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Chapter11/Figures/figure-use-cnn-in-sentence-classification.tex

@@ -8,23 +8,20 @@
 	\tikzstyle{cir} = [thin,fill=blue!8,draw,circle,minimum size =0.5em,drop shadow={shadow xshift=0.15em, shadow yshift=-0.1em}]
 	\tikzstyle{word} = [inner sep=0pt, font=\footnotesize,minimum height=\bcc]
 	
-	\draw[fill=blue!8,xshift=0.3cm,yshift=0.5cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+9*\bcc);
-	\draw[ugreen!60,step=\bcc,xshift=0.3cm,yshift=0.5cm,gray] (0cm,0cm) grid (0cm+6*\bcc,0cm+9*\bcc); 
-	%\draw[line width=0.7pt,xshift=0.3cm,yshift=0.5cm] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+9*\bcc);
-	\draw[red!60,line width=2pt,xshift=0.3cm,yshift=0.5cm] (0cm,0cm+2*\bcc) rectangle (0cm+6*\bcc,0cm+4*\bcc);
-	
+	%\draw[fill=blue!8,xshift=0.3cm,yshift=0.5cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+9*\bcc);
+	%\draw[ugreen!60,step=\bcc,xshift=0.3cm,yshift=0.5cm,gray] (0cm,0cm) grid (0cm+6*\bcc,0cm+9*\bcc); 
+	%\draw[red!60,line width=2pt,xshift=0.3cm,yshift=0.5cm] (0cm,0cm+2*\bcc) rectangle (0cm+6*\bcc,0cm+4*\bcc);
 	
+	% 输入矩阵
 	\draw[thick,fill=blue!8,line width=0.6pt] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+9*\bcc);
 	\draw[step=\bcc,gray] (0cm,0cm) grid (0cm+6*\bcc,0cm+9*\bcc); 
-	%\draw[line width=0.7pt] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+9*\bcc);
 	\draw[red!60,line width=2pt] (0cm,0cm) rectangle (0cm+6*\bcc,0cm+2*\bcc);
 	\draw[ugreen!60,line width=2pt] (0cm,0cm+3*\bcc) rectangle (0cm+6*\bcc,0cm+6*\bcc);
 	\draw[red!60,line width=2pt] (0cm,0cm+7*\bcc) rectangle (0cm+6*\bcc,0cm+9*\bcc);
 
-	
+	% 特征图
 	\draw[fill=blue!8,xshift=5.0cm,yshift=1.3cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+6*\bcc);
 	\draw[step=\bcc,gray,xshift=5.0cm,yshift=1.3cm] (0cm,0cm) grid (0cm+1*\bcc,0cm+6*\bcc);
-	%\draw[xshift=5.0cm,yshift=1.3cm,line width=0.7pt] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+6*\bcc);
 	\draw[ugreen!60,line width=2pt,xshift=5.0cm,yshift=1.3cm] (0cm,0cm+2*\bcc) rectangle (0cm+1*\bcc,0cm+3*\bcc);
 	
 	\draw [gray,fill=blue!8,line width=0.6pt](8cm,2.6cm) -- (8.4cm, 2.6cm) -- (9cm,1cm) -- (8.6cm, 1cm) -- (8cm,2.6cm);
@@ -40,15 +37,12 @@
 	
 	\draw[fill=blue!8,xshift=5.2cm,yshift=1.0cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+6*\bcc);
 	\draw[step=\bcc,gray,xshift=5.2cm,yshift=1.0cm] (0cm,0cm) grid (0cm+1*\bcc,0cm+6*\bcc); 
-	%\draw[line width=0.7pt,xshift=5.2cm,yshift=1.0cm] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+6*\bcc);
 	
 	\draw[fill=blue!8,xshift=5.4cm,yshift=0.3cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+7*\bcc);
 	\draw[step=\bcc,gray,xshift=5.4cm,yshift=0.3cm] (0cm,0cm) grid (0cm+1*\bcc,0cm+7*\bcc);
-	%\draw[line width=0.7pt,xshift=5.4cm,yshift=0.3cm] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+7*\bcc); 
 	
 	\draw[fill=blue!8,xshift=5.6cm,yshift=0cm,line width=0.6pt] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+7*\bcc);
 	\draw[step=\bcc,gray,xshift=5.6cm,yshift=0cm] (0cm,0cm) grid (0cm+1*\bcc,0cm+7*\bcc); 
-	%\draw[line width=0.7pt,xshift=5.6cm,yshift=0cm] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+7*\bcc);
 	\draw[red!60,line width=2pt,xshift=5.6cm,yshift=0cm] (0cm,0cm) rectangle (0cm+1*\bcc,0cm+1*\bcc);
 	\draw[red!60,line width=2pt,xshift=5.6cm,yshift=0cm] (0cm,0cm+2*\bcc) rectangle (0cm+1*\bcc,0cm+3*\bcc);
 	\draw[red!60,line width=2pt,xshift=5.6cm,yshift=0cm] (0cm,0cm+6*\bcc) rectangle (0cm+1*\bcc,0cm+7*\bcc);
@@ -81,18 +75,13 @@
 	\node[draw,rectangle callout,callout relative pointer={(0.28,-0.6)}] at (-0.3cm,4.6cm) {\textrm{卷积核}};
 	\node[draw,rectangle callout,callout relative pointer={(0.1,-0.5)}] at (5cm,4.6cm) {\textrm{特征图}};
 
-	%\draw [thick] (0cm, -0.3cm) -- (0cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{$m \times k$ representation of \\ sentence with static and \\ non-static channels} (2.4cm,-0.5cm) -- (2.4cm, -0.3cm);	
-	%\draw [thick] (3.6cm, -0.3cm) -- (3.6cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{Convolutional layer with \\ multiple filter widths and \\ feature maps} (6cm,-0.5cm) -- (6cm, -0.3cm);
-	%\draw [thick] (7.2cm, -0.3cm) -- (7.2cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{Max-over-time\\  pooling} (9cm,-0.5cm) -- (9cm, -0.3cm);
-	%\draw [thick] (10cm, -0.3cm) -- (10cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{Fully connected layer \\ with dropout and \\ softmax output} (11.7cm,-0.5cm) -- (11.7cm, -0.3cm);
+
 	\draw [thick] (0cm, -0.3cm) -- (0cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{维度大小为 $m \times K$ \\ 的静态与非静态通道\\的句子表示} (2.4cm,-0.5cm) -- (2.4cm, -0.3cm);	
 	\draw [thick] (3.6cm, -0.3cm) -- (3.6cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{具有多个不同大小\\的卷积核和特征图\\的卷积层} (6cm,-0.5cm) -- (6cm, -0.3cm);
 	\draw [thick] (7.2cm, -0.3cm) -- (7.2cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{最大池化} (9cm,-0.5cm) -- (9cm, -0.3cm);
 	\draw [thick] (10cm, -0.3cm) -- (10cm, -0.5cm)  -- node[font=\tiny, align=center,yshift=-0.5cm]{带有Dropout\\和Softmax输出\\的全连接层} (11.7cm,-0.5cm) -- (11.7cm, -0.3cm);
 	
 	
-	 %\node [font=\Large] at (5.2cm,-2cm){$h_i = dot(F,x_{i:i+l-1})+b$};
-	
 \end{scope}
 
 \end{tikzpicture}
\ No newline at end of file

Chapter12/chapter12.tex

@@ -324,11 +324,11 @@
 
 \begin{itemize}
 \vspace{0.5em}
-\item 首先，将$\mathbi{Q}$、$\mathbi{K}$、$\mathbi{V}$分别通过线性（Linear）变换的方式映射为$h$个子集。即$\mathbi{Q}_i = \mathbi{Q}\mathbi{W}_i^Q $、$\mathbi{K}_i = \mathbi{K}\mathbi{W}_i^K $、$\mathbi{V}_i = \mathbi{V}\mathbi{W}_i^V $，其中$i$表示第$i$个头， $\mathbi{W}_i^Q  \in \mathbb{R}^{d_{model} \times d_k}$,  $\mathbi{W}_i^K  \in \mathbb{R}^{d_{model} \times d_k}$,  $\mathbi{W}_i^V  \in \mathbb{R}^{d_{model} \times d_v}$是参数矩阵; $d_k=d_v=d_{model} / h$，对于不同的头采用不同的变换矩阵，这里$d_{model}$表示每个隐层向量的维度；
+\item 首先，将$\mathbi{Q}$、$\mathbi{K}$、$\mathbi{V}$分别通过线性（Linear）变换的方式映射为$h$个子集。即$\mathbi{Q}_i = \mathbi{Q}\mathbi{W}_i^{\,Q} $、$\mathbi{K}_i = \mathbi{K}\mathbi{W}_i^{\,K} $、$\mathbi{V}_i = \mathbi{V}\mathbi{W}_i^{\,V} $，其中$i$表示第$i$个头， $\mathbi{W}_i^{\,Q}  \in \mathbb{R}^{d_{model} \times d_k}$,  $\mathbi{W}_i^{\,K}  \in \mathbb{R}^{d_{model} \times d_k}$,  $\mathbi{W}_i^{\,V}  \in \mathbb{R}^{d_{model} \times d_v}$是参数矩阵; $d_k=d_v=d_{model} / h$，对于不同的头采用不同的变换矩阵，这里$d_{model}$表示每个隐层向量的维度；
 \vspace{0.5em}
 \item 其次，对每个头分别执行点乘注意力操作，并得到每个头的注意力操作的输出$\mathbi{head}_i$；
 \vspace{0.5em}
-\item 最后，将$h$个头的注意力输出在最后一维$d_v$进行拼接（Concat）重新得到维度为$h \times d_v$的输出，并通过对其左乘一个权重矩阵$\mathbi{W}^o$进行线性变换，从而对多头计算得到的信息进行融合，且将多头注意力输出的维度映射为模型的隐层大小（即$d_{model}$），这里参数矩阵$\mathbi{W}^o \in \mathbb{R}^{h \times d_v \times d_{model}}$。
+\item 最后，将$h$个头的注意力输出在最后一维$d_v$进行拼接（Concat）重新得到维度为$h \times d_v$的输出，并通过对其左乘一个权重矩阵$\mathbi{W}^{\,o}$进行线性变换，从而对多头计算得到的信息进行融合，且将多头注意力输出的维度映射为模型的隐层大小（即$d_{model}$），这里参数矩阵$\mathbi{W}^{\,o} \in \mathbb{R}^{h \times d_v \times d_{model}}$。
 \vspace{0.5em}
 \end{itemize}
 
@@ -343,8 +343,8 @@
 
 \parinterval 多头机制可以被形式化描述为如下公式：
 \begin{eqnarray}
-\textrm{MultiHead}(\mathbi{Q}, \mathbi{K} , \mathbi{V})& = & \textrm{Concat} (\mathbi{head}_1, ... , \mathbi{head}_h ) \mathbi{W}^o \label{eq:12-48} \\
-\mathbi{head}_i & = &\textrm{Attention} (\mathbi{Q}\mathbi{W}_i^Q , \mathbi{K}\mathbi{W}_i^K  , \mathbi{V}\mathbi{W}_i^V )
+\textrm{MultiHead}(\mathbi{Q}, \mathbi{K} , \mathbi{V})& = & \textrm{Concat} (\mathbi{head}_1, ... , \mathbi{head}_h ) \mathbi{W}^{\,o} \label{eq:12-48} \\
+\mathbi{head}_i & = &\textrm{Attention} (\mathbi{Q}\mathbi{W}_i^{\,Q} , \mathbi{K}\mathbi{W}_i^{\,K}  , \mathbi{V}\mathbi{W}_i^{\,V} )
 \label{eq:12-49}
 \end{eqnarray}