dict | 标记的词典，共计106个标记 |
| predicate_dict | predicate dictionary, total 3162 predicates | | predicate_dict | 谓词的词典，共计3162个词 |
| emb | a pre-trained word vector lookup table, 32-dimentional | | emb | 一个训练好的词表，32维 |
We trained a language model on the English Wikipedia to get a word vector lookup table used to initialize the SRL model. While training the SRL model, the word vector lookup table is no longer updated. To learn more about the language model and the word vector lookup table, please refer to the tutorial [word vector](https://github.com/PaddlePaddle/book/blob/develop/04.word2vec/README.md). There are 995,000,000 tokens in the training corpus, and the dictionary size is 4900,000 words. In the CoNLL 2005 training corpus, 5% of the words are not in the 4900,000 words, and we see them all as unknown words, represented by `<unk>`. 我们在英文维基百科上训练语言模型得到了一份词向量用来初始化SRL模型。在SRL模型训练过程中，词向量不再被更新。关于语言模型和词向量可以参考[词向量](https://github.com/PaddlePaddle/book/blob/develop/04.word2vec/README.md) 这篇教程。我们训练语言模型的语料共有995,000,000个token，词典大小控制为4900,000词。CoNLL 2005训练语料中有5%的词不在这4900,000个词中，我们将它们全部看作未登录词，用`<unk>`表示。
Here we fetch the dictionary, and print its size: 获取词典，打印词典大小：
```python ```python
import math import math
...@@ -270,51 +248,50 @@ print label_dict_len ...@@ -270,51 +248,50 @@ print label_dict_len
print pred_len print pred_len
``` ```
## Model Configuration ## 模型配置说明
- Define input data dimensions and model hyperparameters. - 定义输入数据维度及模型超参数。
```python ```python
mark_dict_len = 2 # value range of region mark. Region mark is either 0 or 1, so range is 2 mark_dict_len = 2 # 谓上下文区域标志的维度，是一个0-1 2值特征，因此维度为2
word_dim = 32 # word vector dimension word_dim = 32 # 词向量维度
mark_dim = 5 # adjacent dimension mark_dim = 5 # 谓词上下文区域通过词表被映射为一个实向量，这个是相邻的维度
hidden_dim = 512 # the dimension of LSTM hidden layer vector is 128 (512/4) hidden_dim = 512 # LSTM隐层向量的维度 ： 512 / 4
depth = 8 # depth of stacked LSTM depth = 8 # 栈式LSTM的深度
# There are 9 features per sample, so we will define 9 data layers. # 一条样本总共9个特征，下面定义了9个data层，每个层类型为integer_value_sequence，表示整数ID的序列类型.
# They type for each layer is integer_value_sequence. def d_type(size):
def d_type(value_range): return paddle.data_type.integer_value_sequence(size)
return paddle.data_type.integer_value_sequence(value_range)
# 句子序列
# word sequence
word = paddle.layer.data(name='word_data', type=d_type(word_dict_len)) word = paddle.layer.data(name='word_data', type=d_type(word_dict_len))
# predicate # 谓词
predicate = paddle.layer.data(name='verb_data', type=d_type(pred_len)) predicate = paddle.layer.data(name='verb_data', type=d_type(pred_len))
# 5 features for predicate context # 谓词上下文5个特征
ctx_n2 = paddle.layer.data(name='ctx_n2_data', type=d_type(word_dict_len)) ctx_n2 = paddle.layer.data(name='ctx_n2_data', type=d_type(word_dict_len))
ctx_n1 = paddle.layer.data(name='ctx_n1_data', type=d_type(word_dict_len)) ctx_n1 = paddle.layer.data(name='ctx_n1_data', type=d_type(word_dict_len))
ctx_0 = paddle.layer.data(name='ctx_0_data', type=d_type(word_dict_len)) ctx_0 = paddle.layer.data(name='ctx_0_data', type=d_type(word_dict_len))
ctx_p1 = paddle.layer.data(name='ctx_p1_data', type=d_type(word_dict_len)) ctx_p1 = paddle.layer.data(name='ctx_p1_data', type=d_type(word_dict_len))
ctx_p2 = paddle.layer.data(name='ctx_p2_data', type=d_type(word_dict_len)) ctx_p2 = paddle.layer.data(name='ctx_p2_data', type=d_type(word_dict_len))
# region marker sequence # 谓词上下区域标志
mark = paddle.layer.data(name='mark_data', type=d_type(mark_dict_len)) mark = paddle.layer.data(name='mark_data', type=d_type(mark_dict_len))
# label sequence # 标注序列
target = paddle.layer.data(name='target', type=d_type(label_dict_len)) target = paddle.layer.data(name='target', type=d_type(label_dict_len))
``` ```
Note that `hidden_dim = 512` means a LSTM hidden vector of 128 dimension (512/4). Please refer to PaddlePaddle's official documentation for detail: [lstmemory](http://www.paddlepaddle.org/doc/ui/api/trainer_config_helpers/layers.html#lstmemory)。 这里需要特别说明的是hidden_dim = 512指定了LSTM隐层向量的维度为128维，关于这一点请参考PaddlePaddle官方文档中[lstmemory](http://www.paddlepaddle.org/doc/ui/api/trainer_config_helpers/layers.html#lstmemory)的说明。
- Transform the word sequence itself, the predicate, the predicate context, and the region mark sequence into embedded vector sequences. - 将句子序列、谓词、谓词上下文、谓词上下文区域标记通过词表，转换为实向量表示的词向量序列。
```python ```python
# Since word vectorlookup table is pre-trained, we won't update it this time. # 在本教程中，我们加载了预训练的词向量，这里设置了：is_static=True
# is_static being True prevents updating the lookup table during training. # is_static 为 True 时保证了在训练 SRL 模型过程中，词表不再更新
emb_para = paddle.attr.Param(name='emb', initial_std=0., is_static=True) emb_para = paddle.attr.Param(name='emb', initial_std=0., is_static=True)
# hyperparameter configurations # 设置超参数
default_std = 1 / math.sqrt(hidden_dim) / 3.0 default_std = 1 / math.sqrt(hidden_dim) / 3.0
std_default = paddle.attr.Param(initial_std=default_std) std_default = paddle.attr.Param(initial_std=default_std)
std_0 = paddle.attr.Param(initial_std=0.) std_0 = paddle.attr.Param(initial_std=0.)
...@@ -336,7 +313,7 @@ emb_layers.append(predicate_embedding) ...@@ -336,7 +313,7 @@ emb_layers.append(predicate_embedding)
emb_layers.append(mark_embedding) emb_layers.append(mark_embedding)
``` ```
- 8 LSTM units are trained through alternating left-to-right / right-to-left order denoted by the variable `reverse`. - 8个LSTM单元以“正向/反向”的顺序对所有输入序列进行学习。
```python ```python
hidden_0 = paddle.layer.mixed( hidden_0 = paddle.layer.mixed(
...@@ -360,7 +337,7 @@ lstm_0 = paddle.layer.lstmemory( ...@@ -360,7 +337,7 @@ lstm_0 = paddle.layer.lstmemory(
bias_attr=std_0, bias_attr=std_0,
param_attr=lstm_para_attr) param_attr=lstm_para_attr)
# stack L-LSTM and R-LSTM with direct edges #stack L-LSTM and R-LSTM with direct edges
input_tmp = [hidden_0, lstm_0] input_tmp = [hidden_0, lstm_0]
for i in range(1, depth): for i in range(1, depth):
...@@ -386,13 +363,12 @@ for i in range(1, depth): ...@@ -386,13 +363,12 @@ for i in range(1, depth):
input_tmp = [mix_hidden, lstm] input_tmp = [mix_hidden, lstm]
``` ```
- In PaddlePaddle, state features and transition features of a CRF are implemented by a fully connected layer and a CRF layer seperately. The fully connected layer with linear activation learns the state features, here we use paddle.layer.mixed (paddle.layer.fc can be uesed as well), and the CRF layer in PaddlePaddle: paddle.layer.crf only learns the transition features, which is a cost layer and is the last layer of the network. paddle.layer.crf outputs the log probability of true tag sequence as the cost by given the input sequence and it requires the true tag sequence as target in the learning process. - 在PaddlePaddle中，CRF的状态特征和转移特征分别由一个全连接层和一个PaddlePaddle中的CRF层分别学习。在这个例子中，我们用线性激活的paddle.layer.mixed 来学习CRF的状态特征（也可以使用paddle.layer.fc），而 paddle.layer.crf只学习转移特征。paddle.layer.crf层是一个 cost 层，处于整个网络的末端，输出给定输入序列下，标记序列的log probability作为代价。训练阶段，该层需要输入正确的标记序列作为学习目标。
```python ```python
# The output of the top LSTM unit and its input are feed into a fully connected layer, # 取最后一个栈式LSTM的输出和这个LSTM单元的输入到隐层映射，
# size of which equals to size of tag labels. # 经过一个全连接层映射到标记字典的维度，来学习 CRF 的状态特征
# The fully connected layer learns the state features
feature_out = paddle.layer.mixed( feature_out = paddle.layer.mixed(
size=label_dict_len, size=label_dict_len,
...@@ -401,8 +377,10 @@ feature_out = paddle.layer.mixed( ...@@ -401,8 +377,10 @@ feature_out = paddle.layer.mixed(
paddle.layer.full_matrix_projection( paddle.layer.full_matrix_projection(
input=input_tmp[0], param_attr=hidden_para_attr), input=input_tmp[0], param_attr=hidden_para_attr),
paddle.layer.full_matrix_projection( paddle.layer.full_matrix_projection(
input=input_tmp[1], param_attr=lstm_para_attr)], ) input=input_tmp[1], param_attr=lstm_para_attr)
], )
# 学习 CRF 的转移特征
crf_cost = paddle.layer.crf( crf_cost = paddle.layer.crf(
size=label_dict_len, size=label_dict_len,
input=feature_out, input=feature_out,
...@@ -413,7 +391,7 @@ crf_cost = paddle.layer.crf( ...@@ -413,7 +391,7 @@ crf_cost = paddle.layer.crf(
learning_rate=mix_hidden_lr)) learning_rate=mix_hidden_lr))
``` ```
- The CRF decoding layer is used for evaluation and inference. It shares weights with CRF layer. The sharing of parameters among multiple layers is specified by using the same parameter name in these layers. If true tag sequence is provided in training process, `paddle.layer.crf_decoding` calculates labelling error for each input token and `evaluator.sum` sum the error over the entire sequence. Otherwise, `paddle.layer.crf_decoding` generates the labelling tags. - CRF解码和CRF层参数名字相同，即：加载了`paddle.layer.crf`层学习到的参数。在训练阶段，为`paddle.layer.crf_decoding` 输入了正确的标记序列(target)，这一层会输出是否正确标记，`evaluator.sum` 用来计算序列上的标记错误率，可以用来评估模型。解码阶段，没有输入正确的数据标签，该层通过寻找概率最高的标记序列，解码出标记结果。
```python ```python
crf_dec = paddle.layer.crf_decoding( crf_dec = paddle.layer.crf_decoding(
...@@ -424,25 +402,27 @@ crf_dec = paddle.layer.crf_decoding( ...@@ -424,25 +402,27 @@ crf_dec = paddle.layer.crf_decoding(
evaluator.sum(input=crf_dec) evaluator.sum(input=crf_dec)
``` ```
## Train model ## 训练模型
### Create Parameters ### 定义参数
All necessary parameters will be traced created given output layers that we need to use. 首先依据模型配置的`crf_cost`定义模型参数。
```python ```python
# create parameters
parameters = paddle.parameters.create(crf_cost) parameters = paddle.parameters.create(crf_cost)
``` ```
We can print out parameter name. It will be generated if not specified. 可以打印参数名字，如果在网络配置中没有指定名字，则默认生成。
```python ```python
print parameters.keys() print parameters.keys()
``` ```
Now we load the pre-trained word lookup tables from word embeddings trained on the English language Wikipedia. 如上文提到，我们用基于英文维基百科训练好的词向量来初始化序列输入、谓词上下文总共6个特征的embedding层参数，在训练中不更新。
```python ```python
# 这里加载PaddlePaddle上版保存的二进制模型
def load_parameter(file_name, h, w): def load_parameter(file_name, h, w):
with open(file_name, 'rb') as f: with open(file_name, 'rb') as f:
f.read(16) f.read(16)
...@@ -450,11 +430,12 @@ def load_parameter(file_name, h, w): ...@@ -450,11 +430,12 @@ def load_parameter(file_name, h, w):
parameters.set('emb', load_parameter(conll05.get_embedding(), 44068, 32)) parameters.set('emb', load_parameter(conll05.get_embedding(), 44068, 32))
``` ```
### Create Trainer ### 构造训练(Trainer)
We will create trainer given model topology, parameters, and optimization method. We will use the most basic **SGD** method, which is a momentum optimizer with 0 momentum. Meanwhile, we will set learning rate and regularization. 然后根据网络拓扑结构和模型参数来构造出trainer用来训练，在构造时还需指定优化方法，这里使用最基本的SGD方法(momentum设置为0)，同时设定了学习率、正则等。
```python ```python
# create optimizer
optimizer = paddle.optimizer.Momentum( optimizer = paddle.optimizer.Momentum(
momentum=0, momentum=0,
learning_rate=1e-3, learning_rate=1e-3,
...@@ -468,9 +449,9 @@ trainer = paddle.trainer.SGD(cost=crf_cost, ...@@ -468,9 +449,9 @@ trainer = paddle.trainer.SGD(cost=crf_cost,
extra_layers=crf_dec) extra_layers=crf_dec)
``` ```
### Trainer ### 训练
As mentioned in data preparation section, we will use CoNLL 2005 test corpus as the training data set. `conll05.test()` outputs one training instance at a time. It is shuffled and batched into mini batches, and used as input. 数据介绍部分提到CoNLL 2005训练集付费，这里我们使用测试集训练供大家学习。`conll05.test()`每次产生一条样本，包含9个特征，shuffle和组完batch后作为训练的输入。
```python ```python
reader = paddle.batch( reader = paddle.batch(
...@@ -478,7 +459,8 @@ reader = paddle.batch( ...@@ -478,7 +459,8 @@ reader = paddle.batch(
conll05.test(), buf_size=8192), batch_size=2) conll05.test(), buf_size=8192), batch_size=2)
``` ```
`feeding` is used to specify the correspondence between data instance and data layer. For example, according to following `feeding`, the 0th column of data instance produced by`conll05.test()` is matched to the data layer named `word_data`. 通过`feeding`来指定每一个数据和data_layer的对应关系。 例如 下面`feeding`表示: `conll05.test()`产生数据的第0列对应`word_data`层的特征。
```python ```python
feeding = { feeding = {
...@@ -494,7 +476,7 @@ feeding = { ...@@ -494,7 +476,7 @@ feeding = {
} }
``` ```
`event_handler` can be used as callback for training events, it will be used as an argument for the `train` method. Following `event_handler` prints cost during training. 可以使用`event_handler`回调函数来观察训练过程，或进行测试等。这里我们打印了训练过程的cost，该回调函数是`trainer.train`函数里设定。
```python ```python
def event_handler(event): def event_handler(event):
...@@ -515,19 +497,19 @@ def event_handler(event): ...@@ -515,19 +497,19 @@ def event_handler(event):
print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics) print "\nTest with Pass %d, %s" % (event.pass_id, result.metrics)
``` ```
`trainer.train` will train the model. 通过`trainer.train`函数训练：
```python ```python
trainer.train( trainer.train(
reader=reader, reader=reader,
event_handler=event_handler, event_handler=event_handler,
num_passes=10000, num_passes=1,
feeding=feeding) feeding=feeding)
``` ```
### Application ### 应用模型
Aftern training is done, we need to select an optimal model based one performance index to do inference. In this task, one can simply select the model with the least number of marks on the test set. The `paddle.layer.crf_decoding` layer is used in the inference, but its inputs does not include the ground truth label. 训练完成之后，需要依据某个我们关心的性能指标选择最优的模型进行预测，可以简单的选择测试集上标记错误最少的那个模型。预测时使用 `paddle.layer.crf_decoding`，和训练不同的是，该层没有正确的标签层作为输入。如下所示：
```python ```python
predict = paddle.layer.crf_decoding( predict = paddle.layer.crf_decoding(
...@@ -536,7 +518,7 @@ predict = paddle.layer.crf_decoding( ...@@ -536,7 +518,7 @@ predict = paddle.layer.crf_decoding(
param_attr=paddle.attr.Param(name='crfw')) param_attr=paddle.attr.Param(name='crfw'))
``` ```
Here, using one testing sample as an example. 这里选用测试集的一条数据作为示例。
```python ```python
test_creator = paddle.dataset.conll05.test() test_creator = paddle.dataset.conll05.test()
...@@ -547,8 +529,7 @@ for item in test_creator(): ...@@ -547,8 +529,7 @@ for item in test_creator():
break break
``` ```
The inference interface `paddle.infer` returns the index of predicting labels. Then printing the tagging results based dictionary `labels_reverse`. 推断接口`paddle.infer`返回标签的索引，并查询词典`labels_reverse`，打印出标记的结果。
```python ```python
labs = paddle.infer( labs = paddle.infer(
...@@ -561,11 +542,11 @@ pre_lab = [labels_reverse[i] for i in labs] ...@@ -561,11 +542,11 @@ pre_lab = [labels_reverse[i] for i in labs]
print pre_lab print pre_lab
``` ```
## Conclusion ## 总结
Semantic Role Labeling is an important intermediate step in a wide range of natural language processing tasks. In this tutorial, we use SRL as an example to illustrate using PaddlePaddle to do sequence tagging tasks. The models proposed are from our published paper\[[10](#Reference)\]. We only use test data for illustration since the training data on the CoNLL 2005 dataset is not completely public. This aims to propose an end-to-end neural network model with fewer dependencies on natural language processing tools but is comparable, or even better than traditional models in terms of performance. Please check out our paper for more information and discussions. 语义角色标注是许多自然语言理解任务的重要中间步骤。这篇教程中我们以语义角色标注任务为例，介绍如何利用PaddlePaddle进行序列标注任务。教程中所介绍的模型来自我们发表的论文\[[10](#参考文献)\]。由于 CoNLL 2005 SRL任务的训练数据目前并非完全开放，教程中只使用测试数据作为示例。在这个过程中，我们希望减少对其它自然语言处理工具的依赖，利用神经网络数据驱动、端到端学习的能力，得到一个和传统方法可比、甚至更好的模型。在论文中我们证实了这种可能性。关于模型更多的信息和讨论可以在论文中找到。
## Reference ## 参考文献
1. Sun W, Sui Z, Wang M, et al. [Chinese semantic role labeling with shallow parsing](http://www.aclweb.org/anthology/D09-1#page=1513)[C]//Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 3-Volume 3. Association for Computational Linguistics, 2009: 1475-1483. 1. Sun W, Sui Z, Wang M, et al. [Chinese semantic role labeling with shallow parsing](http://www.aclweb.org/anthology/D09-1#page=1513)[C]//Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 3-Volume 3. Association for Computational Linguistics, 2009: 1475-1483.
2. Pascanu R, Gulcehre C, Cho K, et al. [How to construct deep recurrent neural networks](https://arxiv.org/abs/1312.6026)[J]. arXiv preprint arXiv:1312.6026, 2013. 2. Pascanu R, Gulcehre C, Cho K, et al. [How to construct deep recurrent neural networks](https://arxiv.org/abs/1312.6026)[J]. arXiv preprint arXiv:1312.6026, 2013.
3. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](https://arxiv.org/abs/1406.1078)[J]. arXiv preprint arXiv:1406.1078, 2014. 3. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](https://arxiv.org/abs/1406.1078)[J]. arXiv preprint arXiv:1406.1078, 2014.
...@@ -578,7 +559,7 @@ Semantic Role Labeling is an important intermediate step in a wide range of natu ...@@ -578,7 +559,7 @@ Semantic Role Labeling is an important intermediate step in a wide range of natu
10. Zhou J, Xu W. [End-to-end learning of semantic role labeling using recurrent neural networks](http://www.aclweb.org/anthology/P/P15/P15-1109.pdf)[C]//Proceedings of the Annual Meeting of the Association for Computational Linguistics. 2015. 10. Zhou J, Xu W. [End-to-end learning of semantic role labeling using recurrent neural networks](http://www.aclweb.org/anthology/P/P15/P15-1109.pdf)[C]//Proceedings of the Annual Meeting of the Association for Computational Linguistics. 2015.
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This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>. <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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# Machine Translation # 机器翻译
The source codes is located at [book/machine_translation](https://github.com/PaddlePaddle/book/tree/develop/08.machine_translation). Please refer to the PaddlePaddle [installation tutorial](https://github.com/PaddlePaddle/book/blob/develop/README.en.md#running-the-book) if you are a first time user. 本教程源代码目录在[book/machine_translation](https://github.com/PaddlePaddle/book/tree/develop/08.machine_translation)， 初次使用请参考PaddlePaddle[安装教程](https://github.com/PaddlePaddle/book/blob/develop/README.md#运行这本书)。
## Background ## 背景介绍
Machine translation (MT) leverages computers to translate from one language to another. The language to be translated is referred to as the source language, while the language to be translated into is referred to as the target language. Thus, Machine translation is the process of translating from the source language to the target language. It is one of the most important research topics in the field of natural language processing. 机器翻译（machine translation, MT）是用计算机来实现不同语言之间翻译的技术。被翻译的语言通常称为源语言（source language），翻译成的结果语言称为目标语言（target language）。机器翻译即实现从源语言到目标语言转换的过程，是自然语言处理的重要研究领域之一。
Early machine translation systems are mainly rule-based i.e. they rely on a language expert to specify the translation rules between the two languages. It is quite difficult to cover all the rules used in one languge. So it is quite a challenge for language experts to specify all possible rules in two or more different languages. Hence, a major challenge in conventional machine translation has been the difficulty in obtaining a complete rule set \[[1](#References)\]。 早期机器翻译系统多为基于规则的翻译系统，需要由语言学家编写两种语言之间的转换规则，再将这些规则录入计算机。该方法对语言学家的要求非常高，而且我们几乎无法总结一门语言会用到的所有规则，更何况两种甚至更多的语言。因此，传统机器翻译方法面临的主要挑战是无法得到一个完备的规则集合\[[1](#参考文献)\]。
为解决以上问题，统计机器翻译（Statistical Machine Translation, SMT）技术应运而生。在统计机器翻译技术中，转化规则是由机器自动从大规模的语料中学习得到的，而非我们人主动提供规则。因此，它克服了基于规则的翻译系统所面临的知识获取瓶颈的问题，但仍然存在许多挑战：1）人为设计许多特征（feature），但永远无法覆盖所有的语言现象；2）难以利用全局的特征；3）依赖于许多预处理环节，如词语对齐、分词或符号化（tokenization）、规则抽取、句法分析等，而每个环节的错误会逐步累积，对翻译的影响也越来越大。
To address the aforementioned problems, statistical machine translation techniques have been developed. These techniques learn the translation rules from a large corpus, instead of being designed by a language expert. While these techniques overcome the bottleneck of knowledge acquisition, there are still quite a lot of challenges, for example: 近年来，深度学习技术的发展为解决上述挑战提供了新的思路。将深度学习应用于机器翻译任务的方法大致分为两类：1）仍以统计机器翻译系统为框架，只是利用神经网络来改进其中的关键模块，如语言模型、调序模型等（见图1的左半部分）；2）不再以统计机器翻译系统为框架，而是直接用神经网络将源语言映射到目标语言，即端到端的神经网络机器翻译（End-to-End Neural Machine Translation, End-to-End NMT）（见图1的右半部分），简称为NMT模型。
1. human designed features cannot cover all possible linguistic variations;
2. it is difficult to use global features;
3. the techniques heavily rely on pre-processing techniques like word alignment, word segmentation and tokenization, rule-extraction and syntactic parsing etc. The error introduced in any of these steps could accumulate and impact translation quality.
The recent development of deep learning provides new solutions to these challenges. The two main categories for deep learning based machine translation techniques are:
1. techniques based on the statistical machine translation system but with some key components improved with neural networks, e.g., language model, reordering model (please refer to the left part of Figure 1);
2. techniques mapping from source language to target language directly using a neural network, or end-to-end neural machine translation (NMT).
<p align="center"> <p align="center">
<img src="image/nmt_en.png" width=400><br/> <img src="image/nmt.png" width=400><br/>
Figure 1. Neural Network based Machine Translation 图1. 基于神经网络的机器翻译系统
</p> </p>
本教程主要介绍NMT模型，以及如何用PaddlePaddle来训练一个NMT模型。
This tutorial will mainly introduce an NMT model and how to use PaddlePaddle to train it. ## 效果展示
## Illustrative Results
Let's consider an example of Chinese-to-English translation. The model is given the following segmented sentence in Chinese 以中英翻译（中文翻译到英文）的模型为例，当模型训练完毕时，如果输入如下已分词的中文句子：
```text ```text
这些 是 希望 的 曙光 和 解脱 的 迹象 . 这些 是 希望 的 曙光 和 解脱 的 迹象 .
``` ```
After training and with a beam-search size of 3, the generated translations are as follows: 如果设定显示翻译结果的条数（即[柱搜索算法](#柱搜索算法)的宽度）为3，生成的英语句子如下：
```text ```text
0 -5.36816 These are signs of hope and relief . <e> 0 -5.36816 These are signs of hope and relief . <e>
1 -6.23177 These are the light of hope and relief . <e> 1 -6.23177 These are the light of hope and relief . <e>
2 -7.7914 These are the light of hope and the relief of hope . <e> 2 -7.7914 These are the light of hope and the relief of hope . <e>
``` ```
- The first column corresponds to the id of the generated sentence; the second column corresponds to the score of the generated sentence (in descending order), where a larger value indicates better quality; the last column corresponds to the generated sentence. - 左起第一列是生成句子的序号；左起第二列是该条句子的得分（从大到小），分值越高越好；左起第三列是生成的英语句子。
- There are two special tokens: `<e>` denotes the end of a sentence while `<unk>` denotes unknown word, i.e., a word not in the training dictionary. - 另外有两个特殊标志：`<e>`表示句子的结尾，`<unk>`表示未登录词（unknown word），即未在训练字典中出现的词。
## Overview of the Model ## 模型概览
This section will introduce Gated Recurrent Unit (GRU), Bi-directional Recurrent Neural Network, the Encoder-Decoder framework used in NMT, attention mechanism, as well as the beam search algorithm. 本节依次介绍GRU（Gated Recurrent Unit，门控循环单元），双向循环神经网络（Bi-directional Recurrent Neural Network），NMT模型中典型的编码器-解码器（Encoder-Decoder）框架和注意力（Attention）机制，以及柱搜索（beam search）算法。
### Gated Recurrent Unit (GRU) ### GRU
We already introduced RNN and LSTM in the [Sentiment Analysis](https://github.com/PaddlePaddle/book/blob/develop/understand_sentiment/README.md) chapter. 我们已经在[情感分析](https://github.com/PaddlePaddle/book/blob/develop/understand_sentiment/README.md)一章中介绍了循环神经网络（RNN）及长短时间记忆网络（LSTM）。相比于简单的RNN，LSTM增加了记忆单元（memory cell）、输入门（input gate）、遗忘门（forget gate）及输出门（output gate），这些门及记忆单元组合起来大大提升了RNN处理远距离依赖问题的能力。
Compared to a simple RNN, the LSTM added memory cell, input gate, forget gate and output gate. These gates combined with the memory cell greatly improve the ability to handle long-term dependencies.
GRU\[[2](#References)\] proposed by Cho et al is a simplified LSTM and an extension of a simple RNN. It is shown in the figure below.
A GRU unit has only two gates:
- reset gate: when this gate is closed, the history information is discarded, i.e., the irrelevant historical information has no effect on the future output.
- update gate: it combines the input gate and the forget gate and is used to control the impact of historical information on the hidden output. The historical information is passed over when the update gate is close to 1.
GRU\[[2](#参考文献)\]是Cho等人在LSTM上提出的简化版本，也是RNN的一种扩展，如下图所示。GRU单元只有两个门：
- 重置门（reset gate）：如果重置门关闭，会忽略掉历史信息，即历史不相干的信息不会影响未来的输出。
- 更新门（update gate）：将LSTM的输入门和遗忘门合并，用于控制历史信息对当前时刻隐层输出的影响。如果更新门接近1，会把历史信息传递下去。
<p align="center"> <p align="center">
<img src="image/gru_en.png" width=700><br/> <img src="image/gru.png" width=700><br/>
Figure 2. A GRU Gate 图2. GRU（门控循环单元）
</p> </p>
Generally speaking, sequences with short distance dependencies will have an active reset gate while sequences with long distance dependency will have an active update date. 一般来说，具有短距离依赖属性的序列，其重置门比较活跃；相反，具有长距离依赖属性的序列，其更新门比较活跃。另外，Chung等人\[[3](#参考文献)\]通过多组实验表明，GRU虽然参数更少，但是在多个任务上都和LSTM有相近的表现。
In addition, Chung et al.\[[3](#References)\] have empirically shown that although GRU has less parameters, it has similar performance to LSTM on several different tasks.
### Bi-directional Recurrent Neural Network ### 双向循环神经网络
We already introduced an instance of bi-directional RNN in the [Semantic Role Labeling](https://github.com/PaddlePaddle/book/blob/develop/label_semantic_roles/README.md) chapter. Here we present another bi-directional RNN model with a different architecture proposed by Bengio et al. in \[[2](#References),[4](#References)\]. This model takes a sequence as input and outputs a fixed dimensional feature vector at each step, encoding the context information at the corresponding time step. 我们已经在[语义角色标注](https://github.com/PaddlePaddle/book/blob/develop/label_semantic_roles/README.md)一章中介绍了一种双向循环神经网络，这里介绍Bengio团队在论文\[[2](#参考文献),[4](#参考文献)\]中提出的另一种结构。该结构的目的是输入一个序列，得到其在每个时刻的特征表示，即输出的每个时刻都用定长向量表示到该时刻的上下文语义信息。
Specifically, this bi-directional RNN processes the input sequence in the original and reverse order respectively, and then concatenates the output feature vectors at each time step as the final output. Thus the output node at each time step contains information from the past and future as context. The figure below shows an unrolled bi-directional RNN. This network contains a forward RNN and backward RNN with six weight matrices: weight matrices from input to forward hidden layer and backward hidden ($W_1, W_3$), weight matrices from hidden to itself ($W_2, W_5$), matrices from forward hidden and backward hidden to output layer ($W_4, W_6$). Note that there are no connections between forward hidden and backward hidden layers. 具体来说，该双向循环神经网络分别在时间维以顺序和逆序——即前向（forward）和后向（backward）——依次处理输入序列，并将每个时间步RNN的输出拼接成为最终的输出层。这样每个时间步的输出节点，都包含了输入序列中当前时刻完整的过去和未来的上下文信息。下图展示的是一个按时间步展开的双向循环神经网络。该网络包含一个前向和一个后向RNN，其中有六个权重矩阵：输入到前向隐层和后向隐层的权重矩阵（$W_1, W_3$），隐层到隐层自己的权重矩阵（$W_2,W_5$），前向隐层和后向隐层到输出层的权重矩阵（$W_4, W_6$）。注意，该网络的前向隐层和后向隐层之间没有连接。
<p align="center"> <p align="center">
<img src="image/bi_rnn_en.png" width=450><br/> <img src="image/bi_rnn.png" width=450><br/>
Figure 3. Temporally unrolled bi-directional RNN 图3. 按时间步展开的双向循环神经网络
</p> </p>
### Encoder-Decoder Framework ### 编码器-解码器框架
The Encoder-Decoder\[[2](#References)\] framework aims to solve the mapping of a sequence to another sequence, for sequences with arbitrary lengths. The source sequence is encoded into a vector via an encoder, which is then decoded to a target sequence via a decoder by maximizing the predictive probability. Both the encoder and the decoder are typically implemented via RNN.
编码器-解码器（Encoder-Decoder）\[[2](#参考文献)\]框架用于解决由一个任意长度的源序列到另一个任意长度的目标序列的变换问题。即编码阶段将整个源序列编码成一个向量，解码阶段通过最大化预测序列概率，从中解码出整个目标序列。编码和解码的过程通常都使用RNN实现。
<p align="center"> <p align="center">
<img src="image/encoder_decoder_en.png" width=700><br/> <img src="image/encoder_decoder.png" width=700><br/>
Figure 4. Encoder-Decoder Framework 图4. 编码器-解码器框架
</p> </p>
#### Encoder #### 编码器
There are three steps for encoding a sentence:
1. One-hot vector representation of a word: Each word $x_i$ in the source sentence $x=\left \{ x_1,x_2,...,x_T \right \}$ is represented as a vector $w_i\epsilon \left \{ 0,1 \right \}^{\left | V \right |},i=1,2,...,T$ where $w_i$ has the same dimensionality as the size of the dictionary, i.e., $\left | V \right |$, and has an element of one at the location corresponding to the location of the word in the dictionary and zero elsewhere. 编码阶段分为三步：
2. Word embedding as a representation in the low-dimensional semantic space: There are two problems with one-hot vector representation 1. one-hot vector表示：将源语言句子$x=\left \{ x_1,x_2,...,x_T \right \}$的每个词$x_i$表示成一个列向量$w_i\epsilon \left \{ 0,1 \right \}^{\left | V \right |},i=1,2,...,T$。这个向量$w_i$的维度与词汇表大小$\left | V \right |$ 相同，并且只有一个维度上有值1（该位置对应该词在词汇表中的位置），其余全是0。
* the dimensionality of the vector is typically large, leading to the curse of dimensionality; 2. 映射到低维语义空间的词向量：one-hot vector表示存在两个问题，1）生成的向量维度往往很大，容易造成维数灾难；2）难以刻画词与词之间的关系（如语义相似性，也就是无法很好地表达语义）。因此，需再one-hot vector映射到低维的语义空间，由一个固定维度的稠密向量（称为词向量）表示。记映射矩阵为$C\epsilon R^{K\times \left | V \right |}$，用$s_i=Cw_i$表示第$i$个词的词向量，$K$为向量维度。
* it is hard to capture the relationships between words, i.e., semantic similarities. Therefore, it is useful to project the one-hot vector into a low-dimensional semantic space as a dense vector with fixed dimensions, i.e., $s_i=Cw_i$ for the $i$-th word, with $C\epsilon R^{K\times \left | V \right |}$ as the projection matrix and $K$ is the dimensionality of the word embedding vector. 3. 用RNN编码源语言词序列：这一过程的计算公式为$h_i=\varnothing _\theta \left ( h_{i-1}, s_i \right )$，其中$h_0$是一个全零的向量，$\varnothing _\theta$是一个非线性激活函数，最后得到的$\mathbf{h}=\left \{ h_1,..., h_T \right \}$就是RNN依次读入源语言$T$个词的状态编码序列。整句话的向量表示可以采用$\mathbf{h}$在最后一个时间步$T$的状态编码，或使用时间维上的池化（pooling）结果。
3. Encoding of the source sequence via RNN: This can be described mathematically as: 第3步也可以使用双向循环神经网络实现更复杂的句编码表示，具体可以用双向GRU实现。前向GRU按照词序列$(x_1,x_2,...,x_T)$的顺序依次编码源语言端词，并得到一系列隐层状态$(\overrightarrow{h_1},\overrightarrow{h_2},...,\overrightarrow{h_T})$。类似的，后向GRU按照$(x_T,x_{T-1},...,x_1)$的顺序依次编码源语言端词，得到$(\overleftarrow{h_1},\overleftarrow{h_2},...,\overleftarrow{h_T})$。最后对于词$x_i$，通过拼接两个GRU的结果得到它的隐层状态，即$h_i=\left [ \overrightarrow{h_i^T},\overleftarrow{h_i^T} \right ]^{T}$。
$$h_i=\varnothing _\theta \left ( h_{i-1}, s_i \right )$$
where
$h_0$ is a zero vector,
$\varnothing _\theta$ is a non-linear activation function, and
$\mathbf{h}=\left \{ h_1,..., h_T \right \}$
is the sequential encoding of the first $T$ words from the source sequence. The vector representation of the whole sentence can be represented as the encoding vector at the last time step $T$ from $\mathbf{h}$, or by temporal pooling over $\mathbf{h}$.
Bi-directional RNN can also be used in step (3) for more a complicated sentence encoding. This can be implemented using a bi-directional GRU. Forward GRU encodes the source sequence in its original order $(x_1,x_2,...,x_T)$, and generates a sequence of hidden states $(\overrightarrow{h_1},\overrightarrow{h_2},...,\overrightarrow{h_T})$. The backward GRU encodes the source sequence in reverse order, i.e., $(x_T,x_T-1,...,x_1)$ and generates $(\overleftarrow{h_1},\overleftarrow{h_2},...,\overleftarrow{h_T})$. Then for each word $x_i$, its complete hidden state is the concatenation of the corresponding hidden states from the two GRUs, i.e., $h_i=\left [ \overrightarrow{h_i^T},\overleftarrow{h_i^T} \right ]^{T}$.
<p align="center"> <p align="center">
<img src="image/encoder_attention_en.png" width=500><br/> <img src="image/encoder_attention.png" width=500><br/>
Figure 5. Encoder using bi-directional GRU 图5. 使用双向GRU的编码器
</p> </p>
#### Decoder #### 解码器
The goal of the decoder is to maximize the probability of the next correct word in the target language. The main idea is as follows: 机器翻译任务的训练过程中，解码阶段的目标是最大化下一个正确的目标语言词的概率。思路是：
1. At each time step $i$, given the encoding vector (or context vector) $c$ of the source sentence, the $i$-th word $u_i$ from the ground-truth target language and the RNN hidden state $z_i$, the next hidden state $z_{i+1}$ is computed as: 1. 每一个时刻，根据源语言句子的编码信息（又叫上下文向量，context vector）$c$、真实目标语言序列的第$i$个词$u_i$和$i$时刻RNN的隐层状态$z_i$，计算出下一个隐层状态$z_{i+1}$。计算公式如下：
$$z_{i+1}=\phi _{\theta '}\left ( c,u_i,z_i \right )$$ $$z_{i+1}=\phi _{\theta '}\left ( c,u_i,z_i \right )$$
where $\phi _{\theta '}$ is a non-linear activation function and $c=q\mathbf{h}$ is the context vector of the source sentence. Without using [attention](#Attention Mechanism), if the output of the [encoder](#Encoder) is the encoding vector at the last time step of the source sentence, then $c$ can be defined as $c=h_T$. $u_i$ denotes the $i$-th word from the target language sentence and $u_0$ denotes the beginning of the target language sentence (i.e., `<s>`), indicating the beginning of decoding. $z_i$ is the RNN hidden state at time step $i$ and $z_0$ is an all zero vector.
2. Calculate the probability $p_{i+1}$ for the $i+1$-th word in the target language sequence by normalizing $z_{i+1}$ using `softmax` as follows 其中$\phi _{\theta '}$是一个非线性激活函数；$c=q\mathbf{h}$是源语言句子的上下文向量，在不使用[注意力机制](#注意力机制)时，如果[编码器](#编码器)的输出是源语言句子编码后的最后一个元素，则可以定义$c=h_T$；$u_i$是目标语言序列的第$i$个单词，$u_0$是目标语言序列的开始标记`<s>`，表示解码开始；$z_i$是$i$时刻解码RNN的隐层状态，$z_0$是一个全零的向量。
2. 将$z_{i+1}$通过`softmax`归一化，得到目标语言序列的第$i+1$个单词的概率分布$p_{i+1}$。概率分布公式如下：
$$p\left ( u_{i+1}|u_{&lt;i+1},\mathbf{x} \right )=softmax(W_sz_{i+1}+b_z)$$ $$p\left ( u_{i+1}|u_{&lt;i+1},\mathbf{x} \right )=softmax(W_sz_{i+1}+b_z)$$
where $W_sz_{i+1}+b_z$ scores each possible words and is then normalized via softmax to produce the probability $p_{i+1}$ for the $i+1$-th word. 其中$W_sz_{i+1}+b_z$是对每个可能的输出单词进行打分，再用softmax归一化就可以得到第$i+1$个词的概率$p_{i+1}$。
3. Compute the cost accoding to $p_{i+1}$ and $u_{i+1}$. 3. 根据$p_{i+1}$和$u_{i+1}$计算代价。
4. Repeat Steps 1-3, until all the words in the target language sentence have been processed. 4. 重复步骤1~3，直到目标语言序列中的所有词处理完毕。
The generation process of machine translation is to translate the source sentence into a sentence in the target language according to a pre-trained model. There are some differences between the decoding step in generation and training. Please refer to [Beam Search Algorithm](#Beam Search Algorithm) for details. 机器翻译任务的生成过程，通俗来讲就是根据预先训练的模型来翻译源语言句子。生成过程中的解码阶段和上述训练过程的有所差异，具体介绍请见[柱搜索算法](#柱搜索算法)。
### Attention Mechanism ### 注意力机制
There are a few problems with the fixed dimensional vector representation from the encoding stage: 如果编码阶段的输出是一个固定维度的向量，会带来以下两个问题：1）不论源语言序列的长度是5个词还是50个词，如果都用固定维度的向量去编码其中的语义和句法结构信息，对模型来说是一个非常高的要求，特别是对长句子序列而言；2）直觉上，当人类翻译一句话时，会对与当前译文更相关的源语言片段上给予更多关注，且关注点会随着翻译的进行而改变。而固定维度的向量则相当于，任何时刻都对源语言所有信息给予了同等程度的关注，这是不合理的。因此，Bahdanau等人\[[4](#参考文献)\]引入注意力（attention）机制，可以对编码后的上下文片段进行解码，以此来解决长句子的特征学习问题。下面介绍在注意力机制下的解码器结构。
* It is very challenging to encode both the semantic and syntactic information a sentence with a fixed dimensional vector regardless of the length of the sentence.
* Intuitively, when translating a sentence, we typically pay more attention to the parts in the source sentence more relevant to the current translation. Moreover, the focus changes along the process of the translation. With a fixed dimensional vector, all the information from the source sentence is treated equally in terms of attention. This is not reasonable. Therefore, Bahdanau et al. \[[4](#References)\] introduced attention mechanism, which can decode based on different fragments of the context sequence in order to address the difficulty of feature learning for long sentences. Decoder with attention will be explained in the following.
Different from the simple decoder, $z_i$ is computed as: 与简单的解码器不同，这里$z_i$的计算公式为：
$$z_{i+1}=\phi _{\theta '}\left ( c_i,u_i,z_i \right )$$ $$z_{i+1}=\phi _{\theta '}\left ( c_i,u_i,z_i \right )$$
It is observed that for each word $u_i$ in the target language sentence, there is a corresponding context vector $c_i$ as the encoding of the source sentence, which is computed as: 可见，源语言句子的编码向量表示为第$i$个词的上下文片段$c_i$，即针对每一个目标语言中的词$u_i$，都有一个特定的$c_i$与之对应。$c_i$的计算公式如下：
$$c_i=\sum _{j=1}^{T}a_{ij}h_j, a_i=\left[ a_{i1},a_{i2},...,a_{iT}\right ]$$ $$c_i=\sum _{j=1}^{T}a_{ij}h_j, a_i=\left[ a_{i1},a_{i2},...,a_{iT}\right ]$$
It is noted that the attention mechanism is achieved by a weighted average over the RNN hidden states $h_j$. The weight $a_{ij}$ denotes the strength of attention of the $i$-th word in the target language sentence to the $j$-th word in the source sentence and is calculated as 从公式中可以看出，注意力机制是通过对编码器中各时刻的RNN状态$h_j$进行加权平均实现的。权重$a_{ij}$表示目标语言中第$i$个词对源语言中第$j$个词的注意力大小，$a_{ij}$的计算公式如下：
\begin{align} \begin{align}
a_{ij}&=\frac{exp(e_{ij})}{\sum_{k=1}^{T}exp(e_{ik})}\\\\ a_{ij}&=\frac{exp(e_{ij})}{\sum_{k=1}^{T}exp(e_{ik})}\\\\
e_{ij}&=align(z_i,h_j)\\\\ e_{ij}&=align(z_i,h_j)\\\\
\end{align} \end{align}
where $align$ is an alignment model that measures the fitness between the $i$-th word in the target language sentence and the $j$-th word in the source sentence. More concretely, the fitness is computed with the $i$-th hidden state $z_i$ of the decoder RNN and the $j$-th context vector $h_j$ of the source sentence. Hard alignment is used in the conventional alignment model, which means each word in the target language explicitly corresponds to one or more words from the target language sentence. In an attention model, soft alignment is used, where any word in source sentence is related to any word in the target language sentence, where the strength of the relation is a real number computed via the model, thus can be incorporated into the NMT framework and can be trained via back-propagation. 其中，$align$可以看作是一个对齐模型，用来衡量目标语言中第$i$个词和源语言中第$j$个词的匹配程度。具体而言，这个程度是通过解码RNN的第$i$个隐层状态$z_i$和源语言句子的第$j$个上下文片段$h_j$计算得到的。传统的对齐模型中，目标语言的每个词明确对应源语言的一个或多个词（hard alignment）；而在注意力模型中采用的是soft alignment，即任何两个目标语言和源语言词间均存在一定的关联，且这个关联强度是由模型计算得到的实数，因此可以融入整个NMT框架，并通过反向传播算法进行训练。
<p align="center"> <p align="center">
<img src="image/decoder_attention_en.png" width=500><br/> <img src="image/decoder_attention.png" width=500><br/>
Figure 6. Decoder with Attention Mechanism 图6. 基于注意力机制的解码器
</p> </p>
### Beam Search Algorithm ### 柱搜索算法
[Beam Search](http://en.wikipedia.org/wiki/Beam_search) is a heuristic search algorithm that explores a graph by expanding the most promising node in a limited set. It is typically used when the solution space is huge (e.g., for machine translation, speech recognition), and there is not enough memory for all the possible solutions. For example, if we want to translate “`<s>你好<e>`” into English, even if there are only three words in the dictionary (`<s>`, `<e>`, `hello`), it is still possible to generate an infinite number of sentences, where the word `hello` can appear different number of times. Beam search could be used to find a good translation among them.
Beam search builds a search tree using breadth first search and sorts the nodes according to a heuristic cost (sum of the log probability of the generated words) at each level of the tree. Only a fixed number of nodes according to the pre-specified beam size (or beam width) are considered. Thus, only nodes with highest scores are expanded in the next level. This reduces the space and time requirements significantly. However, a globally optimal solution is not guaranteed. 柱搜索（[beam search](http://en.wikipedia.org/wiki/Beam_search)）是一种启发式图搜索算法，用于在图或树中搜索有限集合中的最优扩展节点，通常用在解空间非常大的系统（如机器翻译、语音识别）中，原因是内存无法装下图或树中所有展开的解。如在机器翻译任务中希望翻译“`<s>你好<e>`”，就算目标语言字典中只有3个词（`<s>`, `<e>`, `hello`），也可能生成无限句话（`hello`循环出现的次数不定），为了找到其中较好的翻译结果，我们可采用柱搜索算法。
The goal is to maximize the probability of the generated sequence when using beam search in decoding, The procedure is as follows: 柱搜索算法使用广度优先策略建立搜索树，在树的每一层，按照启发代价（heuristic cost）（本教程中，为生成词的log概率之和）对节点进行排序，然后仅留下预先确定的个数（文献中通常称为beam width、beam size、柱宽度等）的节点。只有这些节点会在下一层继续扩展，其他节点就被剪掉了，也就是说保留了质量较高的节点，剪枝了质量较差的节点。因此，搜索所占用的空间和时间大幅减少，但缺点是无法保证一定获得最优解。
1. At each time step $i$, compute the hidden state $z_{i+1}$ of the next time step according to the context vector $c$ of the source sentence, the $i$-th word $u_i$ generated for the target language sentence and the RNN hidden state $z_i$. 使用柱搜索算法的解码阶段，目标是最大化生成序列的概率。思路是：
2. Normalize $z_{i+1}$ using `softmax` to get the probability $p_{i+1}$ for the $i+1$-th word for the target language sentence.
3. Sample the word $u_{i+1}$ according to $p_{i+1}$.
4. Repeat Steps 1-3, until end-of-sentence token `<e>` is generated or the maximum length of the sentence is reached.
Note: $z_{i+1}$ and $p_{i+1}$ are computed the same way as in [Decoder](#Decoder). In generation mode, each step is greedy in so there is no guarantee of a global optimum. 1. 每一个时刻，根据源语言句子的编码信息$c$、生成的第$i$个目标语言序列单词$u_i$和$i$时刻RNN的隐层状态$z_i$，计算出下一个隐层状态$z_{i+1}$。
2. 将$z_{i+1}$通过`softmax`归一化，得到目标语言序列的第$i+1$个单词的概率分布$p_{i+1}$。
3. 根据$p_{i+1}$采样出单词$u_{i+1}$。
4. 重复步骤1~3，直到获得句子结束标记`<e>`或超过句子的最大生成长度为止。
## Data Preparation 注意：$z_{i+1}$和$p_{i+1}$的计算公式同[解码器](#解码器)中的一样。且由于生成时的每一步都是通过贪心法实现的，因此并不能保证得到全局最优解。
This tutorial uses a dataset from [WMT-14](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/), where [bitexts (after selection)](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/bitexts.tgz) is used as the training set, and [dev+test data](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/dev+test.tgz) is used as test and generation set. ## 数据介绍
本教程使用[WMT-14](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/)数据集中的[bitexts(after selection)](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/bitexts.tgz)作为训练集，[dev+test data](http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/dev+test.tgz)作为测试集和生成集。
### Data Preprocessing ### 数据预处理
There are two steps for pre-processing: 我们的预处理流程包括两步：
- Merge the source and target parallel corpus files into one file - 将每个源语言到目标语言的平行语料库文件合并为一个文件：
- Merge `XXX.src` and `XXX.trg` file pair as `XXX` - 合并每个`XXX.src`和`XXX.trg`文件为`XXX`。
- The $i$-th row in `XXX` is the concatenation of the $i$-th row from `XXX.src` with the $i$-th row from `XXX.trg`, separated with '\t'. - `XXX`中的第$i$行内容为`XXX.src`中的第$i$行和`XXX.trg`中的第$i$行连接，用'\t'分隔。
- 创建训练数据的“源字典”和“目标字典”。每个字典都有**DICTSIZE**个单词，包括：语料中词频最高的（DICTSIZE - 3）个单词，和3个特殊符号`<s>`（序列的开始）、`<e>`（序列的结束）和`<unk>`（未登录词）。
- Create source dictionary and target dictionary, each containing **DICTSIZE** number of words, including the most frequent (DICTSIZE - 3) fo word from the corpus and 3 special token `<s>` (begin of sequence), `<e>` (end of sequence) and `<unk>` (unknown words that are not in the vocabulary). ### 示例数据
### A Subset of Dataset 因为完整的数据集数据量较大，为了验证训练流程，PaddlePaddle接口paddle.dataset.wmt14中默认提供了一个经过预处理的[较小规模的数据集](http://paddlepaddle.bj.bcebos.com/demo/wmt_shrinked_data/wmt14.tgz)。
Because the full dataset is very big, to reduce the time for downloading the full dataset. PadddlePaddle package `paddle.dataset.wmt14` provides a preprocessed `subset of dataset`(http://paddlepaddle.bj.bcebos.com/demo/wmt_shrinked_data/wmt14.tgz). 该数据集有193319条训练数据，6003条测试数据，词典长度为30000。因为数据规模限制，使用该数据集训练出来的模型效果无法保证。
This subset has 193319 instances of training data and 6003 instances of test data. Dictionary size is 30000. Because of the limitation of size of the subset, the effectiveness of trained model from this subset is not guaranteed. ## 流程说明
## Training Instructions ### paddle初始化
### Initialize PaddlePaddle
```python ```python
# 加载 paddle的python包
import sys import sys
import paddle.v2 as paddle import paddle.v2 as paddle
# train with a single CPU # 配置只使用cpu，并且使用一个cpu进行训练
paddle.init(use_gpu=False, trainer_count=1) paddle.init(use_gpu=False, trainer_count=1)
# False: training, True: generating # 训练模式False，生成模式True
is_generating = False is_generating = False
``` ```
### Model Configuration ### 模型结构
1. 首先，定义了一些全局变量。
1. Define some global variables
```python ```python
dict_size = 30000 # dict dim dict_size = 30000 # 字典维度
source_dict_dim = dict_size # source language dictionary size source_dict_dim = dict_size # 源语言字典维度
target_dict_dim = dict_size # destination language dictionary size target_dict_dim = dict_size # 目标语言字典维度
word_vector_dim = 512 # word embedding dimension word_vector_dim = 512 # 词向量维度
encoder_size = 512 # hidden layer size of GRU in encoder encoder_size = 512 # 编码器中的GRU隐层大小
decoder_size = 512 # hidden layer size of GRU in decoder decoder_size = 512 # 解码器中的GRU隐层大小
beam_size = 3 # expand width in beam search beam_size = 3 # 柱宽度
max_length = 250 # a stop condition of sequence generation max_length = 250 # 生成句子的最大长度
``` ```
2. Implement Encoder as follows: 2. 其次，实现编码器框架。分为三步：
- Input is a sequence of words represented by an integer word index sequence. So we define data layer of data type `integer_value_sequence`. The value range of each element in the sequence is `[0, source_dict_dim)`
- 输入是一个文字序列，被表示成整型的序列。序列中每个元素是文字在字典中的索引。所以，我们定义数据层的数据类型为`integer_value_sequence`（整型序列），序列中每个元素的范围是`[0, source_dict_dim)`。
```python ```python
src_word_id = paddle.layer.data( src_word_id = paddle.layer.data(
name='source_language_word', name='source_language_word',
type=paddle.data_type.integer_value_sequence(source_dict_dim)) type=paddle.data_type.integer_value_sequence(source_dict_dim))
``` ```
- 将上述编码映射到低维语言空间的词向量$\mathbf{s}$。
- Map the one-hot vector (represented by word index) into a word vector $\mathbf{s}$ in a low-dimensional semantic space
```python ```python
src_embedding = paddle.layer.embedding( src_embedding = paddle.layer.embedding(
...@@ -291,8 +255,7 @@ is_generating = False ...@@ -291,8 +255,7 @@ is_generating = False
size=word_vector_dim, size=word_vector_dim,
param_attr=paddle.attr.ParamAttr(name='_source_language_embedding')) param_attr=paddle.attr.ParamAttr(name='_source_language_embedding'))
``` ```
- 用双向GRU编码源语言序列，拼接两个GRU的编码结果得到$\mathbf{h}$。
- Use bi-direcitonal GRU to encode the source language sequence, and concatenate the encoding outputs from the two GRUs to get $\mathbf{h}$
```python ```python
src_forward = paddle.networks.simple_gru( src_forward = paddle.networks.simple_gru(
...@@ -302,9 +265,9 @@ is_generating = False ...@@ -302,9 +265,9 @@ is_generating = False
encoded_vector = paddle.layer.concat(input=[src_forward, src_backward]) encoded_vector = paddle.layer.concat(input=[src_forward, src_backward])
``` ```
3. Implement Attention-based Decoder as follows: 3. 接着，定义基于注意力机制的解码器框架。分为三步：
- Get a projection of the encoding (c.f. 2.3) of the source language sequence by passing it into a feed forward neural network - 对源语言序列编码后的结果（见2的最后一步），过一个前馈神经网络（Feed Forward Neural Network），得到其映射。
```python ```python
with paddle.layer.mixed(size=decoder_size) as encoded_proj: with paddle.layer.mixed(size=decoder_size) as encoded_proj:
...@@ -312,7 +275,7 @@ is_generating = False ...@@ -312,7 +275,7 @@ is_generating = False
input=encoded_vector) input=encoded_vector)
``` ```
- Use a non-linear transformation of the last hidden state of the backward GRU on the source language sentence as the initial state of the decoder RNN $c_0=h_T$ - 构造解码器RNN的初始状态。由于解码器需要预测时序目标序列，但在0时刻并没有初始值，所以我们希望对其进行初始化。这里采用的是将源语言序列逆序编码后的最后一个状态进行非线性映射，作为该初始值，即$c_0=h_T$。
```python ```python
backward_first = paddle.layer.first_seq(input=src_backward) backward_first = paddle.layer.first_seq(input=src_backward)
...@@ -322,13 +285,12 @@ is_generating = False ...@@ -322,13 +285,12 @@ is_generating = False
input=backward_first) input=backward_first)
``` ```
- Define the computation in each time step for the decoder RNN, i.e., according to the current context vector $c_i$, hidden state for the decoder $z_i$ and the $i$-th word $u_i$ in the target language to predict the probability $p_{i+1}$ for the $i+1$-th word. - 定义解码阶段每一个时间步的RNN行为，即根据当前时刻的源语言上下文向量$c_i$、解码器隐层状态$z_i$和目标语言中第$i$个词$u_i$，来预测第$i+1$个词的概率$p_{i+1}$。
- decoder_mem记录了前一个时间步的隐层状态$z_i$，其初始状态是decoder_boot。
- decoder_mem records the hidden state $z_i$ from the previous time step, with an initial state as decoder_boot. - context通过调用`simple_attention`函数，实现公式$c_i=\sum {j=1}^{T}a_{ij}h_j$。其中，enc_vec是$h_j$，enc_proj是$h_j$的映射（见3.1），权重$a_{ij}$的计算已经封装在`simple_attention`函数中。
- context is computed via `simple_attention` as $c_i=\sum {j=1}^{T}a_{ij}h_j$, where enc_vec is the projection of $h_j$ and enc_proj is the projection of $h_j$ (c.f. 3.1). $a_{ij}$ is calculated within `simple_attention`. - decoder_inputs融合了$c_i$和当前目标词current_word（即$u_i$）的表示。
- decoder_inputs fuse $c_i$ with the representation of the current_word (i.e., $u_i$). - gru_step通过调用`gru_step_layer`函数，在decoder_inputs和decoder_mem上做了激活操作，即实现公式$z_{i+1}=\phi _{\theta '}\left ( c_i,u_i,z_i \right )$。
- gru_step uses `gru_step_layer` function to compute $z_{i+1}=\phi _{\theta '}\left ( c_i,u_i,z_i \right )$. - 最后，使用softmax归一化计算单词的概率，将out结果返回，即实现公式$p\left ( u_i|u_{&lt;i},\mathbf{x} \right )=softmax(W_sz_i+b_z)$。
- Softmax normalization is used in the end to computed the probability of words, i.e., $p\left ( u_i|u_{&lt;i},\mathbf{x} \right )=softmax(W_sz_i+b_z)$. The output is returned.
```python ```python
def gru_decoder_with_attention(enc_vec, enc_proj, current_word): def gru_decoder_with_attention(enc_vec, enc_proj, current_word):
...@@ -360,7 +322,7 @@ is_generating = False ...@@ -360,7 +322,7 @@ is_generating = False
return out return out
``` ```
4. Define the name for the decoder and the first two input for `gru_decoder_with_attention`. Note that `StaticInput` is used for the two inputs. Please refer to [StaticInput Document](https://github.com/PaddlePaddle/Paddle/blob/develop/doc/howto/deep_model/rnn/recurrent_group_cn.md#输入) for more details. 4. 定义解码器框架名字，和`gru_decoder_with_attention`函数的前两个输入。注意：这两个输入使用`StaticInput`，具体说明可见[StaticInput文档](https://github.com/PaddlePaddle/Paddle/blob/develop/doc/howto/deep_model/rnn/recurrent_group_cn.md#输入)。
```python ```python
decoder_group_name = "decoder_group" decoder_group_name = "decoder_group"
...@@ -369,18 +331,18 @@ is_generating = False ...@@ -369,18 +331,18 @@ is_generating = False
group_inputs = [group_input1, group_input2] group_inputs = [group_input1, group_input2]
``` ```
5. Training mode: 5. 训练模式下的解码器调用：
- word embedding from the target language trg_embedding is passed to `gru_decoder_with_attention` as current_word. - 首先，将目标语言序列的词向量trg_embedding，直接作为训练模式下的current_word传给`gru_decoder_with_attention`函数。
- `recurrent_group` calls `gru_decoder_with_attention` in a recurrent way - 其次，使用`recurrent_group`函数循环调用`gru_decoder_with_attention`函数。
- the sequence of next words from the target language is used as label (lbl) - 接着，使用目标语言的下一个词序列作为标签层lbl，即预测目标词。
- multi-class cross-entropy (`classification_cost`) is used to calculate the cost - 最后，用多类交叉熵损失函数`classification_cost`来计算损失值。
```python ```python
if not is_generating: if not is_generating:
trg_embedding = paddle.layer.embedding( trg_embedding = paddle.layer.embedding(
input=paddle.layer.data( input=paddle.layer.data(
name='target_language_word', name='target_language_word',
type=paddle.data_type.integer_value_sequence(target_dict_dim)), type=paddle.data_type.integer_value_sequence(target_dict_dim)),
size=word_vector_dim, size=word_vector_dim,
param_attr=paddle.attr.ParamAttr(name='_target_language_embedding')) param_attr=paddle.attr.ParamAttr(name='_target_language_embedding'))
...@@ -400,12 +362,12 @@ is_generating = False ...@@ -400,12 +362,12 @@ is_generating = False
name='target_language_next_word', name='target_language_next_word',
type=paddle.data_type.integer_value_sequence(target_dict_dim)) type=paddle.data_type.integer_value_sequence(target_dict_dim))
cost = paddle.layer.classification_cost(input=decoder, label=lbl) cost = paddle.layer.classification_cost(input=decoder, label=lbl)
``` ```
6. Generating mode: 6. 生成模式下的解码器调用：
- the decoder predicts a next target word based on the the last generated target word. Embedding of the last generated word is automatically gotten by GeneratedInputs. - 首先，在序列生成任务中，由于解码阶段的RNN总是引用上一时刻生成出的词的词向量，作为当前时刻的输入，因此，使用`GeneratedInput`来自动完成这一过程。具体说明可见[GeneratedInput文档](https://github.com/PaddlePaddle/Paddle/blob/develop/doc/howto/deep_model/rnn/recurrent_group_cn.md#输入)。
- `beam_search` calls `gru_decoder_with_attention` in a recurrent way, to predict sequence id. - 其次，使用`beam_search`函数循环调用`gru_decoder_with_attention`函数，生成出序列id。
```python ```python
if is_generating: if is_generating:
...@@ -434,13 +396,13 @@ is_generating = False ...@@ -434,13 +396,13 @@ is_generating = False
max_length=max_length) max_length=max_length)
``` ```
Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with a few simplifications. Please refer to [issue #1133](https://github.com/PaddlePaddle/Paddle/issues/1133) for more details. 注意：我们提供的配置在Bahdanau的论文\[[4](#参考文献)\]上做了一些简化，可参考[issue #1133](https://github.com/PaddlePaddle/Paddle/issues/1133)。
## Model Training ### 训练模型
1. Create Parameters 1. 参数定义
Create every parameter that `cost` layer needs. And we can get parameter names. If the parameter name is not specified during model configuration, it will be generated. 依据模型配置的`cost`定义模型参数。可以打印参数名字，如果在网络配置中没有指定名字，则默认生成。
```python ```python
if not is_generating: if not is_generating:
...@@ -449,9 +411,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -449,9 +411,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
print param print param
``` ```
2. Define DataSet 2. 数据定义
Create [**data reader**](https://github.com/PaddlePaddle/Paddle/tree/develop/doc/design/reader#python-data-reader-design-doc) for WMT-14 dataset. 获取wmt14的dataset reader。
```python ```python
if not is_generating: if not is_generating:
...@@ -460,9 +422,10 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -460,9 +422,10 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
paddle.dataset.wmt14.train(dict_size=dict_size), buf_size=8192), paddle.dataset.wmt14.train(dict_size=dict_size), buf_size=8192),
batch_size=5) batch_size=5)
``` ```
3. Create trainer
We need to tell trainer what to optimize, and how to optimize. Here trainer will optimize `cost` layer using stochastic gradient descent (SDG). 3. 构造trainer
根据优化目标cost,网络拓扑结构和模型参数来构造出trainer用来训练，在构造时还需指定优化方法，这里使用最基本的SGD方法。
```python ```python
if not is_generating: if not is_generating:
...@@ -474,9 +437,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -474,9 +437,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
update_equation=optimizer) update_equation=optimizer)
``` ```
4. Define event handler 4. 构造event_handler
The event handler is a callback function invoked by trainer when an event happens. Here we will print log in event handler. 可以通过自定义回调函数来评估训练过程中的各种状态，比如错误率等。下面的代码通过event.batch_id % 2 == 0 指定每2个batch打印一次日志，包含cost等信息。
```python ```python
if not is_generating: if not is_generating:
...@@ -487,7 +450,7 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -487,7 +450,7 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
event.pass_id, event.batch_id, event.cost, event.metrics) event.pass_id, event.batch_id, event.cost, event.metrics)
``` ```
5. Start training 5. 启动训练
```python ```python
if not is_generating: if not is_generating:
...@@ -495,29 +458,30 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -495,29 +458,30 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
reader=wmt14_reader, event_handler=event_handler, num_passes=2) reader=wmt14_reader, event_handler=event_handler, num_passes=2)
``` ```
The training log is as follows: 训练开始后，可以观察到event_handler输出的日志如下：
```text ```text
Pass 0, Batch 0, Cost 247.408008, {'classification_error_evaluator': 1.0} Pass 0, Batch 0, Cost 148.444983, {'classification_error_evaluator': 1.0}
Pass 0, Batch 10, Cost 212.058789, {'classification_error_evaluator': 0.8737863898277283} .........
... Pass 0, Batch 10, Cost 335.896802, {'classification_error_evaluator': 0.9325153231620789}
``` .........
```
## Model Usage ### 生成模型
1. Download Pre-trained Model 1. 加载预训练的模型
As the training of an NMT model is very time consuming, we provide a pre-trained model. The model is trained with a cluster of 50 physical nodes (each node has two 6-core CPU) over 5 days. The provided model has the [BLEU Score](#BLEU Score) of 26.92, and the size of 205M. 由于NMT模型的训练非常耗时，我们在50个物理节点（每节点含有2颗6核CPU）的集群中，花了5天时间训练了一个模型供大家直接下载使用。该模型大小为205MB，[BLEU评估](#BLEU评估)值为26.92。
```python ```python
if is_generating: if is_generating:
parameters = paddle.dataset.wmt14.model() parameters = paddle.dataset.wmt14.model()
``` ```
2. Define DataSet 2. 数据定义
Get the first 3 samples of wmt14 generating set as the source language sequences. 从wmt14的生成集中读取前3个样本作为源语言句子。
```python ```python
if is_generating: if is_generating:
gen_creator = paddle.dataset.wmt14.gen(dict_size) gen_creator = paddle.dataset.wmt14.gen(dict_size)
gen_data = [] gen_data = []
gen_num = 3 gen_num = 3
...@@ -525,26 +489,26 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -525,26 +489,26 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
gen_data.append((item[0], )) gen_data.append((item[0], ))
if len(gen_data) == gen_num: if len(gen_data) == gen_num:
break break
``` ```
3. 构造infer
3. Create infer
Use inference interface `paddle.infer` return the prediction probability (see field `prob`) and labels (see field `id`) of each generated sequence. 根据网络拓扑结构和模型参数构造出infer用来生成，在预测时还需要指定输出域`field`，这里使用生成句子的概率`prob`和句子中每个词的`id`。
```python ```python
if is_generating: if is_generating:
beam_result = paddle.infer( beam_result = paddle.infer(
output_layer=beam_gen, output_layer=beam_gen,
parameters=parameters, parameters=parameters,
input=gen_data, input=gen_data,
field=['prob', 'id']) field=['prob', 'id'])
``` ```
4. Print generated translation
Print sequence and its `beam_size` generated translation results based on the dictionary. 4. 打印生成结果
```python 根据源/目标语言字典，将源语言句子和`beam_size`个生成句子打印输出。
if is_generating:
```python
if is_generating:
# get the dictionary # get the dictionary
src_dict, trg_dict = paddle.dataset.wmt14.get_dict(dict_size) src_dict, trg_dict = paddle.dataset.wmt14.get_dict(dict_size)
...@@ -566,9 +530,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -566,9 +530,9 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
[src_dict.get(w) for w in gen_data[i][0]]), "\n" [src_dict.get(w) for w in gen_data[i][0]]), "\n"
for j in xrange(beam_size): for j in xrange(beam_size):
print "prob = %f:" % (prob[i][j]), seq_list[i * beam_size + j] print "prob = %f:" % (prob[i][j]), seq_list[i * beam_size + j]
``` ```
The generating log is as follows: 生成开始后，可以观察到输出的日志如下：
```text ```text
src: <s> Les <unk> se <unk> au sujet de la largeur des sièges alors que de grosses commandes sont en jeu <e> src: <s> Les <unk> se <unk> au sujet de la largeur des sièges alors que de grosses commandes sont en jeu <e>
...@@ -577,11 +541,11 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with ...@@ -577,11 +541,11 @@ Note: Our configuration is based on Bahdanau et al. \[[4](#Reference)\] but with
prob = -19.512890: The <unk> will be rotated about the width of the seats , while large commands are at play . <e> prob = -19.512890: The <unk> will be rotated about the width of the seats , while large commands are at play . <e>
``` ```
## Summary ## 总结
End-to-end neural machine translation is a recently developed way to perform machine translations. In this chapter, we introduced the typical "Encoder-Decoder" framework and "attention" mechanism. Since NMT is a typical Sequence-to-Sequence (Seq2Seq) learning problem, tasks such as query rewriting, abstraction generation, and single-turn dialogues can all be solved with the model presented in this chapter. 端到端的神经网络机器翻译是近几年兴起的一种全新的机器翻译方法。本章中，我们介绍了NMT中典型的“编码器-解码器”框架和“注意力”机制。由于NMT是一个典型的Seq2Seq（Sequence to Sequence，序列到序列）学习问题，因此，Seq2Seq中的query改写（query rewriting）、摘要、单轮对话等问题都可以用本教程的模型来解决。
## References ## 参考文献
1. Koehn P. [Statistical machine translation](https://books.google.com.hk/books?id=4v_Cx1wIMLkC&printsec=frontcover&hl=zh-CN&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)[M]. Cambridge University Press, 2009. 1. Koehn P. [Statistical machine translation](https://books.google.com.hk/books?id=4v_Cx1wIMLkC&printsec=frontcover&hl=zh-CN&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)[M]. Cambridge University Press, 2009.
2. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](http://www.aclweb.org/anthology/D/D14/D14-1179.pdf)[C]//Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014: 1724-1734. 2. Cho K, Van Merriënboer B, Gulcehre C, et al. [Learning phrase representations using RNN encoder-decoder for statistical machine translation](http://www.aclweb.org/anthology/D/D14/D14-1179.pdf)[C]//Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014: 1724-1734.
...@@ -590,7 +554,7 @@ End-to-end neural machine translation is a recently developed way to perform mac ...@@ -590,7 +554,7 @@ End-to-end neural machine translation is a recently developed way to perform mac
5. Papineni K, Roukos S, Ward T, et al. [BLEU: a method for automatic evaluation of machine translation](http://dl.acm.org/citation.cfm?id=1073135)[C]//Proceedings of the 40th annual meeting on association for computational linguistics. Association for Computational Linguistics, 2002: 311-318. 5. Papineni K, Roukos S, Ward T, et al. [BLEU: a method for automatic evaluation of machine translation](http://dl.acm.org/citation.cfm?id=1073135)[C]//Proceedings of the 40th annual meeting on association for computational linguistics. Association for Computational Linguistics, 2002: 311-318.
<br/> <br/>
This tutorial is contributed by <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a>, and licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>. <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
</div> </div>
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# 深度学习入门 # 深度学习入门
[![Build Status](https://travis-ci.org/PaddlePaddle/book.svg?branch=develop)](https://travis-ci.org/PaddlePaddle/book) [![Build Status](https://travis-ci.org/PaddlePaddle/book.svg?branch=develop)](https://travis-ci.org/PaddlePaddle/book)
[![Documentation Status](https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat)](http://book.paddlepaddle.org/index.en.html) [![Documentation Status](https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat)](http://book.paddlepaddle.org/)
[![Documentation Status](https://img.shields.io/badge/中文文档-最新-brightgreen.svg)](http://book.paddlepaddle.org) [![Documentation Status](https://img.shields.io/badge/中文文档-最新-brightgreen.svg)](http://book.paddlepaddle.org/index.cn.html)
[![License](https://img.shields.io/badge/license-Apache%202-blue.svg)](LICENSE) [![License](https://img.shields.io/badge/license-Apache%202-blue.svg)](LICENSE)
1. [新手入门](http://book.paddlepaddle.org/01.fit_a_line) 1. [新手入门](http://book.paddlepaddle.org/01.fit_a_line/index.cn.html)
1. [识别数字](http://book.paddlepaddle.org/02.recognize_digits) 1. [识别数字](http://book.paddlepaddle.org/02.recognize_digits/index.cn.html)
1. [图像分类](http://book.paddlepaddle.org/03.image_classification) 1. [图像分类](http://book.paddlepaddle.org/03.image_classification/index.cn.html)
1. [词向量](http://book.paddlepaddle.org/04.word2vec) 1. [词向量](http://book.paddlepaddle.org/04.word2vec/index.cn.html)
1. [个性化推荐](http://book.paddlepaddle.org/05.recommender_system) 1. [个性化推荐](http://book.paddlepaddle.org/05.recommender_system/index.cn.html)
1. [情感分析](http://book.paddlepaddle.org/06.understand_sentiment) 1. [情感分析](http://book.paddlepaddle.org/06.understand_sentiment/index.cn.html)
1. [语义角色标注](http://book.paddlepaddle.org/07.label_semantic_roles) 1. [语义角色标注](http://book.paddlepaddle.org/07.label_semantic_roles/index.cn.html)
1. [机器翻译](http://book.paddlepaddle.org/08.machine_translation) 1. [机器翻译](http://book.paddlepaddle.org/08.machine_translation/index.cn.html)
## 运行这本书 ## 运行这本书
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# Deep Learning with PaddlePaddle # Deep Learning with PaddlePaddle
1. [Fit a Line](http://book.paddlepaddle.org/01.fit_a_line/index.en.html) [![Build Status](https://travis-ci.org/PaddlePaddle/book.svg?branch=develop)](https://travis-ci.org/PaddlePaddle/book)
1. [Recognize Digits](http://book.paddlepaddle.org/02.recognize_digits/index.en.html) [![Documentation Status](https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat)](http://book.paddlepaddle.org/)
1. [Image Classification](http://book.paddlepaddle.org/03.image_classification/index.en.html) [![Documentation Status](https://img.shields.io/badge/中文文档-最新-brightgreen.svg)](http://book.paddlepaddle.org/index.cn.html)
1. [Word to Vector](http://book.paddlepaddle.org/04.word2vec/index.en.html) [![License](https://img.shields.io/badge/license-Apache%202-blue.svg)](LICENSE)
1. [Recommender System](http://book.paddlepaddle.org/05.recommender_system/index.en.html)
1. [Understand Sentiment](http://book.paddlepaddle.org/06.understand_sentiment/index.en.html) 1. [Fit a Line](http://book.paddlepaddle.org/01.fit_a_line/)
1. [Label Semantic Roles](http://book.paddlepaddle.org/07.label_semantic_roles/index.en.html) 1. [Recognize Digits](http://book.paddlepaddle.org/02.recognize_digits/)
1. [Machine Translation](http://book.paddlepaddle.org/08.machine_translation/index.en.html) 1. [Image Classification](http://book.paddlepaddle.org/03.image_classification/)
1. [Word to Vector](http://book.paddlepaddle.org/04.word2vec/)
1. [Recommender System](http://book.paddlepaddle.org/05.recommender_system/)
1. [Understand Sentiment](http://book.paddlepaddle.org/06.understand_sentiment/)
1. [Label Semantic Roles](http://book.paddlepaddle.org/07.label_semantic_roles/)
1. [Machine Translation](http://book.paddlepaddle.org/08.machine_translation/)
## Running the Book ## Running the Book
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index.en.html → index.cn.html
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<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="zh-Hans">
<head> <head>
<meta charset="UTF-8"> <meta charset="UTF-8">
<title>Deep Learning 101</title> <title>深度学习入门</title>
<link href="http://cdn.bootcss.com/bootstrap/4.0.0-alpha.6/css/bootstrap.min.css" rel="stylesheet"> <link href="http://cdn.bootcss.com/bootstrap/4.0.0-alpha.6/css/bootstrap.min.css" rel="stylesheet">
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...@@ -26,6 +26,10 @@ ...@@ -26,6 +26,10 @@
} }
.left-panel .card-header a {
font-size: 14px;
}
.left-panel .card-block a:not(.click_active) { .left-panel .card-block a:not(.click_active) {
background: #e4e6e9; background: #e4e6e9;
...@@ -70,17 +74,17 @@ ...@@ -70,17 +74,17 @@
<ul class="nav navbar-nav"> <ul class="nav navbar-nav">
<li class="nav-item"> <li class="nav-item">
<a class="nav-link" href="http://paddlepaddle.org"> <a class="nav-link" href="http://paddlepaddle.org">
Home 首页
</a>
</li>
<li class="nav-item ">
<a class="nav-link" href="./index.html">
中文
</a> </a>
</li> </li>
<li class="nav-item active"> <li class="nav-item active">
<a class="nav-link" href="#"> <a class="nav-link" href="#">
Deep Learning 101 深度学习入门
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English
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...@@ -96,7 +100,7 @@ ...@@ -96,7 +100,7 @@
<div class="card-header" role="tab" id="headingOne"> <div class="card-header" role="tab" id="headingOne">
<h5 class="mb-0"> <h5 class="mb-0">
<a aria-expanded="true" aria-controls="collapseOne"> <a aria-expanded="true" aria-controls="collapseOne">
Deep Learning 101<span class="sr-only">(current)</span> 深度学习入门
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...@@ -104,36 +108,36 @@ ...@@ -104,36 +108,36 @@
<div class="card-block pl-0 pr-0 pt-0 pb-0"> <div class="card-block pl-0 pr-0 pt-0 pb-0">
<div class="list-group "> <div class="list-group ">
<a href="./01.fit_a_line/index.en.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./01.fit_a_line/index.cn.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
Linear Regression 新手入门
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Recognize Digits 识别数字
</a> </a>
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Image Classification 图像分类
</a> </a>
<a href="./04.word2vec/index.en.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./04.word2vec/index.cn.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
Word2Vec 词向量
</a> </a>
<a href="./05.recommender_system/index.en.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./05.recommender_system/index.cn.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
Personalized Recommendation 个性化推荐
</a> </a>
<a href="./06.understand_sentiment/index.en.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./06.understand_sentiment/index.cn.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
Sentiment Analysis 情感分析
</a> </a>
<a href="./07.label_semantic_roles/index.en.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./07.label_semantic_roles/index.cn.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
Semantic Role Labeling 语义角色标注
</a> </a>
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Machine Translation 机器翻译
</a> </a>
</div> </div>
...@@ -143,7 +147,7 @@ ...@@ -143,7 +147,7 @@
</div> </div>
</div> </div>
<div class="col"> <div class="col">
<iframe src="./01.fit_a_line/index.en.html" style="border: none; overflow-y : hidden" width="100%" height="100%" name="content_iframe" id="content_iframe"> <iframe src="./01.fit_a_line/index.html" style="border: none; overflow-y : hidden" width="100%" height="100%" name="content_iframe" id="content_iframe">
</iframe> </iframe>
</div> </div>
</div> </div>
......
index.html
浏览文件 @ 75490426
<!DOCTYPE html> <!DOCTYPE html>
<html lang="zh-Hans"> <html lang="en">
<head> <head>
<meta charset="UTF-8"> <meta charset="UTF-8">
<title>深度学习入门</title> <title>Deep Learning 101</title>
<link href="http://cdn.bootcss.com/bootstrap/4.0.0-alpha.6/css/bootstrap.min.css" rel="stylesheet"> <link href="http://cdn.bootcss.com/bootstrap/4.0.0-alpha.6/css/bootstrap.min.css" rel="stylesheet">
<script src="http://cdn.bootcss.com/tether/1.4.0/js/tether.js"></script> <script src="http://cdn.bootcss.com/tether/1.4.0/js/tether.js"></script>
<script src="http://cdn.bootcss.com/jquery/3.1.0/jquery.slim.js"></script> <script src="http://cdn.bootcss.com/jquery/3.1.0/jquery.slim.js"></script>
...@@ -26,10 +26,6 @@ ...@@ -26,10 +26,6 @@
} }
.left-panel .card-header a {
font-size: 14px;
}
.left-panel .card-block a:not(.click_active) { .left-panel .card-block a:not(.click_active) {
background: #e4e6e9; background: #e4e6e9;
...@@ -74,17 +70,17 @@ ...@@ -74,17 +70,17 @@
<ul class="nav navbar-nav"> <ul class="nav navbar-nav">
<li class="nav-item"> <li class="nav-item">
<a class="nav-link" href="http://paddlepaddle.org"> <a class="nav-link" href="http://paddlepaddle.org">
首页 Home
</a> </a>
</li> </li>
<li class="nav-item active"> <li class="nav-item ">
<a class="nav-link" href="#"> <a class="nav-link" href="./index.html">
深度学习入门 中文
</a> </a>
</li> </li>
<li class="nav-item "> <li class="nav-item active">
<a class="nav-link" href="./index.en.html"> <a class="nav-link" href="#">
English Deep Learning 101
</a> </a>
</li> </li>
<li class="nav-item"> <li class="nav-item">
...@@ -100,7 +96,7 @@ ...@@ -100,7 +96,7 @@
<div class="card-header" role="tab" id="headingOne"> <div class="card-header" role="tab" id="headingOne">
<h5 class="mb-0"> <h5 class="mb-0">
<a aria-expanded="true" aria-controls="collapseOne"> <a aria-expanded="true" aria-controls="collapseOne">
深度学习入门 Deep Learning 101<span class="sr-only">(current)</span>
</a> </a>
</h5> </h5>
</div> </div>
...@@ -109,35 +105,35 @@ ...@@ -109,35 +105,35 @@
<div class="list-group "> <div class="list-group ">
<a href="./01.fit_a_line/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./01.fit_a_line/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
新手入门 Linear Regression
</a> </a>
<a href="./02.recognize_digits/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./02.recognize_digits/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
识别数字 Recognize Digits
</a> </a>
<a href="./03.image_classification/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./03.image_classification/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
图像分类 Image Classification
</a> </a>
<a href="./04.word2vec/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./04.word2vec/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
词向量 Word2Vec
</a> </a>
<a href="./05.recommender_system/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./05.recommender_system/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
个性化推荐 Personalized Recommendation
</a> </a>
<a href="./06.understand_sentiment/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./06.understand_sentiment/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
情感分析 Sentiment Analysis
</a> </a>
<a href="./07.label_semantic_roles/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./07.label_semantic_roles/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
语义角色标注 Semantic Role Labeling
</a> </a>
<a href="./08.machine_translation/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;"> <a href="./08.machine_translation/index.html" target="content_iframe" class="list-group-item list-group-item-action" style="border: 0px; border-bottom: 2px solid #dddfe3;">
机器翻译 Machine Translation
</a> </a>
</div> </div>
...@@ -147,7 +143,7 @@ ...@@ -147,7 +143,7 @@
</div> </div>
</div> </div>
<div class="col"> <div class="col">
<iframe src="./01.fit_a_line/index.html" style="border: none; overflow-y : hidden" width="100%" height="100%" name="content_iframe" id="content_iframe"> <iframe src="./01.fit_a_line/index.en.html" style="border: none; overflow-y : hidden" width="100%" height="100%" name="content_iframe" id="content_iframe">
</iframe> </iframe>
</div> </div>
</div> </div>
......
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