new page of tensor

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

@@ -105,7 +105,7 @@
 \subsection{神经网络的简单实现：张量计算}
 
 %%%------------------------------------------------------------------------------------------------------------
-%%% 何为张量
+%%% 张量
 \begin{frame}{如何描述神经网络 - 张量计算}
 \begin{itemize}
 \item 对于神经网络，输入$\textbf{x}$和输出$\textbf{y}$的形式并不仅仅是向量
@@ -141,11 +141,23 @@
 \node [anchor=center,fill=purple!20] (b2) at (b) {\LARGE{$\textbf{b}$}};
 \node [anchor=south] (blabel) at ([yshift=1.3em]b.north) {向量 e.g.,};
 \draw [<-] ([yshift=0.2em]b2.north) -- (blabel.south);
-\node [anchor=west] (bsample) at ([xshift=-0.5em]blabel.east) {\footnotesize{$(1 \ \ 3)$}};
+\node [anchor=west] (bsample) at ([xshift=-0.5em]blabel.east) {\footnotesize{$(1, 3)$}};
 }
 
+\end{tikzpicture}
+\end{center}
 
+\begin{itemize}
+\item<3-> $\textbf{x}$和$\textbf{y}$实际上是一个叫tensor的东西，即\textbf{张量}。比如，
+\end{itemize}
 
+\begin{center}
+\begin{tikzpicture}
+\begin{scope}
+\visible<4->{\node [anchor=west] (vector) at (0,0) {$\textbf{x} = (1,  3)$};}
+\visible<5->{\node [anchor=west] (matrix) at ([xshift=0.1in]vector.east) {$\textbf{x} = \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right)$};}
+\visible<6->{\node [anchor=west] (tensor3d) at ([xshift=0.1in]matrix.east) {啥？$\textbf{x} = \left(\begin{array}{c} \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right) \\ \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right) \end{array}\right)$};}
+\end{scope}
 \end{tikzpicture}
 \end{center}
 

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

@@ -1596,6 +1596,66 @@ cycle}
 \subsection{神经网络的简单实现：张量计算}
 
 %%%------------------------------------------------------------------------------------------------------------
+%%% 张量
+\begin{frame}{如何描述神经网络 - 张量计算}
+\begin{itemize}
+\item 对于神经网络，输入$\textbf{x}$和输出$\textbf{y}$的形式并不仅仅是向量
+\end{itemize}
+
+\begin{center}
+\begin{tikzpicture}
+
+\node [anchor=center] (y) at (0,0) {\LARGE{$\textbf{y}$}};
+\node [anchor=west] (eq) at (y.east) {\LARGE{$=$}};
+\node [anchor=west] (func) at (eq.east) {\LARGE{$f$}};
+\node [anchor=west] (brace01) at (func.east) {\LARGE{$($}};
+\node [anchor=west] (x) at (brace01.east) {\LARGE{$\textbf{x}$}};
+\node [anchor=west] (dot) at (x.east) {\LARGE{$\cdot$}};
+\node [anchor=west] (w) at (dot.east) {\LARGE{$\textbf{w}$}};
+\node [anchor=west] (plus) at (w.east) {\LARGE{$+$}};
+\node [anchor=west] (b) at (plus.east) {\LARGE{$\textbf{b}$}};
+\node [anchor=west] (brace02) at (b.east) {\LARGE{$)$}};
+
+\visible<2->{
+\node [anchor=center,fill=yellow!30] (x2) at (x) {\LARGE{$\textbf{x}$}};
+\node [anchor=south] (xlabel) at ([xshift=-3em,yshift=1.5em]x.north) {\alert{向量？矩阵？...}};
+\draw [<-] ([yshift=0.2em,xshift=-0.5em]x2.north) -- ([xshift=1em]xlabel.south);
+
+\node [anchor=center,fill=red!20] (y2) at (y) {\LARGE{$\textbf{y}$}};
+\draw [<-] ([yshift=0.2em,xshift=0.5em]y2.north) -- ([xshift=-1em]xlabel.south);
+
+\node [anchor=center,fill=green!20] (w2) at (w) {\LARGE{$\textbf{w}$}};
+\node [anchor=north] (wlabel) at ([yshift=-1.0em]w.south) {矩阵 e.g.,};
+\draw [<-] ([yshift=-0.2em]w2.south) -- (wlabel.north);
+\node [anchor=west] (wsample) at ([xshift=-0.5em]wlabel.east) {\footnotesize{$\left(\begin{array}{c c} 1 & 2 \\ 3 & 4 \end{array}\right)$}};
+
+\node [anchor=center,fill=purple!20] (b2) at (b) {\LARGE{$\textbf{b}$}};
+\node [anchor=south] (blabel) at ([yshift=1.3em]b.north) {向量 e.g.,};
+\draw [<-] ([yshift=0.2em]b2.north) -- (blabel.south);
+\node [anchor=west] (bsample) at ([xshift=-0.5em]blabel.east) {\footnotesize{$(1, 3)$}};
+}
+
+\end{tikzpicture}
+\end{center}
+
+\begin{itemize}
+\item<3-> $\textbf{x}$和$\textbf{y}$实际上是一个叫tensor的东西，即\textbf{张量}。比如，
+\end{itemize}
+
+\begin{center}
+\begin{tikzpicture}
+\begin{scope}
+\visible<4->{\node [anchor=west] (vector) at (0,0) {$\textbf{x} = (1,  3)$};}
+\visible<5->{\node [anchor=west] (matrix) at ([xshift=0.1in]vector.east) {$\textbf{x} = \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right)$};}
+\visible<6->{\node [anchor=west] (tensor3d) at ([xshift=0.1in]matrix.east) {啥？$\textbf{x} = \left(\begin{array}{c} \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right) \\ \left(\begin{array}{c c} -1 & 3 \\ 0.2 & 2 \end{array}\right) \end{array}\right)$};}
+\end{scope}
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
+
+
+%%%------------------------------------------------------------------------------------------------------------
 \subsection{参数学习 - 反向传播}
 
 \end{CJK}