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Section06-Neural-Machine-Translation/section06-test.tex

@@ -138,83 +138,25 @@
 \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{$\alpha_{i,n}$}};
-
-\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)$};
-}
-
-\begin{pgfonlayer}{background}
-\visible<2->{
-\node [rectangle,inner sep=0.4em,rounded corners=1pt,fill=blue!10,drop shadow] [fit = (math1)] (box1) {};
-}
-\visible<3->{
-\node [rectangle,inner sep=0.4em,rounded corners=1pt,fill=orange!10,drop shadow] [fit = (math2) (math3)] (box2) {};
-}
-\end{pgfonlayer}
-
-\visible<2->{
-\draw [->,dotted,thick,blue] (box1.west) .. controls +(west:1.2) and +(east:2.0) .. ([xshift=-0.3em]ci.east);
-}
-\visible<3->{
-\draw [->,dotted,thick,orange] ([yshift=1em]box2.west) .. controls +(west:1.2) and +(east:1.0) .. ([xshift=-0.35em]alphan.east);
-}
-
-\end{scope}
-
-\end{tikzpicture}
-\end{center}
+根据源于句子$\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$y_i$时只考虑前一个状态$s_{i-1}$（这里，$s_{i-1}$表示RNN第$i-1$步骤的隐层状态）
+    \end{enumerate}
+    
+\end{itemize}
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------