bug fixes (section6 slides)

Section06-Neural-Machine-Translation/section06.tex

@@ -1115,7 +1115,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
 \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|\textbf{s}_{j-1}, \textbf{C})
+\textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \textrm{P}(y_j|\textbf{s}_{j-1}, y_{j-1},\textbf{C})
 \end{displaymath}
 
 对于上图中的模型，进一步化简为：\\
@@ -1124,8 +1124,8 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
 \begin{displaymath}
 \textrm{P}(y_j|\textbf{y}_{<j}, \textbf{x}) \triangleq \left\{
     \begin{matrix}
-        \textrm{P}(y_j|\textbf{C})\ \ \ \  & j = 1 \\
-        \textrm{P}(y_j|\textbf{s}_{j-1}) & j > 1
+        \textrm{P}(y_j|\textbf{C},y_{j-1})\ \ \ \  & j = 1 \\
+        \textrm{P}(y_j|\textbf{s}_{j-1},y_{j-1}) & j > 1
     \end{matrix} \right.
 \end{displaymath}
 
@@ -1224,6 +1224,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
                 \coordinate (start) at (5.8\base,0.3\base);
                 \visible<2->{
                     \node [anchor=south west] (one) at (start) {\scriptsize{$\begin{bmatrix} 0 \\ 0 \\ 0 \\ \vdots \\ 0 \\ {\color{ugreen} 1} \\ 0 \\ 0 \end{bmatrix}$}};
+                    \node [anchor=south west,inner sep=0pt] (T) at ([yshift=-0.5em,xshift=-0.5em]one.north east) {\tiny{T}};
                 }
                 \visible<3->{
                     \node [draw=ugreen,fill=green!20!white,rounded corners=0.3em,minimum width=3.8cm,minimum height=0.9em,anchor=south west] (emb) at ([shift={(1.25cm,0.8cm)}]start) {};
@@ -2494,12 +2495,13 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
 \item 对比
 \end{itemize}
 
+\vspace{-0.5em}
 \begin{center}
-{\small
+{\footnotesize
 \begin{tabular}{l | l}
 引入注意力机制以前 & 引入注意力机制以后 \\ \hline
-$\textrm{``Have''} = \argmax_{y} \textrm{P}(y|0, \alert{\textbf{C}})$ & $\textrm{``Have''} = \argmax_{y} \textrm{P}(y|0, \alert{\textbf{C}_1})$ \\
-$\textrm{``you''} = \argmax_{y} \textrm{P}(y|\textbf{s}_1, \alert{\textbf{C}})$ & $\textrm{``you''} = \argmax_{y} \textrm{P}(y|\textbf{s}_1, \alert{\textbf{C}_2})$
+$\textrm{``Have''} = \argmax_{y_1} \textrm{P}(y_1|\alert{\textbf{C}},y_0)$ & $\textrm{``Have''} = \argmax_{y_1} \textrm{P}(y_1|0,\alert{\textbf{C}_1}, y_0)$ \\
+$\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, \alert{\textbf{C}_2},y_1)$
 \end{tabular}
 }
 \end{center}
@@ -4160,7 +4162,7 @@ $\textrm{``you''} = \argmax_{y} \textrm{P}(y|\textbf{s}_1, \alert{\textbf{C}})$
 \node [posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east) {\tiny{$\textbf{Postion}$}};
 \node [anchor=north] (outputs) at ([yshift=-3em]sa2.south) {\tiny{$\textbf{解码器输入: $<$SOS$>$ I  am  fine}$}};
 \node [anchor=east] (decoder) at ([xshift=-1em,yshift=-1.5em]o1.west) {\scriptsize{\textbf{解码器}}};
-\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}}; 
+\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}};
 
 \draw [->] (sa2.north) -- (res3.south);
 \draw [->] (res3.north) -- (ed1.south);
@@ -4390,7 +4392,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
 \node [posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east) {\tiny{$\textbf{Postion}$}};
 \node [anchor=north] (outputs) at ([yshift=-3em]sa2.south) {\tiny{$\textbf{解码器输入: $<$SOS$>$ I  am  fine}$}};
 \node [anchor=east] (decoder) at ([xshift=-1em,yshift=-1.5em]o1.west) {\scriptsize{\textbf{解码器}}};
-\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}}; 
+\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}};
 
 \draw [->] (sa2.north) -- (res3.south);
 \draw [->] (res3.north) -- (ed1.south);
@@ -4776,7 +4778,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
 \node [posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east) {\tiny{$\textbf{Postion}$}};
 \node [anchor=north] (outputs) at ([yshift=-3em]sa2.south) {\tiny{$\textbf{解码器输入: $<$SOS$>$ I  am  fine}$}};
 \node [anchor=east] (decoder) at ([xshift=-1em,yshift=-1.5em]o1.west) {\scriptsize{\textbf{解码器}}};
-\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}}; 
+\node [anchor=north] (decoutputs) at ([yshift=1.5em]o1.north) {\tiny{$\textbf{解码器输出: I  am  fine $<$EOS$>$ }$}};
 
 \draw [->] (sa2.north) -- (res3.south);
 \draw [->] (res3.north) -- (ed1.south);