new pages

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

@@ -26,6 +26,7 @@
 \usetikzlibrary{matrix}
 \usetikzlibrary{arrows,decorations.pathreplacing}
 \usetikzlibrary{shadows} % LATEX and plain TEX when using Tik Z
+\usetikzlibrary{shadows.blur}
 
 \usepgflibrary{arrows} % LATEX and plain TEX and pure pgf
 \usetikzlibrary{arrows} % LATEX and plain TEX when using Tik Z
@@ -115,51 +116,80 @@
 \newcounter{mycount4}
 
 %%%------------------------------------------------------------------------------------------------------------
-%%% 定义XTensor
-\begin{frame}{定义XTensor}
+%%% 利用XTensor构建神经网络
+\begin{frame}{构建神经网络}
 \begin{itemize}
-\item 张量由类XTensor表示，利用InitTensor定义，参数：
-    \begin{itemize}
-    \item 指向XTensor类型变量的指针
-    \item 张量的阶
-    \item 各个方向维度的大小（维度的约定和传统多维数组一样）
-    \item 张量的数据类型等（有缺省值）
-    \end{itemize}
+\item 可以很方便的构建一个单层网络
 \end{itemize}
 
-\vspace{-0.4em}
-\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
-\begin{flushleft}
-{\scriptsize
+\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 tensor;} \hspace{12em} \= // 声明张量tensor \\
-\texttt{int sizes[6] = \{2,3,4,2,3,4\};} \> // 张量的形状为2*3*4*2*3*4 \\
-\texttt{InitTensor(\&tensor, 6, sizes, X\_FLOAT);} \> // 定义形状为sizes的6阶张量
+\texttt{XTensor x, y, w, b;} \\
+\texttt{InitTensor3D(\&x, 3, 4, 5);} \\
+\texttt{InitTensor2D(\&w, 5, 3);} \\
+\texttt{InitTensor1D(\&b, 3);} \\
+\texttt{...} \\
+\texttt{y = Sigmoid(MMul(x, w) + b);}
 \end{tabbing}
 }
-\end{flushleft}
+\tcblower
+\begin{center}
+\begin{tikzpicture}
+\node [draw,circle,inner sep=2pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (x) at (0,0) {\footnotesize{$\textrm{x}$}};
+\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=4em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (layer) at ([yshift=0.7em]x.north) {\scriptsize{layer}};
+\node [anchor=south,draw,circle,inner sep=2pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (y) at ([yshift=0.7em]layer.north) {\scriptsize{$\textrm{y}$}};
+\draw [thick,->] (x.north) -- (layer.south);
+\draw [thick,->] (layer.north) -- (y.south);
+\node [anchor=west,align=left] (xshape) at (x.east) {\tiny{shape: 3*4*5}};
+\node [anchor=west,align=left] (yshape) at (y.east) {\tiny{shape: 3*4*3}};
+\end{tikzpicture}
+\end{center}
 \end{tcolorbox}
 
 \visible<2->{
 \begin{itemize}
-\item 更简便的定义方式
+\item 一个多层网络
 \end{itemize}
 
-\vspace{-0.4em}
-\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
-\begin{flushleft}
-{\scriptsize
+\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 a, b, c, d, e;} \hspace{8.5em} \= // 声明张量tensor \\
-\texttt{InitTensor1D(\&a, 10, X\_FLOAT);} \> // 10维的浮点型向量\\
-\texttt{InitTensor1D(\&b, 10);} \> // 10维的向量，缺省类型(浮点)\\
-\texttt{InitTensor2D(\&c, 10, 20);} \> // 10*20的矩阵(缺省为浮点型) \\
-\texttt{InitTensor3D(\&d, 10, 20, 30, X\_INT);} \> // 10*20*30的整型型3阶张量\\
-\texttt{InitTensor4D(\&e, 10, 20, 30, 40);} \> // 10*20*30*40的4阶张量\\
- \> // (缺省为浮点型)
+\texttt{XTensor x, y, h1, h2;} \\
+\texttt{XTensor w1, b1, w2, w3;} \\
+\texttt{InitTensor3D(\&x, 3, 4, 5);} \\
+\texttt{InitTensor2D(\&w1, 5, 3);} \\
+\texttt{InitTensor1D(\&b1, 3);} \\
+\texttt{InitTensor2D(\&w2, 3, 6);} \\
+\texttt{InitTensor2D(\&w3, 6, 4);} \\
+\texttt{...} \\
+\texttt{h1 = Sigmoid(MMul(x, w1) + b1);} \\
+\texttt{h2 = HandTanH(MMul(h1, w2));} \\
+\texttt{y = Relu(MMul(h2, w3));}
 \end{tabbing}
 }
-\end{flushleft}
+\tcblower
+\begin{center}
+\begin{tikzpicture}
+\node [draw,circle,inner sep=2pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (x) at (0,0) {\footnotesize{$\textrm{x}$}};
+\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=4em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (layer1) at ([yshift=0.7em]x.north) {\scriptsize{layer1}};
+\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=4em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (layer2) at ([yshift=1.0em]layer.north) {\scriptsize{layer2}};
+\node [anchor=south,draw,rounded corners,inner sep=2pt,minimum width=4em,fill=green!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (layer3) at ([yshift=1.0em]layer2.north) {\scriptsize{layer3}};
+\node [anchor=south,draw,circle,inner sep=2pt,fill=red!30!white,blur shadow={shadow xshift=1pt,shadow yshift=-1pt}] (y) at ([yshift=0.7em]layer3.north) {\scriptsize{$\textrm{y}$}};
+\draw [thick,->] (x.north) -- (layer1.south);
+\draw [thick,->] (layer1.north) -- (layer2.south);
+\draw [thick,->] (layer2.north) -- (layer3.south);
+\draw [thick,->] (layer3.north) -- (y.south);
+\node [anchor=west,align=left] (xshape) at (x.east) {\tiny{shape: 3*4*5}};
+\node [anchor=west,align=left] (yshape) at (y.east) {\tiny{shape: 3*4*4}};
+\node [anchor=south west,align=left,inner sep=2pt] (l1shape) at (layer1.north) {\tiny{shape: 3*4*3}};
+\node [anchor=south west,align=left,inner sep=2pt] (l2shape) at (layer2.north) {\tiny{shape: 3*4*6}};
+\end{tikzpicture}
+\end{center}
 \end{tcolorbox}
 }
 

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

@@ -2127,10 +2127,10 @@ cycle}
 \node [anchor=north] (xlabel) at (0,-1.2) {$\textbf{w}$};
 }
 
-\visible<3>{\draw [->,thick] (-1.5in+2em+1.5em,-0.3) .. controls +(east:2) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
-\visible<4>{\draw [->,thick] (-1.5in+2em+1.0em,-0.5) .. controls +(east:2) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
-\visible<5>{\draw [->,thick] (-1.5in+2em+0.5em,-0.7) .. controls +(east:2.5) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
-\visible<6->{\draw [->,thick] (-1.5in+2em,-0.9) .. controls +(east:3) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
+\visible<3>{\draw [->,thick,dashed] (-1.5in+2em+1.5em,-0.3) .. controls +(east:2) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
+\visible<4>{\draw [->,thick,dashed] (-1.5in+2em+1.0em,-0.5) .. controls +(east:2) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
+\visible<5>{\draw [->,thick,dashed] (-1.5in+2em+0.5em,-0.7) .. controls +(east:2.5) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
+\visible<6->{\draw [->,thick,dashed] (-1.5in+2em,-0.9) .. controls +(east:3) and +(west:1) .. (-0.55,0.8) node [pos=0.5,left] {\scriptsize{\textbf{矩阵乘}}};}
 \end{scope}
 
 \begin{scope}[yshift=6.5em,xshift=1em+3in]
@@ -2318,7 +2318,7 @@ cycle}
 
 \ \ \ \ \texttt{InitTensor2D(\&tensor, 2, 2, X\_FLOAT);} \> // 定义张量为2*2的矩阵 \\
 
-\ \ \ \ \texttt{tensor.SetDataRand();} \> // 用[0,1]的均匀分布初始化张量 \\
+\ \ \ \ \texttt{tensor.SetDataRand();} \> // [0,1]均匀分布初始化张量 \\
 
 \ \ \ \ \texttt{tensor.Dump(stdout);} \> // 输出张量内容 \\
 
@@ -2331,7 +2331,7 @@ cycle}
 \end{tcolorbox}
 
 \begin{itemize}
-\item<2-> 运行这个程序会看到张量每个元素的值
+\item<2-> 运行这个程序会显示张量每个元素的值
 \end{itemize}
 
 \visible<2->{
@@ -2349,11 +2349,162 @@ cycle}
 
 \vspace{-0.5em}
 \begin{itemize}
-\item<2-> 还可以看到：二阶张量(order=2)，形状是$2 \times 2$ (dimsize=2,2)，数据类型是单精度浮点(dtype=X\_FLOAT)，是一个非稀疏张量(dense=1.000)
+\item<2-> 还可以了解到：二阶张量(order=2)，形状是$2 \times 2$ (dimsize=2,2)，数据类型是单精度浮点(dtype=X\_FLOAT)，是一个非稀疏张量(dense=1.000)
 \end{itemize}
 
 \end{frame}
 
+%%%------------------------------------------------------------------------------------------------------------
+%%% 定义XTensor
+\begin{frame}{定义XTensor}
+\begin{itemize}
+\item 张量由类XTensor表示，利用InitTensor定义，参数：
+    \begin{itemize}
+    \item 指向XTensor类型变量的指针
+    \item 张量的阶
+    \item 各个方向维度的大小（与传统多维数组约定一样）
+    \item 张量的数据类型等（有缺省值）
+    \end{itemize}
+\end{itemize}
+
+\vspace{-0.0em}
+\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
+\begin{flushleft}
+{\scriptsize
+\begin{tabbing}
+\texttt{XTensor tensor;} \hspace{12em} \= // 声明张量tensor \\
+\texttt{int sizes[6] = \{2,3,4,2,3,4\};} \> // 张量的形状为2*3*4*2*3*4 \\
+\texttt{InitTensor(\&tensor, 6, sizes, X\_FLOAT);} \> // 定义形状为sizes的6阶张量
+\end{tabbing}
+}
+\end{flushleft}
+\end{tcolorbox}
+
+\visible<2->{
+\begin{itemize}
+\item 更简便的定义方式
+\end{itemize}
+
+\vspace{-0.2em}
+\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
+\begin{flushleft}
+{\scriptsize
+\begin{tabbing}
+\texttt{XTensor a, b, c;} \hspace{11.5em} \= // 声明张量tensor \\
+\texttt{InitTensor1D(\&a, 10, X\_INT);} \> // 10维的整数型向量\\
+\texttt{InitTensor1D(\&b, 10);} \> // 10维的向量，缺省类型(浮点)\\
+\texttt{InitTensor4D(\&c, 10, 20, 30, 40);} \> // 10*20*30*40的4阶张量(浮点)
+\end{tabbing}
+}
+\end{flushleft}
+\end{tcolorbox}
+}
+
+\visible<3->{
+\begin{itemize}
+\item 直接在GPU上定义张量
+\end{itemize}
+
+\vspace{-0.2em}
+\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
+\begin{flushleft}
+{\scriptsize
+\begin{tabbing}
+\texttt{XTensor tensorGPU;} \hspace{10.5em} \= // 声明张量tensor \\
+\texttt{InitTensor2D(\&tensorGPU, 10, 20,} $\backslash$ \> // 在编号为0的GPU上定义张量 \\
+\hspace{6.7em} \texttt{X\_FLOAT, 0);}
+\end{tabbing}
+}
+\end{flushleft}
+\end{tcolorbox}
+}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% XTensor的代数运算
+\begin{frame}{代数运算}
+\begin{itemize}
+\item 各种单元算子（1阶运算）+、-、*、$\backslash$、Log、Exp、 Power、Absolute等，还有Sigmoid、Softmax等激活函数
+\end{itemize}
+
+\vspace{-0.2em}
+\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
+\begin{flushleft}
+{\scriptsize
+\begin{tabbing}
+\texttt{XTensor a, b, c, d, e;} \hspace{7em} \= // 声明张量tensor \\
+\texttt{InitTensor3D(\&a, 2, 3, 4);} \> // a为2*3*4的3阶张量 \\
+\texttt{InitTensor3D(\&b, 2, 3, 4);} \> // b为2*3*4的3阶张量 \\
+\texttt{InitTensor3D(\&c, 2, 3, 4);} \> // c为2*3*4的3阶张量 \\
+\texttt{a.SetDataRand();} \> // 随机初始化a \\
+\texttt{b.SetDataRand();} \> // 随机初始化b \\
+\texttt{c.SetDataRand();} \> // 随机初始化c \\
+\texttt{d = a + b * c;} \> // d被赋值为 a + b * c \\
+\texttt{d = ((a + b) * d - b / c ) * d;} \> // d可以被嵌套使用 \\
+\texttt{e = Sigmoid(d);} \> // d经过激活函数Sigmoid赋值给e
+\end{tabbing}
+}
+\end{flushleft}
+\end{tcolorbox}
+
+\visible<2->{
+\begin{itemize}
+\item 高阶运算，最常用的是矩阵乘法(MMul)
+\end{itemize}
+
+\vspace{-0.2em}
+\begin{tcolorbox}[enhanced,frame engine=empty,boxrule=0.1mm,size=title,colback=blue!10!white]
+\begin{flushleft}
+{\scriptsize
+\begin{tabbing}
+\texttt{XTensor a, b, c;} \hspace{10.0em} \= // 声明张量tensor \\
+\texttt{InitTensor4D(\&a, 2, 2, 3, 4);} \> // a为2*2*3*4的4阶张量 \\
+\texttt{InitTensor2D(\&b, 4, 5);} \> // b为4*5的矩阵 \\
+\texttt{a.SetDataRand();} \> // 随机初始化a \\
+\texttt{b.SetDataRand();} \> // 随机初始化b \\
+\texttt{c = MMul(a, b);} \> // 矩阵乘的结果为2*2*3*5的4阶张量
+\end{tabbing}
+}
+\end{flushleft}
+\end{tcolorbox}
+}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% XTensor的其它函数
+\begin{frame}{其它常用函数}
+\begin{itemize}
+\item 其它函数，列不全，可以参考网站上的详细说明
+\end{itemize}
+
+\footnotesize{
+\begin{center}
+\begin{tabular}{l|l}
+函数 & 描述 \\ \hline
+\texttt{a.Reshape(o, s)} & 把a变换为阶为o、形状为s的张量\\
+\texttt{a.Get(pos)} & 取张量中位置为pos的元素 \\
+\texttt{a.Set(v, pos)} & 把张量中位置为pos的元素的值设为v \\
+\texttt{a.Dump(file)} & 把张量存到file中，file为文件句柄 \\
+\texttt{a.Read(file)} & 从file中读取张量，file为文件句柄 \\ \hline
+\texttt{Power(a, p)}  & 计算指数$\textrm{a}^{\textrm{p}}$ \\
+\texttt{Linear(a, s, b)}  & 计算 a * s + b，s和b都是一个数 \\
+\texttt{CopyValues(a)} & 构建a的一个拷贝 \\
+\texttt{ReduceMax(a, d)} & 对a沿着方向d进行规约，得到最大值 \\
+\texttt{ReduceSum(a, d)} & 对a沿着方向d进行规约，得到和 \\
+\texttt{Concatenate(a, b, d)} & 把两个张量a和b沿d方向级联\\
+\texttt{Merge(a, d)} & 对张量a沿d方向合并\\
+\texttt{Split(a, d, n)} & 对张量a沿d方向分裂成n份\\ \hline
+\texttt{Sigmoid(a)}  & 对a进行Sigmoid变换 \\
+\texttt{Softmax(a)}  & 对a进行Softmax变换，沿最后一个方向 \\
+\texttt{HardTanH(a)} & 对a进行hard tanh变换(双曲正切的近似)\\
+\texttt{Relu(a)}     & 对a进行Relu变换\\
+\end{tabular}
+\end{center}
+}
+
+\end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
 \subsection{参数学习 - 反向传播}