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Section05-Neural-Networks-and-Language-Modeling/section05-test.tex

@@ -107,104 +107,69 @@
 %%%------------------------------------------------------------------------------------------------------------
 \section{为什么要谈神经网络}
 
-%%%------------------------------------------------------------------------------------------------------------
-\subsection{神经网络的简单实现：张量计算}
-
 \newcounter{mycount1}
 \newcounter{mycount2}
 \newcounter{mycount3}
 \newcounter{mycount4}
 
 %%%------------------------------------------------------------------------------------------------------------
-%%% 利用XTensor构建更复杂的神经网络
-\begin{frame}{更复杂一点的例子}
+\subsection{参数学习 - 反向传播}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% 神经网络 = 表达式
+\begin{frame}{神经网络 = 表达式}
 \begin{itemize}
-\item 任何网络都可以构建，比如RNN、Transformer 等
+\item 所有的神经网络都可以看做由变量和函数组成的表达式\\
 \end{itemize}
 
-\begin{tcolorbox}
-[bicolor,sidebyside,righthand width=4cm,size=title,frame engine=empty,
- colback=blue!10!white,colbacklower=black!5!white]
- {\scriptsize
-\begin{tabbing}
-\texttt{XTensor x[3], y[3], r, wh;} \\
-\texttt{XTensor h1, h2, w1, b1, h3, h4;} \\
-\texttt{XList splits;} \\
-\texttt{...} \\
-\texttt{for(unsigned i = 0; i < 3; i++)\{} \\
-\texttt{\hspace{2em}r = Concatenate(x[i] + r) * wh;}\\
-\texttt{\hspace{2em}splits.Add(\&r);}\\
-\texttt{\}}\\
-\visible<2->{
-\texttt{} \\
-\texttt{h1 = Merge(splits, 0);}\\
-\texttt{h2 = Relu(h1 * w1 + b1);}\\
-\texttt{h3 = h1 + h2;} \\
-\texttt{h4 = Softmax(h3);} \\
-}
-\visible<3->{
-\texttt{} \\
-\texttt{Split(h4, splits, 0);} \\
-\texttt{} \\
-\texttt{for(unsigned i = 0; i < 3; i++)\{} \\
-\texttt{\hspace{2em}y[i] = *(XTensor*)splits.Get(i);}\\
-\texttt{\hspace{2em}y[i].Dump(stdout);}\\
-\texttt{\}}
-}
-\end{tabbing}
-}
-\tcblower
 \begin{center}
 \begin{tikzpicture}
-\node [draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (x1) at (0,0) {\footnotesize{$\textrm{x}_1$}};
-\node [anchor=west,draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (x2) at ([xshift=2em]x1.east) {\footnotesize{$\textrm{x}_2$}};
-\node [anchor=west,draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (x3) at ([xshift=2em]x2.east) {\footnotesize{$\textrm{x}_3$}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=2.5em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (rlayer1) at ([yshift=1em]x1.north) {\tiny{rlayer}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=2.5em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (rlayer2) at ([yshift=1em]x2.north) {\tiny{rlayer}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=2.5em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (rlayer3) at ([yshift=1em]x3.north) {\tiny{rlayer}};
-\draw [->,thick] (x1.north) -- (rlayer1.south);
-\draw [->,thick] (x2.north) -- (rlayer2.south);
-\draw [->,thick] (x3.north) -- (rlayer3.south);
-\draw [->,thick] (rlayer1.east) -- (rlayer2.west);
-\draw [->,thick] (rlayer2.east) -- (rlayer3.west);
-\draw [->,thick] (rlayer1.north) -- ([yshift=1em]rlayer1.north);
-\draw [->,thick] (rlayer2.north) -- ([yshift=1em]rlayer2.north);
-\draw [->,thick] (rlayer3.north) -- ([yshift=1em]rlayer3.north);
+\node [anchor=north west] (eq1) at (0,0) {$\textbf{y} = \textbf{x} + \textbf{b}$};
+\node [anchor=north west] (eq2) at (eq1.south west) {$\textbf{y} = \textrm{Relu}(\textbf{x} \cdot \textbf{w} + \textbf{b})$};
+\node [anchor=north west] (eq3) at (eq2.south west) {$\textbf{y} = (\textrm{Relu}(\textbf{x} \cdot \textbf{w}_1 + \textbf{b}) + \textbf{x}) \cdot \textbf{w}_2$};
+\node [anchor=north west] (eq4) at (eq3.south west) {$\textbf{y} = \textrm{Sigmoid}(\textrm{Relu}(\textbf{x} \cdot \textbf{w}_1 + \textbf{b}_1) + \textbf{x}) \cdot \textbf{w}_2 + \textbf{b}_2$};
 
 \visible<2->{
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=9.4em,minimum height=1.0em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (h1) at ([yshift=1em]rlayer2.north) {\tiny{h1 = Merge($\cdot$)}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=9.4em,minimum height=1.0em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (h2) at ([yshift=1em]h1.north) {\tiny{h2 = Relu($\cdot$)}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=9.4em,minimum height=1.0em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (h3) at ([yshift=1em]h2.north) {\tiny{h3 = Sum($\cdot$)}};
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=9.4em,minimum height=1.0em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (h4) at ([yshift=1em]h3.north) {\tiny{h4 = Softmax($\cdot$)}};
-\draw [->,thick] (h1.north) -- (h2.south);
-\draw [->,thick] (h2.north) -- (h3.south);
-\draw [->,thick] (h3.north) -- (h4.south);
-\draw [->,thick,rounded corners] (h1.east) -- ([xshift=0.5em]h1.east) -- ([xshift=0.5em,yshift=0.5em]h2.north east) -- ([xshift=-2em,yshift=0.5em]h2.north east) -- ([xshift=-2em,yshift=1em]h2.north east);
+\node [anchor=north west,minimum height=1.2em,minimum width=1.2em,fill=green!30!white] (xlabel) at ([yshift=-0.5em,xshift=0.3em]eq4.south west) {};
+\node [anchor=west] (xlabel2) at (xlabel.east) {输入变量 - 由用户指定};
 }
 
+\begin{pgfonlayer}{background}
+\visible<2->{
+\node [anchor=south, minimum height=1.6em,minimum width=0.8em,fill=green!30!white] (x1) at ([xshift=-1.3em]eq4.south) {};
+\node [anchor=south, minimum height=1.6em,minimum width=0.8em,fill=green!30!white] (x2) at ([xshift=4.9em]eq4.south) {};
+}
+\end{pgfonlayer}
+
 \visible<3->{
-\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=9.4em,minimum height=1.0em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (slayer) at ([yshift=1em]h4.north) {\tiny{Split($\cdot$)}};
-\node [anchor=south,draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (y2) at ([yshift=1em]slayer.north) {\footnotesize{$\textrm{y}_2$}};
-\node [anchor=east,draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (y1) at ([xshift=-2em]y2.west) {\footnotesize{$\textrm{y}_1$}};
-\node [anchor=west,draw,circle,inner sep=1pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (y3) at ([xshift=2em]y2.east) {\footnotesize{$\textrm{y}_3$}};
-\draw [<-,thick] (y1.south) -- ([yshift=-1em]y1.south);
-\draw [<-,thick] (y2.south) -- ([yshift=-1em]y2.south);
-\draw [<-,thick] (y3.south) -- ([yshift=-1em]y3.south);
+\node [anchor=north west,minimum height=1.2em,minimum width=1.2em,fill=red!30!white] (wlabel) at ([yshift=-0.3em]xlabel.south west) {};
+\node [anchor=west] (wlabel2) at (wlabel.east) {模型参数 - 怎么设置？？？};
 }
 
-\visible<2->{
-\draw [->,thick] (h4.north) -- (slayer.south);
+\begin{pgfonlayer}{background}
+\visible<3->{
+\node [anchor=south, minimum height=1.6em,minimum width=1.2em,fill=red!30!white] (w1) at ([xshift=0.2em]eq4.south) {};
+\node [anchor=south, minimum height=1.6em,minimum width=1.2em,fill=red!30!white] (b1) at ([xshift=2.5em]eq4.south) {};
+\node [anchor=south, minimum height=1.6em,minimum width=1.2em,fill=red!30!white] (w2) at ([xshift=6.85em]eq4.south) {};
+\node [anchor=south, minimum height=1.6em,minimum width=1.2em,fill=red!30!white] (b2) at ([xshift=9.2em]eq4.south) {};
 }
+\end{pgfonlayer}
 
 \end{tikzpicture}
 \end{center}
-\end{tcolorbox}
 
-\end{frame}
+\visible<4->{
+\begin{tcolorbox}[enhanced,size=normal,left=2mm,right=1mm,colback=blue!5!white,colframe=blue!75!black,drop fuzzy shadow]
+{\Large
+\textbf{问题来了,}
 
+\vspace{0.4em}
+\textbf{如何确定w和b，使x与y对应得更好？}
+}
+\end{tcolorbox}
+}
 
-%%%------------------------------------------------------------------------------------------------------------
-\subsection{参数学习 - 反向传播}
+\end{frame}
 
 \end{CJK}
 \end{document}