math description of perceptron

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

@@ -686,11 +686,11 @@ y = f(w \cdot x + b)
 \begin{tikzpicture}
 
 {\Large
-\node [anchor=west,draw,ublue,very thick,rounded corners=4pt,text width=18em,align=left,fill=white,drop shadow={shadow xshift=0.2em,shadow yshift=-0.2em}] (p1) at (0,0) {\black{\textbf{1. 人工神经网络的数学描述是什么？}}\\\black{\textbf{\hspace{0.9em} 如何实现这种数学模型？}}};
+\node [anchor=west,draw,ublue,very thick,rounded corners=4pt,text width=18em,align=left,fill=white,drop shadow={shadow xshift=0.2em,shadow yshift=-0.2em}] (p1) at (0,0) {\black{\textbf{1. 人工神经网络的数学描述是什么，}}\\\black{\textbf{\hspace{0.9em} 如何实现这种数学模型？}}};
 
 \node [anchor=north west,draw,ublue,very thick,rounded corners=4pt,text width=18em,align=left,fill=white,drop shadow={shadow xshift=0.2em,shadow yshift=-0.2em}] (p21) at ([yshift=-1em]p1.south west) {\black{\textbf{2. 如何将简单的网络单元组合成更}}\\\black{\textbf{\hspace{0.9em} 强大的模型？}}};
 
-\node [anchor=north west,draw,ublue,very thick,rounded corners=4pt,text width=18em,align=left,fill=white,drop shadow={shadow xshift=0.2em,shadow yshift=-0.2em}] (p22) at ([yshift=-1em]p21.south west) {\black{\textbf{3. 如何对模型中的参数进行学习？}}\\\black{\textbf{\hspace{0.9em} 如何使用学习到的模型进行推断？}}};
+\node [anchor=north west,draw,ublue,very thick,rounded corners=4pt,text width=18em,align=left,fill=white,drop shadow={shadow xshift=0.2em,shadow yshift=-0.2em}] (p22) at ([yshift=-1em]p21.south west) {\black{\textbf{3. 如何对模型中的参数进行学习，}}\\\black{\textbf{\hspace{0.9em} 如何使用学习到的模型进行推断？}}};
 }
 
 \end{tikzpicture}
@@ -702,6 +702,76 @@ y = f(w \cdot x + b)
 \subsection{数学基础：张量计算}
 
 %%%------------------------------------------------------------------------------------------------------------
+%%% 人工神经元的函数形式
+\begin{frame}{人工神经元即一个函数}
+
+\begin{itemize}
+\item 神经元：
+\end{itemize}
+
+\vspace{-1em}
+\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 ([yshift=1.5em]x.north) {输入};
+\draw [<-] ([yshift=0.2em]x2.north) -- (xlabel.south);
+}
+
+\visible<3->{
+\node [anchor=center,fill=green!20] (w2) at (w) {\LARGE{$\textbf{w}$}}; 
+\node [anchor=north] (wlabel) at ([yshift=-1.5em]w.south) {参数(权重)};
+\draw [<-] ([yshift=-0.2em]w2.south) -- (wlabel.north);
+}
+
+\visible<4->{
+\node [anchor=center,fill=purple!20] (b2) at (b) {\LARGE{$\textbf{b}$}}; 
+\node [anchor=south] (blabel) at ([yshift=1.3em]b.north) {偏移};
+\draw [<-] ([yshift=0.2em]b2.north) -- (blabel.south);
+}
+
+\visible<5->{
+\node [anchor=center,fill=blue!20] (func2) at (func) {\LARGE{$f$}};
+\node [anchor=north] (funclabel) at ([yshift=-1.1em]func.south) {激活函数};
+\draw [<-] ([yshift=-0.2em]func2.south) -- (funclabel.north);
+}
+
+\visible<6->{
+\node [anchor=center,fill=red!20] (y2) at (y) {\LARGE{$\textbf{y}$}};
+\node [anchor=south] (ylabel) at ([yshift=1.3em]y.north) {输出};
+\draw [<-] ([yshift=0.2em]y2.north) -- (ylabel.south);
+}
+
+\end{tikzpicture}
+\end{center}
+
+\vspace{-1em}
+\begin{itemize}
+\item<7-> 以感知机为例
+	\begin{itemize}
+	\item 输入：$\textbf{x}=(x_0,...,x_n)$
+	\item 权重：$\textbf{w}=(w_0,...,w_n)$
+	\item 偏移：$\textbf{b} = (-\sigma)$
+	\item 激活函数：$f(z)=1$ 当$z \ge 0$, 其它情况$f(z)=0$
+	\item 输出：$\textbf{y}=f(\textbf{x} \cdot \textbf{z} - \sigma)$
+	\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
 \subsection{多层神经网络}
 
 %%%------------------------------------------------------------------------------------------------------------