@@ -24,7 +24,7 @@ This tutorial explains a deep learning based approach and how to implement it us
## Model Overview
To know more about deep learning based recommendation, let us start from going over the Youtube recommender system[[7](#参考文献)] before introducing our hybrid model.
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
...
...
@@ -42,7 +42,7 @@ Youtube models candidate generation as a multiclass classification problem with
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.
...
...
@@ -55,26 +55,49 @@ where $u$ is the representative vector of user $U$, $V$ is the corpus of all vid
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.
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.
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 [sentiment analysis tutorial](https://github.com/PaddlePaddle/book/blob/develop/understand_sentiment/README.md)）to get a fixed-length representative feature vector.
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.
@@ -434,5 +460,6 @@ print "[Predict] User %d Rating Movie %d With Score %.2f"%(user_id, movie_id, sc
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.
@@ -66,7 +66,7 @@ This tutorial explains a deep learning based approach and how to implement it us
## Model Overview
To know more about deep learning based recommendation, let us start from going over the Youtube recommender system[[7](#参考文献)] before introducing our hybrid model.
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
...
...
@@ -84,7 +84,7 @@ Youtube models candidate generation as a multiclass classification problem with
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.
...
...
@@ -97,26 +97,49 @@ where $u$ is the representative vector of user $U$, $V$ is the corpus of all vid
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.
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.
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 [sentiment analysis tutorial](https://github.com/PaddlePaddle/book/blob/develop/understand_sentiment/README.md)）to get a fixed-length representative feature vector.
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.
@@ -476,6 +502,7 @@ print "[Predict] User %d Rating Movie %d With Score %.2f"%(user_id, movie_id, sc
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.
@@ -26,33 +26,11 @@ This chapter introduces a deep learning model that handles these issues in BOW.
The model we used in this chapter uses **Convolutional Neural Networks** (**CNNs**) and **Recurrent Neural Networks** (**RNNs**) with some specific extensions.
### Convolutional Neural Networks for Texts (CNN)
### Revisit to the 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.
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. Here, we briefly describe a CNN used to classify texts\[[1](#Refernce)\], as shown in Figure 1.
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:
$$\hat c=max(c)$$
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 (as shown in Figure 1 in different colors).
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.
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 \[[2](#Reference),[3](#Reference)\].
...
...
@@ -62,10 +40,10 @@ RNN is an effective model for sequential data. In terms of computability, the RN
Figure 2. An illustration of an unfolded RNN in time.
Figure 1. An illustration of an unfolded RNN in time.
</p>
As shown in Figure 2, 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:
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:
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 3:
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:
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:**
...
...
@@ -106,11 +84,11 @@ where $Recrurent$ is a simple RNN, GRU or 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 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.
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.
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。
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：**
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.
@@ -68,33 +68,11 @@ This chapter introduces a deep learning model that handles these issues in BOW.
The model we used in this chapter uses **Convolutional Neural Networks** (**CNNs**) and **Recurrent Neural Networks** (**RNNs**) with some specific extensions.
### Convolutional Neural Networks for Texts (CNN)
### Revisit to the 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.
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. Here, we briefly describe a CNN used to classify texts\[[1](#Refernce)\], as shown in Figure 1.
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:
$$\hat c=max(c)$$
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 (as shown in Figure 1 in different colors).
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.
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 \[[2](#Reference),[3](#Reference)\].
...
...
@@ -104,10 +82,10 @@ RNN is an effective model for sequential data. In terms of computability, the RN
Figure 2. An illustration of an unfolded RNN in time.
Figure 1. An illustration of an unfolded RNN in time.
</p>
As shown in Figure 2, 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:
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:
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 3:
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:
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:**
...
...
@@ -148,11 +126,11 @@ where $Recrurent$ is a simple RNN, GRU or 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 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.
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.
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。
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：**
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.
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