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#!/bin/bash
for file in `find . -name '*.md' | grep -v '^./README.md'`
do
bash .tmpl/convert-markdown-into-html.sh $file > `dirname $file`/index.html
for i in $(du -a | grep '\.\/.\+\/README.md' | cut -f 2); do
.tmpl/convert-markdown-into-html.sh $i > $(dirname $i)/index.html
done
for i in $(du -a | grep '\.\/.\+\/README.en.md' | cut -f 2); do
.tmpl/convert-markdown-into-html.sh $i > $(dirname $i)/index.en.html
done
fit_a_line/README.en.md
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......@@ -13,8 +13,8 @@ where $\omega_{d}$ and $b$ are the model parameters we want to estimate. Once th
## Results Demonstration
We first show the training result of our model. We use the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) to train a linear model and predict the house prices in Boston. The figure below shows the predictions the model makes for some house prices. The $X$ coordinate of each point represents the median value of the prices of a certain type of houses, while the $Y$ coordinate represents the predicted value by our linear model. When $X=Y$, the point lies exactly on the dotted line. In other words, the more precise the model predicts, the closer the point is to the dotted line.
<p align="center">
<img src = "image/predictions.png" width=400><br/>
Figure 1. Predicted Value V.S. Actual Value (波士顿房价预测->Prediction of Boston house prices; 预测价格->Predicted prices; 单位->Units; 实际价格->Actual prices)
<img src = "image/predictions_en.png" width=400><br/>
Figure 1. Predicted Value V.S. Actual Value
</p>
## Model Overview
......@@ -85,8 +85,8 @@ There are at least three reasons for [Feature Normalization](https://en.wikipedi
- Many Machine Learning techniques or models (e.g., L1/L2 regularization and Vector Space Model) are based on the assumption that all the features have roughly zero means and their value ranges are similar.
<p align="center">
<img src = "image/ranges.png" width=550><br/>
Figure 2. The value ranges of the features (特征尺度->Feature value range)
<img src = "image/ranges_en.png" width=550><br/>
Figure 2. The value ranges of the features
</p>
#### Prepare Training and Test Sets
......
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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 house prices. Some important concepts in Machine Learning will be covered through this example.
The source code for this tutorial is at [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/fit_a_line). If this is your first time using PaddlePaddle, please refer to the [Install Guide](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html).
## Problem
Suppose we have a dataset of $n$ houses. Each house $i$ has $d$ properties and the price $y_i$. A property $x_{i,d}$ describes one aspect of the house, for example, the number of rooms in the house, the number of schools or hospitals in the neighborhood, the nearby traffic condition, etc. Our task is to predict $y_i$ given a set of properties $\{x_{i,1}, ..., x_{i,d}\}$. We assume that the price is a linear combination of all the properties, i.e.,
$$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b, i=1,\ldots,n$$
where $\omega_{d}$ and $b$ are the model parameters we want to estimate. Once they are learned, given a set of properties of a house, we will be able to predict a price for that house. The model we have here is called Linear Regression, namely, we want to regress a value as a linear combination of several values. In practice this linear model for our problem is hardly true, because the real relationship between the house properties and the price is much more complicated. However, due to its simple formulation which makes the model training and analysis easy, Linear Regression has been applied to lots of real problems. It is always an important topic in many classical Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
## Results Demonstration
We first show the training result of our model. We use the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) to train a linear model and predict the house prices in Boston. The figure below shows the predictions the model makes for some house prices. The $X$ coordinate of each point represents the median value of the prices of a certain type of houses, while the $Y$ coordinate represents the predicted value by our linear model. When $X=Y$, the point lies exactly on the dotted line. In other words, 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 house properties $x_{i,d}$ that are related to the median house price $y_i$. Thus our model is:
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
where $\hat{Y}$ is the predicted value used to differentiate from the actual value $Y$. The model parameters to be learned are: $\omega_1, \ldots, \omega_{13}, b$, where $\omega$ are called the weights and $b$ is called the bias.
Now we need an optimization goal, so that with the learned parameters, $\hat{Y}$ is close to $Y$ as much as possible. Here we introduce the concept of [Loss Function (Cost Function)](https://en.wikipedia.org/wiki/Loss_function). The Loss Function has such property: given any pair of the actual value $y_i$ and the predicted value $\hat{y_i}$, its output is always non-negative. This non-negative value reflects 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:
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
For a dataset of size $n$, MSE is the average value of the $n$ predicted errors.
### Training
After defining our model, we have several major steps for the training:
1. Initialize the parameters including the weights $\omega$ and the bias $b$. For example, we can set their mean values as 0s, and their standard deviations as 1s.
2. Feedforward to compute the network output and the Loss Function.
3. Backward to [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.
## Data Preparation
Follow the command below to prepare data:
```bash
cd data && python prepare_data.py
```
This line of code will download the dataset from the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) and perform some [preprocessing](#Preprocessing). The dataset is split into a training set and a test set.
The dataset contains 506 lines in total, each line describing the properties and the median price of a certain type of houses in Boston. The meaning of each line is below:
| Property Name | Explanation | 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 house price.
### Preprocessing
#### Continuous and Discrete Data
We define a feature vector of length 13 for each house, where each entry of the feature vector corresponds to a property of that house. 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 digits such as 0, 1, or 2, it has a quite different meaning from a continuous value. The reason is that the difference between two discrete values has no practical meaning. For example, if we use 0, 1, and 2 to represent `red`, `green`, and `blue` respectively, although the numerical difference between `red` and `green` is smaller than that between `red` and `blue`, we cannot say that the extent to which `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 will usually convert it to $d$ new features where each feature can only take 0 or 1, indicating whether the original $d$th value is present or not. Or we can map the discrete feature to 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
Another observation we have is that there is a huge difference among the value ranges of the 13 features (Figure 2). For example, feature B has a value range of [0.32, 396.90] while feature NOX has a range of [0.3850, 0.8170]. For an effective optimization, here we need data normalization. The goal of data normalization is to scale each feature into roughly the same value range, for example [-0.5, 0.5]. In this example, we adopt a standard way of normalization: substracting the mean value from the feature and divide the result by the original value 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 different importances of different features to the model (at least in the beginning of the training process), which however is an unreasonable assumption. Such assumption makes the optimization more difficult and increases the training time a lot.
- Many Machine Learning techniques or models (e.g., L1/L2 regularization and Vector Space Model) are based on the assumption 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 into two subsets, one for estimating the model parameters, namely, 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 of 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 $8:2$. You can try different split ratios to observe how the two variances change.
Executing the following command to split the dataset and write the training and test set into the `train.list` and `test.list` files, so that later PaddlePaddle can read from them.
```python
python prepare_data.py -r 0.8 #8:2 is the default split ratio
```
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 begins. These hyperparameters are not part of the model parameters and cannot be trained using the same Loss Function (e.g., the number of layers in the network). Thus we will try several sets of hyperparameters to get several models, and compare these trained models on the validation set to pick the best one, and finally it on the test set. Because our model is relatively simple in this problem, we ignore this validation process for now.
### Provide Data to PaddlePaddle
After the data is prepared, we use a Python Data Provider to provide data for PaddlePaddle. A Data Provider is a Python function which will be called by PaddlePaddle during training. In this example, the Data Provider only needs to read the data and return it to the training process of PaddlePaddle line by line.
```python
from paddle.trainer.PyDataProvider2 import *
import numpy as np
#define data type and dimensionality
@provider(input_types=[dense_vector(13), dense_vector(1)])
def process(settings, input_file):
data = np.load(input_file.strip())
for row in data:
yield row[:-1].tolist(), row[-1:].tolist()
```
## Model Configuration
### Data Definition
We first call the function `define_py_data_sources2` to let PaddlePaddle read training and test data from the `dataprovider.py` in the above. PaddlePaddle can accept configuration info from the command line, for example, here we pass a variable named `is_predict` to control the model to have different structures during training and test.
```python
from paddle.trainer_config_helpers import *
is_predict = get_config_arg('is_predict', bool, False)
define_py_data_sources2(
train_list='data/train.list',
test_list='data/test.list',
module='dataprovider',
obj='process')
```
### Algorithm Settings
Next we need to set the details of the optimization algorithm. Due to the simplicity of the Linear Regression model, we only need to set the `batch_size` which defines how many samples are used every time for updating the parameters.
```python
settings(batch_size=2)
```
### Network
Finally, we use `fc_layer` and `LinearActivation` to represent the Linear Regression model.
```python
#input data of 13 dimensional house information
x = data_layer(name='x', size=13)
y_predict = fc_layer(
input=x,
param_attr=ParamAttr(name='w'),
size=1,
act=LinearActivation(),
bias_attr=ParamAttr(name='b'))
if not is_predict: #when training, we use MSE (i.e., regression_cost) as the Loss Function
y = data_layer(name='y', size=1)
cost = regression_cost(input=y_predict, label=y)
outputs(cost) #output MSE to view the loss change
else: #during test, output the prediction value
outputs(y_predict)
```
## Training Model
We can run the PaddlePaddle command line trainer in the root directory of the code. Here we name the configuration file as `trainer_config.py`. We train 30 passes and save the result in the directory `output`:
```bash
./train.sh
```
## Use Model
Now we can use the trained model to do prediction.
```bash
python predict.py
```
Here by default we use the model in `output/pass-00029` for prediction, and compare the actual house price with the predicted one. The result is shown in `predictions.png`.
If you want to use another model or test on other data, you can pass in a new model path or data path:
```bash
python predict.py -m output/pass-00020 -t data/housing.test.npy
```
## Summary
In this chapter, we have introduced the Linear Regression model using the UCI Housing Data Set as an example. We have shown how to train and test this model with PaddlePaddle. Many more complex models and techniques are derived from this simple linear model, thus it is important for us to understand how it works.
## 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/>
<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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......@@ -36,15 +36,8 @@ Figure 2. Fine-grained image classification
A good model should be able to recognize objects of different categories correctly, and meanwhile can correctly classify images taken from different points of view, under different illuminations, with object distortion or partial occlusion (we call these image disturbance). Figure 3 show some images with various disturbance. A good model should be able to classify these images correctly like humans.
<p align="center">
<img src="image/variations.png" width="550" ><br/>
<img src="image/variations_en.png" width="550" ><br/>
Figure 3. Disturbed images [22]
不同视角 ==> various perspective
不同大小 ==> various sizes
形变 ==> shape deformation
遮挡 ==> occlusion
不同光照 ==> various illumination
背景干扰 ==> cluttered background
同类异形 ==> homogeneous
</p>
## Model Overview
......@@ -72,13 +65,8 @@ Figure 4. Top-5 error rates on ILSVRC image classification
Traditional CNNs consist of convolutional and fully-connected layers, and employ softmax multi-category classifier and cross-entropy as loss function. Figure 5 shows a typical CNN. We first introduce the common parts of a CNN.
<p align="center">
<img src="image/lenet.png"><br/>
<img src="image/lenet_en.png"><br/>
Figure 5. A CNN example [20]
输入层 ==> input layer
卷积层 ==> convolutional layer
特征图 ==> feature maps
降采样（池化）层 ==> pooling layer
全连接层 ==> fully-connected layer
</p>
- convolutional layer: It uses convolution operation to extract low-level and high-level features, and to discover local correlation and spatial invariance.
......@@ -113,13 +101,8 @@ NIN model has two main characteristics: 1) it replaces the single-layer convolut
Figure 7 depicts two Inception blocks. Figure 7(a) is the simplest design, the output of which is a concat 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 of outputs. After going through several of such blocks, the number of outputs and parameters will become larger and larger, leading to higher computation complexity. To overcome this drawback, the Inception block in Figure 7(b) employs three 1x1 convolutional layers to reduce dimension or the number of channels, meanwhile improves non-linearity of the network.
<p align="center">
<img src="image/inception.png" width="800" ><br/>
<img src="image/inception_en.png" width="800" ><br/>
Figure 7. Inception block
输入层 ==> input layer
卷积层 ==> convolutional layer
最大池化层 ==> max-pooling layer
Inception简单模块 ==> Inception module, naive version
Inception含降维模块 ==> Inception module with dimensionality reduction
</p>
GoogleNet consists of multiple stacking Inception blocks followed by an avg-pooling layer as in NIN in place of by 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 backpropagating. The loss function of the whole network is the weighted sum of these three classifiers.
......@@ -476,12 +459,8 @@ Tester.cpp:115] Test samples=10000 cost=1.99246 Eval: classification_error_eval
Figure 12 shows the curve of training error rate, which indicates it converges at Pass 200 with error rate 8.54%.
<p align="center">
<img src="image/plot.png" width="400" ><br/>
<img src="image/plot_en.png" width="400" ><br/>
Figure 12. The error rate of VGG model on CIFAR10
训练轮数 ==> epoch
误差 ==> error
训练误差 ==> training error
测试误差 ==> test error
</p>
## Model Application
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import math
import numpy as np
import paddle.v2 as paddle
import paddle.v2.dataset.conll05 as conll05
def db_lstm():
word_dict, verb_dict, label_dict = conll05.get_dict()
word_dict_len = len(word_dict)
label_dict_len = len(label_dict)
pred_len = len(verb_dict)
mark_dict_len = 2
word_dim = 32
mark_dim = 5
hidden_dim = 512
depth = 8
#8 features
def d_type(size):
return paddle.data_type.integer_value_sequence(size)
word = paddle.layer.data(name='word_data', type=d_type(word_dict_len))
predicate = paddle.layer.data(name='verb_data', type=d_type(pred_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_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_p2 = paddle.layer.data(name='ctx_p2_data', type=d_type(word_dict_len))
mark = paddle.layer.data(name='mark_data', type=d_type(mark_dict_len))
target = paddle.layer.data(name='target', type=d_type(label_dict_len))
emb_para = paddle.attr.Param(name='emb', initial_std=0., is_static=True)
std_0 = paddle.attr.Param(initial_std=0.)
default_std = 1 / math.sqrt(hidden_dim) / 3.0
std_default = paddle.attr.Param(initial_std=default_std)
predicate_embedding = paddle.layer.embedding(
size=word_dim,
input=predicate,
param_attr=paddle.attr.Param(
name='vemb', initial_std=default_std))
mark_embedding = paddle.layer.embedding(
size=mark_dim, input=mark, param_attr=std_0)
word_input = [word, ctx_n2, ctx_n1, ctx_0, ctx_p1, ctx_p2]
emb_layers = [
paddle.layer.embedding(
size=word_dim, input=x, param_attr=emb_para) for x in word_input
]
emb_layers.append(predicate_embedding)
emb_layers.append(mark_embedding)
hidden_0 = paddle.layer.mixed(
size=hidden_dim,
bias_attr=std_default,
input=[
paddle.layer.full_matrix_projection(
input=emb, param_attr=std_default) for emb in emb_layers
])
mix_hidden_lr = 1e-3
lstm_para_attr = paddle.attr.Param(initial_std=0.0, learning_rate=1.0)
hidden_para_attr = paddle.attr.Param(
initial_std=default_std, learning_rate=mix_hidden_lr)
lstm_0 = paddle.layer.lstmemory(
input=hidden_0,
act=paddle.activation.Relu(),
gate_act=paddle.activation.Sigmoid(),
state_act=paddle.activation.Sigmoid(),
bias_attr=std_0,
param_attr=lstm_para_attr)
#stack L-LSTM and R-LSTM with direct edges
input_tmp = [hidden_0, lstm_0]
for i in range(1, depth):
mix_hidden = paddle.layer.mixed(
size=hidden_dim,
bias_attr=std_default,
input=[
paddle.layer.full_matrix_projection(
input=input_tmp[0], param_attr=hidden_para_attr),
paddle.layer.full_matrix_projection(
input=input_tmp[1], param_attr=lstm_para_attr)
])
lstm = paddle.layer.lstmemory(
input=mix_hidden,
act=paddle.activation.Relu(),
gate_act=paddle.activation.Sigmoid(),
state_act=paddle.activation.Sigmoid(),
reverse=((i % 2) == 1),
bias_attr=std_0,
param_attr=lstm_para_attr)
input_tmp = [mix_hidden, lstm]
feature_out = paddle.layer.mixed(
size=label_dict_len,
bias_attr=std_default,
input=[
paddle.layer.full_matrix_projection(
input=input_tmp[0], param_attr=hidden_para_attr),
paddle.layer.full_matrix_projection(
input=input_tmp[1], param_attr=lstm_para_attr)
], )
crf_cost = paddle.layer.crf(size=label_dict_len,
input=feature_out,
label=target,
param_attr=paddle.attr.Param(
name='crfw',
initial_std=default_std,
learning_rate=mix_hidden_lr))
crf_dec = paddle.layer.crf_decoding(
name='crf_dec_l',
size=label_dict_len,
input=feature_out,
label=target,
param_attr=paddle.attr.Param(name='crfw'))
return crf_cost, crf_dec
def load_parameter(file_name, h, w):
with open(file_name, 'rb') as f:
f.read(16) # skip header.
return np.fromfile(f, dtype=np.float32).reshape(h, w)
def main():
paddle.init(use_gpu=False, trainer_count=1)
# define network topology
crf_cost, crf_dec = db_lstm()
# create parameters
parameters = paddle.parameters.create([crf_cost, crf_dec])
parameters.set('emb', load_parameter(conll05.get_embedding(), 44068, 32))
# create optimizer
optimizer = paddle.optimizer.Momentum(
momentum=0,
learning_rate=2e-2,
regularization=paddle.optimizer.L2Regularization(rate=8e-4),
model_average=paddle.optimizer.ModelAverage(
average_window=0.5, max_average_window=10000), )
trainer = paddle.trainer.SGD(cost=crf_cost,
parameters=parameters,
update_equation=optimizer)
reader = paddle.reader.batched(
paddle.reader.shuffle(
conll05.test(), buf_size=8192), batch_size=10)
reader_dict = {
'word_data': 0,
'ctx_n2_data': 1,
'ctx_n1_data': 2,
'ctx_0_data': 3,
'ctx_p1_data': 4,
'ctx_p2_data': 5,
'verb_data': 6,
'mark_data': 7,
'target': 8
}
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)
trainer.train(
reader=reader,
event_handler=event_handler,
num_passes=10000,
reader_dict=reader_dict)
if __name__ == '__main__':
main()
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<p align="center">
<img src="image/encoder_decoder.png" width=700><br/>
图4. 编码器-解码器框架
**Note: "源语言词序列" 和 "源语编码状态" 位置标反了,需要互换**
</p>
#### 编码器
......@@ -130,7 +131,7 @@ GRU\[[2](#参考文献)\]是Cho等人在LSTM上提出的简化版本，也是RNN
#### 解码器
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源语言词的概率。思路是：
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. 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：
......@@ -323,7 +324,7 @@ pre-wmt14
- 训练模式：有三个输入序列，其中“源语言序列”和“目标语言序列”作为输入数据，“目标语言的下一个词序列”作为标签数据。
- 生成模式：有两个输入序列，其中“源语言序列”作为输入数据，“源语言序列编号”作为输入数据的编号（该输入非必须，可以省略）。
`hook`函数中的`src_dict_path`是源语言字典路径，`trg_dict_path`是目标语言字典路径，`is_generating`（训练或生成模式）是从模型配置中传入的对象。`hook`函数的具体调用方式请见[训练模型配置说明](#训练模型配置说明)。
`hook`函数中的`src_dict_path`是源语言字典路径，`trg_dict_path`是目标语言字典路径，`is_generating`（训练或生成模式）是从模型配置中传入的对象。`hook`函数的具体调用方式请见[模型配置说明](#模型配置说明)。
```python
def hook(settings, src_dict_path, trg_dict_path, is_generating, file_list,
......@@ -456,12 +457,12 @@ settings(
```python
source_dict_dim = len(open(src_lang_dict, "r").readlines()) # 源语言字典维度
target_dict_dim = len(open(trg_lang_dict, "r").readlines()) # 目标语言字典维度
word_vector_dim = 512 # dimension of word vector # 词向量维度
word_vector_dim = 512 # 词向量维度
encoder_size = 512 # 编码器中的GRU隐层大小
decoder_size = 512 # 解码器中的GRU隐层大小
if is_generating:
beam_size=3 # # 柱搜索算法中的宽度
beam_size=3 # 柱搜索算法中的宽度
max_length=250 # 生成句子的最大长度
gen_trans_file = get_config_arg("gen_trans_file", str, None) # 生成后的文件
```
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......@@ -113,17 +113,10 @@ Softmax回归模型采用了最简单的两层神经网络，即只有输入层
更详细的介绍请参考[维基百科激活函数](https://en.wikipedia.org/wiki/Activation_function)。
## 数据准备
## 数据介绍
### 数据介绍与下载
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：
执行以下命令，下载[MNIST](http://yann.lecun.com/exdb/mnist/)数据库并解压缩，然后将训练集和测试集的地址分别写入train.list和test.list两个文件，供PaddlePaddle读取。
```bash
./data/get_mnist_data.sh
```
将下载下来的数据进行 `gzip` 解压，可以在文件夹 `data/raw_data` 中找到以下文件：
| 文件名称 | 说明 |
|----------------------|-------------------------|
......@@ -132,284 +125,153 @@ Softmax回归模型采用了最简单的两层神经网络，即只有输入层
|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 |
用户可以通过以下脚本随机绘制10张图片（可参考图1）：
```bash
./load_data.py
```
### 提供数据给PaddlePaddle
我们使用python接口传递数据给系统，下面 `mnist_provider.py`针对MNIST数据给出了完整示例。
```python
# Define a py data provider
@provider(
input_types={'pixel': dense_vector(28 * 28),
'label': integer_value(10)})
def process(settings, filename): # settings is not used currently.
# 打开图片文件
with open( filename + "-images-idx3-ubyte", "rb") as f:
# 读取开头的四个参数，magic代表数据的格式，n代表数据的总量，rows和cols分别代表行数和列数
magic, n, rows, cols = struct.upack(">IIII", f.read(16))
# 以无符号字节为单位一个一个的读取数据
images = np.fromfile(
f, 'ubyte',
count=n * rows * cols).reshape(n, rows, cols).astype('float32')
# 将0~255的数据归一化到[-1,1]的区间
images = images / 255.0 * 2.0 - 1.0
# 打开标签文件
with open( filename + "-labels-idx1-ubyte", "rb") as l:
# 读取开头的两个参数
magic, n = struct.upack(">II", l.read(8))
# 以无符号字节为单位一个一个的读取数据
labels = np.fromfile(l, 'ubyte', count=n).astype("int")
for i in xrange(n):
yield {"pixel": images[i, :], 'label': labels[i]}
```
## 模型配置说明
### 数据定义
在模型配置中，定义通过 `define_py_data_sources2` 函数从 `dataprovider` 中读入数据。如果该配置用于预测，则不需要数据定义部分。
```python
if not is_predict:
data_dir = './data/'
define_py_data_sources2(
train_list=data_dir + 'train.list',
test_list=data_dir + 'test.list',
module='mnist_provider',
obj='process')
```
### 算法配置
## 配置说明
指定训练相关的参数。
- batch_size： 表示神经网络每次训练使用的数据为128条。
- 训练速度（learning_rate）： 迭代的速度，与网络的训练收敛速度有关系。
- 训练方法（learning_method）： 代表训练过程在更新权重时采用动量优化器 `MomentumOptimizer` ，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。
- 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。
首先，加载PaddlePaddle的V2 api包。
```python
settings(
batch_size=128,
learning_rate=0.1 / 128.0,
learning_method=MomentumOptimizer(0.9),
regularization=L2Regularization(0.0005 * 128))
```
### 模型结构
#### 整体结构
首先通过`data_layer`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；而预测时直接输出该结果即可。
``` python
data_size = 1 * 28 * 28
label_size = 10
img = data_layer(name='pixel', size=data_size)
predict = softmax_regression(img) # Softmax回归
#predict = multilayer_perceptron(img) #多层感知器
#predict = convolutional_neural_network(img) #LeNet5卷积神经网络
if not is_predict:
lbl = data_layer(name="label", size=label_size)
inputs(img, lbl)
outputs(classification_cost(input=predict, label=lbl))
else:
outputs(predict)
import paddle.v2 as paddle
```
其次，定义三个不同的分类器：
#### 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。
```python
def softmax_regression(img):
predict = fc_layer(input=img, size=10, act=SoftmaxActivation())
predict = paddle.layer.fc(input=img,
size=10,
act=paddle.activation.Softmax())
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。
- 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。
```python
def multilayer_perceptron(img):
# 第一个全连接层，激活函数为ReLU
hidden1 = fc_layer(input=img, size=128, act=ReluActivation())
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 = fc_layer(input=hidden1, size=64, act=ReluActivation())
hidden2 = paddle.layer.fc(input=hidden1,
size=64,
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 = fc_layer(input=hidden2, size=10, act=SoftmaxActivation())
predict = paddle.layer.fc(input=hidden2,
size=10,
act=paddle.activation.Softmax())
return predict
```
#### 卷积神经网络LeNet-5
以下为LeNet-5的网络结构：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。
- 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。
```python
def convolutional_neural_network(img):
# 第一个卷积-池化层
conv_pool_1 = simple_img_conv_pool(
conv_pool_1 = paddle.networks.simple_img_conv_pool(
input=img,
filter_size=5,
num_filters=20,
num_channel=1,
pool_size=2,
pool_stride=2,
act=TanhActivation())
act=paddle.activation.Tanh())
# 第二个卷积-池化层
conv_pool_2 = simple_img_conv_pool(
conv_pool_2 = paddle.networks.simple_img_conv_pool(
input=conv_pool_1,
filter_size=5,
num_filters=50,
num_channel=20,
pool_size=2,
pool_stride=2,
act=TanhActivation())
act=paddle.activation.Tanh())
# 全连接层
fc1 = fc_layer(input=conv_pool_2, size=128, act=TanhActivation())
fc1 = paddle.layer.fc(input=conv_pool_2,
size=128,
act=paddle.activation.Tanh())
# 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 = fc_layer(input=fc1, size=10, act=SoftmaxActivation())
predict = paddle.layer.fc(input=fc1,
size=10,
act=paddle.activation.Softmax())
return predict
```
## 训练模型
### 训练命令及日志
1.通过配置训练脚本 `train.sh` 来执行训练过程：
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。
```bash
config=mnist_model.py # 在mnist_model.py中可以选择网络
output=./softmax_mnist_model
log=softmax_train.log
paddle train \
--config=$config \ # 网络配置的脚本
--dot_period=10 \ # 每训练 `dot_period` 个批次后打印一个 `.`
--log_period=100 \ # 每隔多少batch打印一次日志
--test_all_data_in_one_period=1 \ # 每次测试是否用所有的数据
--use_gpu=0 \ # 是否使用GPU
--trainer_count=1 \ # 使用CPU或GPU的个数
--num_passes=100 \ # 训练进行的轮数（每次训练使用完所有数据为1轮）
--save_dir=$output \ # 模型存储的位置
2>&1 | tee $log
python -m paddle.utils.plotcurve -i $log > plot.png
```
配置好参数之后，执行脚本 `./train.sh` 训练日志类似如下所示：
```
I0117 12:52:29.628617 4538 TrainerInternal.cpp:165] Batch=100 samples=12800 AvgCost=2.63996 CurrentCost=2.63996 Eval: classification_error_evaluator=0.241172 CurrentEval: classification_error_evaluator=0.241172
.........
I0117 12:52:29.768741 4538 TrainerInternal.cpp:165] Batch=200 samples=25600 AvgCost=1.74027 CurrentCost=0.840582 Eval: classification_error_evaluator=0.185234 CurrentEval: classification_error_evaluator=0.129297
.........
I0117 12:52:29.916970 4538 TrainerInternal.cpp:165] Batch=300 samples=38400 AvgCost=1.42119 CurrentCost=0.783026 Eval: classification_error_evaluator=0.167786 CurrentEval: classification_error_evaluator=0.132891
.........
I0117 12:52:30.061213 4538 TrainerInternal.cpp:165] Batch=400 samples=51200 AvgCost=1.23965 CurrentCost=0.695054 Eval: classification_error_evaluator=0.160039 CurrentEval: classification_error_evaluator=0.136797
......I0117 12:52:30.223270 4538 TrainerInternal.cpp:181] Pass=0 Batch=469 samples=60000 AvgCost=1.1628 Eval: classification_error_evaluator=0.156233
I0117 12:52:30.366894 4538 Tester.cpp:109] Test samples=10000 cost=0.50777 Eval: classification_error_evaluator=0.0978
```
2.用脚本 `plot_cost.py` 可以画出训练过程中的误差变化曲线：
```bash
python plot_cost.py softmax_train.log
```
3.用脚本 `evaluate.py ` 可以选出最佳训练的模型：
```bash
python evaluate.py softmax_train.log
```
### softmax回归的训练结果
<p align="center">
<img src="image/softmax_train_log.png" width="400px"><br/>
图7. softmax回归的误差曲线图<br/>
</p>
评估模型结果如下：
```text
Best pass is 00013, testing Avgcost is 0.484447
The classification accuracy is 90.01%
```
```python
def main():
# 该模型运行在单个CPU上
paddle.init(use_gpu=False, trainer_count=1)
从评估结果可以看到，softmax回归模型分类效果最好的时候是pass-00013，分类准确率为90.01%，而最终的pass-00099的准确率为89.3%。从图7中也可以看出，最好的准确率不一定出现在最后一个pass。原因是中间的Pass可能就已经收敛获得局部最优值，后面的Pass只是在该值附近震荡，或者获得更低的局部最优值。
images = paddle.layer.data(
name='pixel', type=paddle.data_type.dense_vector(784))
label = paddle.layer.data(
name='label', type=paddle.data_type.integer_value(10))
### 多层感知器的训练结果
predict = softmax_regression(images) # Softmax回归
#predict = multilayer_perceptron(images) #多层感知器
#predict = convolutional_neural_network(images) #LeNet5卷积神经网络
<p align="center">
<img src="image/mlp_train_log.png" width="400px"><br/>
图8. 多层感知器的误差曲线图
</p>
评估模型结果如下：
```text
Best pass is 00085, testing Avgcost is 0.164746
The classification accuracy is 94.95%
cost = paddle.layer.classification_cost(input=predict, label=label)
```
从评估结果可以看到，最终训练的准确率为94.95%，相比于softmax回归模型有了显著的提升。原因是softmax回归模型较为简单，无法拟合更为复杂的数据，而加入了隐藏层之后的多层感知器则具有更强的拟合能力。
### 卷积神经网络的训练结果
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。
<p align="center">
<img src="image/cnn_train_log.png" width="400px"><br/>
图9. 卷积神经网络的误差曲线图
</p>
```python
parameters = paddle.parameters.create(cost)
评估模型结果如下：
optimizer = paddle.optimizer.Momentum(
learning_rate=0.1 / 128.0,
momentum=0.9,
regularization=paddle.optimizer.L2Regularization(rate=0.0005 * 128))
```text
Best pass is 00076, testing Avgcost is 0.0244684
The classification accuracy is 99.20%
trainer = paddle.trainer.SGD(cost=cost,
parameters=parameters,
update_equation=optimizer)
```
从评估结果可以看到，卷积神经网络的最好分类准确率达到惊人的99.20%。说明对于图像问题而言，卷积神经网络能够比一般的全连接网络达到更好的识别效果，而这与卷积层具有局部连接和共享权重的特性是分不开的。同时，从图9中可以看到，卷积神经网络在很早的时候就能达到很好的效果，说明其收敛速度非常快。
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。
## 应用模型
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。
### 预测命令与结果
脚本 `predict.py` 可以对训练好的模型进行预测，例如softmax回归中：
`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minbatch。
```bash
python predict.py -c mnist_model.py -d data/raw_data/ -m softmax_mnist_model/pass-00047
```python
lists = []
def event_handler(event):
if isinstance(event, paddle.event.EndIteration):
if event.batch_id % 100 == 0:
print "Pass %d, Batch %d, Cost %f, %s" % (
event.pass_id, event.batch_id, event.cost, event.metrics)
if isinstance(event, paddle.event.EndPass):
result = trainer.test(reader=paddle.reader.batched(
paddle.dataset.mnist.test(), batch_size=128))
print "Test with Pass %d, Cost %f, %s\n" % (
event.pass_id, result.cost, result.metrics)
lists.append((event.pass_id, result.cost,
result.metrics['classification_error_evaluator']))
trainer.train(
reader=paddle.batch(
paddle.reader.shuffle(
paddle.dataset.mnist.train(), buf_size=8192),
batch_size=128),
event_handler=event_handler,
num_passes=100)
```
- -c 指定模型的结构
- -d 指定需要预测的数据源，这里用测试数据集进行预测
- -m 指定模型的参数，这里用之前训练效果最好的模型进行预测
根据提示，输入需要预测的图片序号，分类器能够给出各个数字的生成概率、预测的结果（取最大生成概率对应的数字）和实际的标签。
训练过程是完全自动的，event_handler里打印的日志类似如下所示：
```
Input image_id [0~9999]: 3
Predicted probability of each digit:
[[ 1.00000000e+00 1.60381094e-28 1.60381094e-28 1.60381094e-28
1.60381094e-28 1.60381094e-28 1.60381094e-28 1.60381094e-28
1.60381094e-28 1.60381094e-28]]
Predict Number: 0
Actual Number: 0
# Pass 0, Batch 0, Cost 2.780790, {'classification_error_evaluator': 0.9453125}
# Pass 0, Batch 100, Cost 0.635356, {'classification_error_evaluator': 0.2109375}
# Pass 0, Batch 200, Cost 0.326094, {'classification_error_evaluator': 0.1328125}
# Pass 0, Batch 300, Cost 0.361920, {'classification_error_evaluator': 0.1015625}
# Pass 0, Batch 400, Cost 0.410101, {'classification_error_evaluator': 0.125}
# Test with Pass 0, Cost 0.326659, {'classification_error_evaluator': 0.09470000118017197}
```
从结果看出，该分类器接近100%地认为第3张图片上面的数字为0，而实际标签给出的类也确实如此。
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%。
## 总结
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......@@ -86,14 +86,8 @@ $$ crossentropy(label, y) = -\sum_i label_ilog(y_i) $$
Fig. 2 shows a softmax regression network, with weights in black, and bias in red. +1 indicates bias is 1.
<p align="center">
<img src="image/softmax_regression.png" width=400><br/>
<img src="image/softmax_regression_en.png" width=400><br/>
Fig. 2. Softmax regression network architecture<br/>
输入层 -> input layer<br/>
权重W -> weights W<br/>
激活前 -> before activation<br/>
激活函数 -> activation function<br/>
输出层 -> output layer<br/>
偏置b -> bias b<br/>
</p>
### Multilayer Perceptron
......@@ -107,12 +101,9 @@ The Softmax regression model described above uses the simplest two-layer neural
Fig. 3. is Multilayer Perceptron network, with weights in black, and bias in red. +1 indicates bias is 1.
<p align="center">
<img src="image/mlp.png" width=500><br/>
<img src="image/mlp_en.png" width=500><br/>
Fig. 3. Multilayer Perceptron network architecture<br/>
输入层X -> input layer X<br/>
隐藏层$H_1$(含激活函数) -> hidden layer $H_1$ (including activation function)<br/>
隐藏层$H_2$(含激活函数) -> hidden layer $H_2$ (including activation function)<br/>
输出层Y -> output layer Y<br/>
</p>
### Convolutional Neural Network
......@@ -120,10 +111,8 @@ Fig. 3. Multilayer Perceptron network architecture<br/>
#### Convolutional Layer
<p align="center">
<img src="image/conv_layer.png" width=500><br/>
<img src="image/conv_layer_en.png" width=500><br/>
Fig. 4. Convolutional layer<br/>
输入数据 -> input data<br/>
卷积输出 -> convolution output<br/>
</p>
The Convolutional layer is the core of a Convolutional Neural Network. The parameters in this layer are composed of a set of filters or kernels. In the forward step, each kernel moves horizontally and vertically, we compute a dot product of the kernel and the input at the corresponding positions, to this result we add 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.
......@@ -133,9 +122,8 @@ Fig. 4 is a dynamic graph of a convolutional layer, where depths are not shown f
#### Pooling Layer
<p align="center">
<img src="image/max_pooling.png" width="400px"><br/>
<img src="image/max_pooling_en.png" width="400px"><br/>
Fig. 5 Pooling layer<br/>
输入数据 -> input data<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 overfitting to some extent. Usually, a pooling layer is added after a convolutional layer. Pooling layer can be of various types like max pooling, average pooling, etc. Max pooling uses rectangles to segment the input layer into several parts and computes the maximum value in each part as the output (Fig. 5.)
......@@ -143,13 +131,8 @@ A Pooling layer performs downsampling. The main functionality of this layer is t
#### LeNet-5 Network
<p align="center">
<img src="image/cnn.png"><br/>
<img src="image/cnn_en.png"><br/>
Fig. 6. LeNet-5 Convolutional Neural Network architecture<br/>
特征图 -> feature map<br/>
卷积层 -> convolutional layer<br/>
降采样层 -> downsampling layer<br/>
全连接层 -> fully connected layer<br/>
输出层(全连接+Softmax激活) -> output layer (fully connected + softmax activation)<br/>
</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. The following three properties of convolution enable LeNet-5 to better recognize images than Multilayer fully connected perceptrons:
......@@ -396,12 +379,8 @@ python evaluate.py softmax_train.log
### Training Results for Softmax Regression
<p align="center">
<img src="image/softmax_train_log.png" width="400px"><br/>
<img src="image/softmax_train_log_en.png" width="400px"><br/>
Fig. 7 Softmax regression error curve<br/>
训练集 -> training set<br/>
测试集 -> test set<br/>
平均代价 -> average cost<br/>
训练轮数 -> epoch<br/>
</p>
Evaluation results of the models:
......@@ -416,12 +395,8 @@ From the evaluation results, the best pass for softmax regression model is pass-
### Results of Multilayer Perceptron
<p align="center">
<img src="image/mlp_train_log.png" width="400px"><br/>
<img src="image/mlp_train_log_en.png" width="400px"><br/>
Fig. 8. Multilayer Perceptron error curve<br/>
训练集 -> training set<br/>
测试集 -> test set<br/>
平均代价 -> average cost<br/>
训练轮数 -> epoch<br/>
</p>
Evaluation results of the models：
......@@ -436,12 +411,8 @@ From the evaluation results, the final training accuracy is 94.95%. It is signif
### Training results for Convolutional Neural Network
<p align="center">
<img src="image/cnn_train_log.png" width="400px"><br/>
<img src="image/cnn_train_log_en.png" width="400px"><br/>
Fig. 9. Convolutional Neural Network error curve<br/>
训练集 -> training set<br/>
测试集 -> test set<br/>
平均代价 -> average cost<br/>
训练轮数 -> epoch<br/>
</p>
Results of model evaluation：
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......@@ -32,10 +32,10 @@ CNN mainly contains convolution and pooling operation, with various extensions.
<p align="center">
<img src="image/text_cnn.png" width = "80%" align="center"/><br/>
<img src="image/text_cnn_en.png" width = "80%" align="center"/><br/>
Figure 1. CNN for text modeling.
将一句话表示为矩阵 -> represent a sentence as a $n\times k$ matrix; 使用不同大小的卷积层 -> apply convolution of different kernel sizes; 时间维最大池化 -> max-pooling across temporal channel; 全连接层 -> fully-connected layer.
</p>
Assuming the length of the sentence is $n$, where the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
First, we concatenate the words together: we piece every $h$ words as a window of length $h$: $x_{i:i+h-1}$. It refers to $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $i$ is the first word in the window, ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
......@@ -87,10 +87,12 @@ 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 separately; $W$ and $b$ are model parameters. The $tanh$ is a hyperbolic tangent， and $\odot$ denotes an element-wise product operation. Input gate controls the magnitude of new input into the memory cell $c$; forget gate controls memory propagated from the last time step; output gate controls output magnitude. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
<p align="center">
<img src="image/lstm.png" width = "65%" align="center"/><br/>
Figure 3. LSTM at time step $t$ [7]. 输入门 -> input gate, 记忆单元 -> memory cell, 遗忘门 -> forget gate, 输出门 -> output gate.
<img src="image/lstm_en.png" width = "65%" align="center"/><br/>
Figure 3. 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:**
$$ h_t=Recrurent(x_t,h_{t-1})$$
......@@ -102,8 +104,8 @@ For vanilla LSTM, $h_t$ contains input information from previous time-step $1..t
As shown in Figure 4 (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.jpg" width=450><br/>
Figure 4. Stacked Bidirectional LSTM for NLP modeling. 词向量映射 -> word embedding mapping; 全连接层 -> fully-connected layer; 反向LSTM -> reverse-directional LSTM; 池化层 -> pooling layer.
<img src="image/stacked_lstm_en.png" width=450><br/>
Figure 4. Stacked Bidirectional LSTM for NLP modeling.
</p>
## Data Preparation
......@@ -336,6 +338,7 @@ outputs(classification_cost(input=output, label=data_layer('label', 1)))
```
Our model defined in `trainer_config.py` uses the `stacked_lstm_net` structure as default. If you want to use `convolution_net`, you can comment related lines.
```python
stacked_lstm_net(
dict_dim, class_dim=class_dim, stacked_num=3, is_predict=is_predict)
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......@@ -73,10 +73,10 @@ CNN mainly contains convolution and pooling operation, with various extensions.
<p align="center">
<img src="image/text_cnn.png" width = "80%" align="center"/><br/>
<img src="image/text_cnn_en.png" width = "80%" align="center"/><br/>
Figure 1. CNN for text modeling.
Translation of Chinese in the figure: represent a sentence as a $n\times k$ matrix; apply convolution of different kernel sizes; max-pooling across temporal channel; fully-connected layer.
</p>
Assuming the length of the sentence is $n$, where the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
First, we concatenate the words together: we piece every $h$ words as a window of length $h$: $x_{i:i+h-1}$. It refers to $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $i$ is the first word in the window, ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
......@@ -128,10 +128,12 @@ 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 separately; $W$ and $b$ are model parameters. The $tanh$ is a hyperbolic tangent， and $\odot$ denotes an element-wise product operation. Input gate controls the magnitude of new input into the memory cell $c$; forget gate controls memory propagated from the last time step; output gate controls output magnitude. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
<p align="center">
<img src="image/lstm.png" width = "65%" align="center"/><br/>
Figure 3. LSTM at time step $t$ [7]. Translation of Chinese in the figure: input gate, memory cell, forget gate and output gate.
<img src="image/lstm_en.png" width = "65%" align="center"/><br/>
Figure 3. 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:**
$$ h_t=Recrurent(x_t,h_{t-1})$$
......@@ -143,8 +145,8 @@ For vanilla LSTM, $h_t$ contains input information from previous time-step $1..t
As shown in Figure 4 (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.jpg" width=450><br/>
Figure 4. Stacked Bidirectional LSTM for NLP modeling. Translation of Chinese in the Figure: word embedding mapping; fully connected layer; reverse-directional LSTM; max-pooling.
<img src="image/stacked_lstm_en.png" width=450><br/>
Figure 4. Stacked Bidirectional LSTM for NLP modeling.
</p>
## Data Preparation
......@@ -377,6 +379,7 @@ outputs(classification_cost(input=output, label=data_layer('label', 1)))
```
Our model defined in `trainer_config.py` uses the `stacked_lstm_net` structure as default. If you want to use `convolution_net`, you can comment related lines.
```python
stacked_lstm_net(
dict_dim, class_dim=class_dim, stacked_num=3, is_predict=is_predict)
......
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#!/bin/bash
set -e
wget http://www.fit.vutbr.cz/~imikolov/rnnlm/simple-examples.tgz
tar -zxf simple-examples.tgz
echo `pwd`/simple-examples/data/ptb.train.txt > train.list
echo `pwd`/simple-examples/data/ptb.valid.txt > test.list
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