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Toy-MT-Introduction
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Merge branch 'master' of http://47.105.50.196/NiuTrans/Toy-MT-Introduction

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Section06-Neural-Machine-Translation/section06-test.tex
......@@ -83,6 +83,7 @@
\newcounter{mycount3}
\newcounter{mycount4}
\newlength{\mystep}
\newlength{\base}
\usefonttheme[onlylarge]{structurebold}
......@@ -138,83 +139,176 @@
\subsection{注意力机制}
%%%------------------------------------------------------------------------------------------------------------
%%% C_i的定义
\begin{frame}{上下文向量$C_i$}
%%% NMT的数学描述
\begin{frame}{数学建模}
\begin{itemize}
\item 对于目标语位置$i$，$C_i$是目标语$i$使用的上下文向量
\begin{itemize}
\item $h_j$表示编码器第$j$个位置的隐层状态
\item $s_i$表示解码器第$i$个位置的隐层状态
\item<2-> $\alpha_{i,j}$表示注意力权重，表示目标语第$i$个位置与源语第$j$个位置之间的相关性大小
\item<2-> $a(\cdot)$表示注意力函数，计算$s_{i-1}$和$h_j$之间的相关性
\item<3-> $C_i$是所有源语编码表示a$\{h_j\}$的加权求和，权重为$\{\alpha_{i,j}\}$
\end{itemize}
\end{itemize}
\begin{center}
\begin{tikzpicture}
\begin{scope}
\node [anchor=west,draw,fill=red!20!white,inner sep=3pt,minimum width=2em,minimum height=1.2em] (h1) at (0,0) {\scriptsize{$h_1$}};
\node [anchor=west,draw,fill=red!20!white,inner sep=3pt,minimum width=2em,minimum height=1.2em] (h2) at ([xshift=1em]h1.east) {\scriptsize{$h_2$}};
\node [anchor=west,inner sep=0pt,minimum width=3em] (h3) at ([xshift=0.5em]h2.east) {\scriptsize{...}};
\node [anchor=west,draw,fill=red!20!white,inner sep=3pt,minimum width=2em,minimum height=1.2em] (h4) at ([xshift=0.5em]h3.east) {\scriptsize{$h_n$}};
\node [anchor=south,circle,minimum size=1.0em,draw,ublue,thick] (sum) at ([yshift=2em]h2.north east) {};
\draw [thick,-,ublue] (sum.north) -- (sum.south);
\draw [thick,-,ublue] (sum.west) -- (sum.east);
\item 对于源语言序列$\textbf{x} = \{x_1,x_2,...,x_m\}$，生成目标语序列$\textbf{y} = \{y_1,y_2,...,y_n\}$的概率可以被描述为
\node [anchor=south,draw,fill=green!20!white,inner sep=3pt,minimum width=2em,minimum height=1.2em] (th1) at ([yshift=2em,xshift=-1em]sum.north west) {\scriptsize{$s_{i-1}$}};
\node [anchor=west,draw,fill=green!20!white,inner sep=3pt,minimum width=2em,minimum height=1.2em] (th2) at ([xshift=2em]th1.east) {\scriptsize{$s_{i}$}};
\begin{displaymath}
\log\textrm{P}(\textbf{y}|\textbf{x}) = \sum_{j=1}^{n} \log\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x})
\end{displaymath}
\draw [->] (h1.north) .. controls +(north:0.8) and +(west:1) .. (sum.190) node [pos=0.3,left] {\tiny{$\alpha_{i,1}$}};
\draw [->] (h2.north) .. controls +(north:0.6) and +(220:0.2) .. (sum.220) node [pos=0.2,right] {\tiny{$\alpha_{i,2}$}};
\draw [->] (h4.north) .. controls +(north:0.8) and +(east:1) .. (sum.-10) node [pos=0.1,left] (alphan) {\tiny{$\alpha_{i,n}$}};
根据源于句子$\textbf{x}$和已生成的译文$\textbf{y}_{<j} = \{y_1,y_2,...,y_{j-1}\}$生成第$j$个译文$y_j$
\draw [->] ([xshift=-1.5em]th1.west) -- ([xshift=-0.1em]th1.west);
\draw [->] ([xshift=0.1em]th1.east) -- ([xshift=-0.1em]th2.west);
\draw [->] ([xshift=0.1em]th2.east) -- ([xshift=1.5em]th2.east);
\draw [->] (sum.north) .. controls +(north:0.8) and +(west:0.2) .. ([yshift=-0.4em,xshift=-0.1em]th2.west) node [pos=0.2,right] (ci) {\scriptsize{$C_{i}$}};
\node [anchor=south,inner sep=1pt] (output) at ([yshift=0.8em]th2.north) {\tiny{输出层}};
\draw [->] ([yshift=0.1em]th2.north) -- ([yshift=-0.1em]output.south);
\node [anchor=north] (enc1) at (h1.south) {\tiny{编码器输出}};
\node [anchor=north] (enc12) at ([yshift=0.5em]enc1.south) {\tiny{(位置$1$)}};
\node [anchor=north] (enc2) at (h2.south) {\tiny{编码器输出}};
\node [anchor=north] (enc22) at ([yshift=0.5em]enc2.south) {\tiny{(位置$2$)}};
\node [anchor=north] (enc4) at (h4.south) {\tiny{编码器输出}};
\node [anchor=north] (enc42) at ([yshift=0.5em]enc4.south) {\tiny{(位置$4$)}};
\visible<2->{
\node [anchor=west] (math1) at ([xshift=5em,yshift=1em]th2.east) {$C_i = \sum_{j} \alpha_{i,j} h_j \ \ $};
}
\visible<3->{
\node [anchor=north west] (math2) at ([yshift=-2em]math1.south west) {$\alpha_{i,j} = \frac{\exp(\beta_{i,j})}{\sum_j \exp(\beta_{i,j})}$};
\node [anchor=north west] (math3) at ([yshift=-0em]math2.south west) {$\beta_{i,j} = a(s_{i-1}, h_j)$};
}
\item<2-> \textbf{核心}：如何求解$\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x})$。在这个循环神经网络模型中，有三个步骤
\begin{enumerate}
\item 输入的单词用分布式表示，如$\textbf{x}$被表示为词向量序列$e_x(\textbf{x})$，同理$\textbf{y}_{<j}$被表示为$e_y(\textbf{y}_{<j})$
\item 源语言句子被一个RNN编码为一个表示$C$，如前面的例子中是一个实数向量
\item 目标端解码用另一个RNN，因此生成$y_j$时只考虑前一个状态$s_{j-1}$（这里，$s_{j-1}$表示RNN第$j-1$步骤的隐层状态）
\end{enumerate}
\end{itemize}
\end{frame}
\begin{pgfonlayer}{background}
\visible<2->{
\node [rectangle,inner sep=0.4em,rounded corners=1pt,fill=blue!10,drop shadow] [fit = (math1)] (box1) {};
}
\visible<3->{
\node [rectangle,inner sep=0.4em,rounded corners=1pt,fill=orange!10,drop shadow] [fit = (math2) (math3)] (box2) {};
}
\end{pgfonlayer}
%%%------------------------------------------------------------------------------------------------------------
%%% 各部分的解释
\begin{frame}{数学建模(续)}
\vspace{-1.5em}
\begin{center}
% \hspace*{-1.5cm}
\begin{tikzpicture}
\setlength{\base}{0.9cm}
\tikzstyle{rnnnode} = [rounded corners=1pt,minimum height=0.5\base,minimum width=1\base,draw,inner sep=0pt,outer sep=0pt]
\tikzstyle{wordnode} = [font=\tiny]
% RNN translation model
\begin{scope}[local bounding box=RNNMT]
% RNN Encoder
\coordinate (eemb0) at (0,0);
\foreach \x [count=\y from 0] in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=green!30!white,anchor=west] (eemb\x) at ([xshift=0.4\base]eemb\y.east) {\tiny{$e_x()$}};
\foreach \x in {1,2,...,3}
\node[rnnnode,fill=blue!30!white,anchor=south] (enc\x) at ([yshift=0.3\base]eemb\x.north) {};
\node[] (enclabel1) at (enc1) {\tiny{$h_{m-2}$}};
\node[] (enclabel2) at (enc2) {\tiny{$h_{m-1}$}};
\node[rnnnode,fill=purple!30!white] (enclabel3) at (enc3) {\tiny{$h_{m}$}};
\node[wordnode,left=0.4\base of enc1] (init1) {$\cdots$};
\node[wordnode,left=0.4\base of eemb1] (init2) {$\cdots$};
\node[wordnode,below=0pt of eemb1] () {走};
\node[wordnode,below=0pt of eemb2] () {吗};
\node[wordnode,below=0pt of eemb3] () {$\langle$eos$\rangle$};
% RNN Decoder
\foreach \x in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=green!30!white,anchor=south] (demb\x) at ([yshift=\base]enc\x.north) {\tiny{$e_y()$}};
\foreach \x in {1,2,...,3}
\node[rnnnode,fill=blue!30!white,anchor=south] (dec\x) at ([yshift=0.3\base]demb\x.north) {{\tiny{$s_\x$}}};
\foreach \x in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=red!30!white,anchor=south] (softmax\x) at ([yshift=0.3\base]dec\x.north) {\tiny{Softmax}};
\node[wordnode,right=0.4\base of demb3] (end1) {$\cdots$};
\node[wordnode,right=0.4\base of dec3] (end2) {$\cdots$};
\node[wordnode,right=0.4\base of softmax3] (end3) {$\cdots$};
% Decoder input words
\node[wordnode,below=0pt of demb1] (decwordin) {$\langle$sos$\rangle$};
\ExtractX{$(demb2.south)$}
\ExtractY{$(decwordin.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {Do};
\ExtractX{$(demb3.south)$}
\ExtractY{$(decwordin.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {you};
% Decoder output words
\node[wordnode,above=0pt of softmax1] (decwordout) {Do};
\ExtractX{$(softmax2.north)$}
\ExtractY{$(decwordout.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {you};
\ExtractX{$(softmax3.north)$}
\ExtractY{$(decwordout.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {know};
% Connections
\draw[-latex'] (init1.east) to (enc1.west);
\draw[-latex'] (dec3.east) to (end2.west);
\foreach \x in {1,2,...,3}
\draw[-latex'] (eemb\x) to (enc\x);
\foreach \x in {1,2,...,3}
\draw[-latex'] (demb\x) to (dec\x);
\foreach \x in {1,2,...,3}
\draw[-latex'] (dec\x.north) to (softmax\x.south);
\foreach \x [count=\y from 2] in {1,2}
{
\draw[-latex'] (enc\x.east) to (enc\y.west);
\draw[-latex'] (dec\x.east) to (dec\y.west);
}
\coordinate (bridge) at ([yshift=0.4\base]enc2.north west);
\draw[-latex'] (enc3.north) .. controls +(north:0.3\base) and +(east:\base) .. (bridge) .. controls +(west:2.7\base) and +(west:0.3\base) .. (dec1.west);
\visible<2->{
\node [anchor=east] (line1) at ([xshift=-3em,yshift=0.5em]softmax1.west) {\scriptsize{基于RNN的隐层状态$s_i$}};
\node [anchor=north west] (line2) at ([yshift=0.3em]line1.south west) {\scriptsize{预测目标词的概率}};
\node [anchor=north west] (line3) at ([yshift=0.3em]line2.south west) {\scriptsize{通常，用Softmax函数}};
\node [anchor=north west] (line4) at ([yshift=0.3em]line3.south west) {\scriptsize{实现 $\textrm{P}(y_i|...)$}};
}
\visible<3->{
\node [anchor=north west] (line11) at ([yshift=-1.8em]line4.west) {\scriptsize{每个词的one-hot}};
\node [anchor=north west] (line12) at ([yshift=0.3em]line11.south west) {\scriptsize{离散化表示都被转化为}};
\node [anchor=north west] (line13) at ([yshift=0.3em]line12.south west) {\scriptsize{实数向量，即词嵌入}};
\node [anchor=north west] (line14) at ([yshift=0.3em]line13.south west) {\scriptsize{($e_x()$和$e_y()$函数)}};
}
\visible<4->{
\node [anchor=west] (line21) at ([xshift=1.3em,yshift=1.5em]enc3.east) {\scriptsize{源语编码器最后一个}};
\node [anchor=north west] (line22) at ([yshift=0.3em]line21.south west) {\scriptsize{循环单元的输出被}};
\node [anchor=north west] (line23) at ([yshift=0.3em]line22.south west) {\scriptsize{看作是句子的表示,}};
\node [anchor=north west] (line24) at ([yshift=0.3em]line23.south west) {\scriptsize{记为$C$}};
}
\begin{pgfonlayer}{background}
\visible<2->{
\node [rectangle,inner sep=0.2em,rounded corners=1pt,fill=red!10,drop shadow,draw=red] [fit = (line1) (line2) (line3) (line4)] (box1) {};
\node [rectangle,inner sep=0.2em,rounded corners=1pt,very thick,dotted,draw=red] [fit = (softmax1) (softmax2) (softmax3)] (box4) {};
\draw [->,dotted,very thick,red] ([yshift=1em,xshift=2.5em]box1.east) -- ([yshift=1em,xshift=0.1em]box1.east);
}
\visible<3->{
\node [rectangle,inner sep=0.2em,rounded corners=1pt,fill=green!10,drop shadow,draw=ugreen] [fit = (line11) (line12) (line13) (line14)] (box2) {};
\node [rectangle,inner sep=0.2em,rounded corners=1pt,very thick,dotted,draw=ugreen] [fit = (eemb1) (eemb2) (eemb3)] (box5) {};
\node [rectangle,inner sep=0.2em,rounded corners=1pt,very thick,dotted,draw=ugreen] [fit = (demb1) (demb2) (demb3)] (box6) {};
\draw [->,dotted,very thick,ugreen] ([yshift=-1.3em,xshift=2.5em]box2.east) -- ([yshift=-1.3em,xshift=0.1em]box2.east);
\draw [->,dotted,very thick,ugreen] ([xshift=0.1em]box6.west) .. controls +(west:1) and +(east:1) .. ([yshift=1.0em]box2.east) ;
}
\visible<4->{
\node [rectangle,inner sep=0.2em,rounded corners=1pt,fill=purple!10,drop shadow,draw=purple] [fit = (line21) (line22) (line23) (line24)] (box3) {};
\node [rectangle,inner sep=0.2em,rounded corners=1pt,very thick,dotted,draw=purple] [fit = (enc3)] (box7) {};
\draw [->,dotted,very thick,purple] ([xshift=0.1em]box7.east) -- ([xshift=0.8em]box7.east) ;
}
\end{pgfonlayer}
\end{scope}
\end{tikzpicture}
\end{center}
\visible<5->{
\vspace{-1.5em}
\begin{itemize}
\item 可以重新定义\\
\vspace{-0.8em}
\begin{displaymath}
\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \textrm{P}(y_j|s_{j-1}, C)
\end{displaymath}
对于上图中的模型，进一步化简为：\\
\vspace{-0.3em}
\begin{displaymath}
\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \left\{
\begin{matrix}
\textrm{P}(y_j|C)\ \ \ \ & j = 1 \\
\textrm{P}(y_j|s_{j-1}) & j > 1
\end{matrix} \right.
\end{displaymath}
\visible<2->{
\draw [->,dotted,thick,blue] (box1.west) .. controls +(west:1.2) and +(east:2.0) .. ([xshift=-0.3em]ci.east);
}
\visible<3->{
\draw [->,dotted,thick,orange] ([yshift=1em]box2.west) .. controls +(west:1.2) and +(east:1.0) .. ([xshift=-0.35em]alphan.east);
\end{itemize}
}
\end{scope}
\end{tikzpicture}
\end{center}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
......
Section06-Neural-Machine-Translation/section06.tex
......@@ -851,9 +851,176 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
%%%------------------------------------------------------------------------------------------------------------
%%% NMT的数学描述
\begin{frame}{数学建模}
\begin{itemize}
\item 对于源语言序列$\textbf{x} = \{x_1,x_2,...,x_m\}$，生成目标语序列$\textbf{y} = \{y_1,y_2,...,y_n\}$的概率可以被描述为
\begin{displaymath}
\log\textrm{P}(\textbf{y}|\textbf{x}) = \sum_{j=1}^{n} \log\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x})
\end{displaymath}
根据源于句子$\textbf{x}$和已生成的译文$\textbf{y}_{<j} = \{y_1,y_2,...,y_{j-1}\}$生成第$j$个译文$y_j$
\item<2-> \textbf{核心}：如何求解$\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x})$。在这个循环神经网络模型中，有三个步骤
\begin{enumerate}
\item 输入的单词用分布式表示，如$\textbf{x}$被表示为词向量序列$e_x(\textbf{x})$，同理$\textbf{y}_{<j}$被表示为$e_y(\textbf{y}_{<j})$
\item 源语言句子被一个RNN编码为一个表示$C$，如前面的例子中是一个实数向量
\item 目标端解码用另一个RNN，因此生成$y_j$时只考虑前一个状态$s_{j-1}$（这里，$s_{j-1}$表示RNN第$j-1$步骤的隐层状态）
\end{enumerate}
\end{itemize}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
%%% 各部分的解释
\begin{frame}{数学建模(续)}
\vspace{-1.5em}
\begin{center}
% \hspace*{-1.5cm}
\begin{tikzpicture}
\setlength{\base}{0.9cm}
\tikzstyle{rnnnode} = [rounded corners=1pt,minimum height=0.5\base,minimum width=1\base,draw,inner sep=0pt,outer sep=0pt]
\tikzstyle{wordnode} = [font=\tiny]
% RNN translation model
\begin{scope}[local bounding box=RNNMT]
% RNN Encoder
\coordinate (eemb0) at (0,0);
\foreach \x [count=\y from 0] in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=green!30!white,anchor=west] (eemb\x) at ([xshift=0.4\base]eemb\y.east) {\tiny{$e_x()$}};
\foreach \x in {1,2,...,3}
\node[rnnnode,fill=blue!30!white,anchor=south] (enc\x) at ([yshift=0.3\base]eemb\x.north) {};
\node[] (enclabel1) at (enc1) {\tiny{$h_{m-2}$}};
\node[] (enclabel2) at (enc2) {\tiny{$h_{m-1}$}};
\node[rnnnode,fill=purple!30!white] (enclabel3) at (enc3) {\tiny{$h_{m}$}};
\node[wordnode,left=0.4\base of enc1] (init1) {$\cdots$};
\node[wordnode,left=0.4\base of eemb1] (init2) {$\cdots$};
\node[wordnode,below=0pt of eemb1] () {走};
\node[wordnode,below=0pt of eemb2] () {吗};
\node[wordnode,below=0pt of eemb3] () {$\langle$eos$\rangle$};
% RNN Decoder
\foreach \x in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=green!30!white,anchor=south] (demb\x) at ([yshift=\base]enc\x.north) {\tiny{$e_y()$}};
\foreach \x in {1,2,...,3}
\node[rnnnode,fill=blue!30!white,anchor=south] (dec\x) at ([yshift=0.3\base]demb\x.north) {{\tiny{$s_\x$}}};
\foreach \x in {1,2,...,3}
\node[rnnnode,minimum height=0.5\base,fill=red!30!white,anchor=south] (softmax\x) at ([yshift=0.3\base]dec\x.north) {\tiny{Softmax}};
\node[wordnode,right=0.4\base of demb3] (end1) {$\cdots$};
\node[wordnode,right=0.4\base of dec3] (end2) {$\cdots$};
\node[wordnode,right=0.4\base of softmax3] (end3) {$\cdots$};
% Decoder input words
\node[wordnode,below=0pt of demb1] (decwordin) {$\langle$sos$\rangle$};
\ExtractX{$(demb2.south)$}
\ExtractY{$(decwordin.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {Do};
\ExtractX{$(demb3.south)$}
\ExtractY{$(decwordin.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {you};
% Decoder output words
\node[wordnode,above=0pt of softmax1] (decwordout) {Do};
\ExtractX{$(softmax2.north)$}
\ExtractY{$(decwordout.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {you};
\ExtractX{$(softmax3.north)$}
\ExtractY{$(decwordout.base)$}
\node[wordnode,anchor=base] () at (\XCoord,\YCoord) {know};
% Connections
\draw[-latex'] (init1.east) to (enc1.west);
\draw[-latex'] (dec3.east) to (end2.west);
\foreach \x in {1,2,...,3}
\draw[-latex'] (eemb\x) to (enc\x);
\foreach \x in {1,2,...,3}
\draw[-latex'] (demb\x) to (dec\x);
\foreach \x in {1,2,...,3}
\draw[-latex'] (dec\x.north) to (softmax\x.south);
\foreach \x [count=\y from 2] in {1,2}
{
\draw[-latex'] (enc\x.east) to (enc\y.west);
\draw[-latex'] (dec\x.east) to (dec\y.west);
}
\coordinate (bridge) at ([yshift=0.4\base]enc2.north west);
\draw[-latex'] (enc3.north) .. controls +(north:0.3\base) and +(east:\base) .. (bridge) .. controls +(west:2.7\base) and +(west:0.3\base) .. (dec1.west);
\visible<2->{
\node [anchor=east] (line1) at ([xshift=-3em,yshift=0.5em]softmax1.west) {\scriptsize{基于RNN的隐层状态$s_i$}};
\node [anchor=north west] (line2) at ([yshift=0.3em]line1.south west) {\scriptsize{预测目标词的概率}};
\node [anchor=north west] (line3) at ([yshift=0.3em]line2.south west) {\scriptsize{通常，用Softmax函数}};
\node [anchor=north west] (line4) at ([yshift=0.3em]line3.south west) {\scriptsize{实现 $\textrm{P}(y_i|...)$}};
}
\visible<3->{
\node [anchor=north west] (line11) at ([yshift=-1.8em]line4.west) {\scriptsize{每个词的one-hot}};
\node [anchor=north west] (line12) at ([yshift=0.3em]line11.south west) {\scriptsize{离散化表示都被转化为}};
\node [anchor=north west] (line13) at ([yshift=0.3em]line12.south west) {\scriptsize{实数向量，即词嵌入}};
\node [anchor=north west] (line14) at ([yshift=0.3em]line13.south west) {\scriptsize{($e_x()$和$e_y()$函数)}};
}
\visible<4->{
\node [anchor=west] (line21) at ([xshift=1.3em,yshift=1.5em]enc3.east) {\scriptsize{源语编码器最后一个}};
\node [anchor=north west] (line22) at ([yshift=0.3em]line21.south west) {\scriptsize{循环单元的输出被}};
\node [anchor=north west] (line23) at ([yshift=0.3em]line22.south west) {\scriptsize{看作是句子的表示,}};
\node [anchor=north west] (line24) at ([yshift=0.3em]line23.south west) {\scriptsize{记为$C$}};
}
\begin{pgfonlayer}{background}
\visible<2->{
\node [rectangle,inner sep=0.2em,rounded corners=1pt,fill=red!10,drop shadow,draw=red] [fit = (line1) (line2) (line3) (line4)] (box1) {};
\node [rectangle,inner sep=0.2em,rounded corners=1pt,very thick,dotted,draw=red] [fit = (softmax1) (softmax2) (softmax3)] (box4) {};
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\visible<4->{
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}
\end{pgfonlayer}
\end{scope}
\end{tikzpicture}
\end{center}
\visible<5->{
\vspace{-1.5em}
\begin{itemize}
\item 可以重新定义\\
\vspace{-0.8em}
\begin{displaymath}
\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \textrm{P}(y_j|s_{j-1}, C)
\end{displaymath}
对于上图中的模型，进一步化简为：\\
\vspace{-0.3em}
\begin{displaymath}
\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \left\{
\begin{matrix}
\textrm{P}(y_j|C)\ \ \ \ & j = 1 \\
\textrm{P}(y_j|s_{j-1}) & j > 1
\end{matrix} \right.
\end{displaymath}
\end{itemize}
}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
%%% 词嵌入
\begin{frame}{模块1：词嵌入层}
\begin{itemize}
......
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