example of perceptron

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

@@ -311,7 +311,7 @@ y = f(w \cdot x + b)
 \begin{center}
 \begin{tikzpicture}
 \begin{scope}
-\node [anchor=center,circle,draw,thick,minimum size=3em] (neuron) at (0,0) {};
+\node [anchor=center,circle,draw,ublue,very thick,minimum size=3.5em,fill=white,drop shadow] (neuron) at (0,0) {};
 \node [anchor=east] (x1) at ([xshift=-6em]neuron.west) {\Large{$x_1$}};
 \node [anchor=center] (x0) at ([yshift=3em]x1.center) {\Large{$x_0$}};
 \node [anchor=center] (x2) at ([yshift=-3em]x1.center) {\Large{$x_2$}};
@@ -358,7 +358,7 @@ y = f(w \cdot x + b)
     \begin{itemize}
     \item $x_0$：剧场是否离你足够近？
     \item $x_1$：票价是否低于300元？
-    \item $x_2$：女朋友是否愿意一起？
+    \item $x_2$：女朋友是否喜欢音乐会？
     \end{itemize}
 \item<2-> 如何决定？比如，女朋友很希望和你一起，但是剧场很远而且票价500元。如果这些因素对你的决策都是同等重要的，那么会有一个综合得分：
     \begin{displaymath}
@@ -373,26 +373,26 @@ y = f(w \cdot x + b)
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
-%%% 感知机 - 一个例子（cont）
-\begin{frame}{一个例子（继续）}
+%%% 感知机 - 一个例子：权重
+\begin{frame}{一个例子 - 权重}
 \begin{itemize}
 \item 可以看出，实际上这个决策过程本质上就是一个感知机
 \item<2-> 但是，人并不是完美的，往往对有些事情会更在意一些。如果你是\textbf{守财奴}，因此会对票价看的更重一些，这时你会用不均匀的权重计算每个因素的影响，比如：$w_0=0.5$，$w_1=2$，$w_2=0.5$
-\item<3-> 女朋友很希望和你一起，但是剧场很远而且票价500元，会导致你\alert{选择不去}看音乐会（女朋友都不要了，咋整）
+\item<3-> 女友很希望和你一起，但是剧场很远而且票价500元，会导致你\alert{选择不去}看音乐会（女朋友都不要了，咋整）
     \begin{displaymath}
     \sum_i x_i \cdot w_i = 0 \cdot 0.5 + 0 \cdot 2 + 1 \cdot 0.5 = 0.5 < \sigma = 1
     \end{displaymath}
 \end{itemize}
 
-\vspace{-0.8em}
+\vspace{-1.8em}
 \begin{center}
 \begin{tikzpicture}
 \begin{scope}
-\node [anchor=center,circle,draw,thick,minimum size=3em] (neuron) at (0,0) {};
+\node [anchor=center,circle,draw,ublue,very thick,minimum size=3.5em,fill=white,drop shadow] (neuron) at (0,0) {};
 \node [anchor=east] (x1) at ([xshift=-6em]neuron.west) {$x_1$:票价够低？};
 \node [anchor=center] (x0) at ([yshift=3em]x1.center) {$x_0$:距离够近？};
-\node [anchor=center] (x2) at ([yshift=-3em]x1.center) {$x_2$:女友一起？};
-\node [anchor=west] (y) at ([xshift=2em]neuron.east) {$y$:去不去？};
+\node [anchor=center] (x2) at ([yshift=-3em]x1.center) {$x_2$:女友喜欢？};
+\node [anchor=west] (y) at ([xshift=2em]neuron.east) {$y$:去？还是不去？};
 
 \visible<1>{
 \draw [->,thick] (x0.east) -- (neuron.150) node [pos=0.5,above,yshift=0.2em] {\small{$w_0=1$}};
@@ -420,17 +420,17 @@ y = f(w \cdot x + b)
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
-%%% 感知机 - 一个例子（cont2）
-\begin{frame}{一个例子（还在继续）}
+%%% 感知机 - 一个例子：输入形式
+\begin{frame}{一个例子 - 输入形式}
 
 \begin{itemize}
 \item 在遭受了女友一万点伤害之后，你意识到决策不应该只考虑非0即1的因素，应该把"程度"考虑进来：
     \begin{itemize}
     \item $x_0$：10/距离
     \item $x_1$：150/票价
-    \item $x_2$：女朋友是否愿意一起？(这条不敢改)
+    \item $x_2$：女朋友是否喜欢？(这条不敢改)
     \end{itemize}
-\item<2-> 这时，$x_0$和$x_1$是连续变量，$x_2$是一个离散变量
+\item<2-> 新模型中，$x_0$和$x_1$是连续变量，$x_2$是一个离散变量
 \end{itemize}
 
 \visible<2->{
@@ -470,8 +470,164 @@ y = f(w \cdot x + b)
     \begin{displaymath}
     \sum_i x_i \cdot w_i = 0.5 \cdot 0.5 + 0.3 \cdot 2 + 1 \cdot 0.5 = 1.35 \ge \sigma = 1
     \end{displaymath}
-\end{itemize} 
+\end{itemize}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% 感知机 - 一个例子 - 学习
+\begin{frame}{一个例子 - 学习}
+
+\begin{itemize}
+\item 一次成功的音乐会之后，你似乎掌握了真理：只要女朋友开心就好，为何不把这个因素的权重调大。最简单的方式是把$w_0$，$w_1$的权重都置0，同时令$w_3 > 0$
+\item<3-> 很快又有一场音乐会，距你1000公里，票价（不含路费）3000元，当然你女友是一直是喜欢音乐会的。根据新的决策模型，你义无反顾地\alert{决定去听}这场音乐会
+\item<4-> \textbf{之后}，你女朋友又给了你1万点伤害，痛啊！！！
+    \begin{itemize}
+    \item \alert{结果你发现}：女友既要浪漫，同时也爱财
+    \end{itemize}
+\end{itemize}
+
+\begin{center}
+\begin{tikzpicture}
+\begin{scope}
+\node [anchor=center,circle,draw,ublue,very thick,minimum size=3.5em,fill=white,drop shadow] (neuron) at (0,0) {};
+\node [anchor=east] (x1) at ([xshift=-6em]neuron.west) {$x_1$:便宜程度\ \ \ \ };
+\node [anchor=center] (x0) at ([yshift=3em]x1.center) {$x_0$:远近程度\ \ \ \ };
+\node [anchor=center] (x2) at ([yshift=-3em]x1.center) {$x_2$:女友喜欢？};
+\node [anchor=west] (y) at ([xshift=2em]neuron.east) {$y$:去？还是不去？};
+
+\draw [->,thick] (neuron.east) -- (y.west);
+
+\node [anchor=center] (neuronmath) at (neuron.center) {\small{$\sum \ge \sigma$}};
+
+\visible<1>{
+\draw [->,thin] (x0.east) -- (neuron.150) node [pos=0.5,above,yshift=0.2em] {\small{$w_0=.5$}};
+\draw [->,line width=0.8mm] (x1.east) -- (neuron.180) node [pos=0.5,above,yshift=-0.1em] {\textbf{\small{$w_1=2$}}};
+\draw [->,thin] (x2.east) -- (neuron.210) node [pos=0.5,above,yshift=0.1em] {\small{$w_2=.5$}};
+}
+
+\visible<2->{
+\draw [->,dotted] (x0.east) -- (neuron.150) node [pos=0.5,above,yshift=0.2em] {\small{$w_0=0$}};
+\draw [->,dotted] (x1.east) -- (neuron.180) node [pos=0.5,above,yshift=-0.1em] {\textbf{\small{$w_1=0$}}};
+\draw [->,line width=1mm] (x2.east) -- (neuron.210) node [pos=0.5,above,yshift=0.1em] {\small{$w_2=10$}};
+}
 
+
+\end{scope}
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% 感知机 - 一个例子 - 学习(cont)
+\begin{frame}{一个例子 - 权重学习}
+\begin{itemize}
+\item \textbf{痛定思痛}，你发现每个因素的权重需要准确地设置才能达到最好的决策效果
+    \begin{itemize}
+    \item 如何确定最好的权重？
+    \end{itemize}
+\item<2-> \textbf{当然}，你是一个勇于实践的人
+    \begin{itemize}
+    \item 方法很简单：不断地尝试，根据结构不断地调整权重
+    \item<10-> 在进行了很多次实验后，发现了相对好的一组决策模型
+    \end{itemize}
+\end{itemize}
+
+\visible<2->{
+\begin{center}
+\begin{tikzpicture}
+
+\begin{scope}[scale=0.6]
+\visible<3->{
+\draw [->,thick] (0,0) -- (2.5,0);
+\draw [->,thick] (0,0) -- (0, 1.5);
+\draw [-,very thick,ublue,domain=0.6:2,samples=100] plot (\x,{ 1/\x - 0.2});
+\node [anchor=east] (ylabel) at (0, 3.2em) {\footnotesize{$x_0$}};
+\node [anchor=north] (xlabel) at (5em, 0em) {\tiny{距离(km)}};
+}
+
+\visible<4->{
+\draw [-,thick] (0.25,-1.5) -- (2.25,-1.5);
+\node [anchor=east] (wlabel) at (0.25,-1.5) {\footnotesize{$w_0$}};
+}
+
+\visible<5>{\node [anchor=north,fill=ugreen,minimum height=0.5em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+\visible<6>{\node [anchor=north,fill=ugreen,minimum height=0.3em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+\visible<7>{\node [anchor=north,fill=ugreen,minimum height=1.8em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+\visible<8>{\node [anchor=north,fill=ugreen,minimum height=0.3em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+\visible<9>{\node [anchor=north,fill=ugreen,minimum height=0.3em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+\visible<10->{\node [anchor=north,fill=ugreen,minimum height=0.8em,minimum width=1.5em] (w0) at (1.25,-1.5) {};}
+
+\end{scope}
+
+\begin{scope}[scale=0.6,xshift=12em]
+\visible<3->{
+\draw [->,thick] (0,0) -- (2.5,0);
+\draw [->,thick] (0,0) -- (0, 1.5);
+\draw [-,very thick,ublue,domain=0.4:2,samples=100] plot (\x,{ 0.5/\x});
+\node [anchor=east] (ylabel) at (0, 3.2em) {\footnotesize{$x_1$}};
+\node [anchor=north] (xlabel) at (5em, 0em) {\tiny{票价(元)}};
+}
+
+\visible<4->{
+\draw [-,thick] (0.25,-1.5) -- (2.25,-1.5);
+\node [anchor=east] (wlabel) at (0.25,-1.5) {\footnotesize{$w_1$}};
+}
+
+\visible<5>{\node [anchor=north,fill=ugreen,minimum height=0.5em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+\visible<6>{\node [anchor=north,fill=ugreen,minimum height=1.5em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+\visible<7>{\node [anchor=north,fill=ugreen,minimum height=0.8em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+\visible<8>{\node [anchor=north,fill=ugreen,minimum height=0.1em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+\visible<9>{\node [anchor=north,fill=ugreen,minimum height=1.0em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+\visible<10->{\node [anchor=north,fill=ugreen,minimum height=0.3em,minimum width=1.5em] (w1) at (1.25,-1.5) {};}
+
+\end{scope}
+
+\begin{scope}[scale=0.6,xshift=24em]
+\visible<3->{
+\draw [->,thick] (0,0) -- (2.5,0);
+\draw [->,thick] (0,0) -- (0, 1.5);
+\node [anchor=east] (ylabel) at (0, 3.2em) {\footnotesize{$x_2$}};
+\node [anchor=south, fill=ublue, minimum width=0.8em, minimum height=0.1em, inner sep=0] (histogram1) at (1.5em, 0) {};
+\node [anchor=south, fill=ublue, minimum width=0.8em, minimum height=2em, inner sep=0] (histogram2) at (4.0em, 0) {};
+\node [anchor=north,align=left] (hlabel1) at (histogram1.south) {\tiny{女友no}};
+\node [anchor=north,align=left] (hlabel2) at ([xshift=0.5em]histogram2.south) {\tiny{女友yes}};
+}
+
+\visible<4->{
+\draw [-,thick] (0.25,-1.5) -- (2.25,-1.5);
+\node [anchor=east] (wlabel) at (0.25,-1.5) {\footnotesize{$w_2$}};
+}
+
+\visible<5>{\node [anchor=north,fill=ugreen,minimum height=0.5em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+\visible<6>{\node [anchor=north,fill=ugreen,minimum height=1.2em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+\visible<7>{\node [anchor=north,fill=ugreen,minimum height=0.8em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+\visible<8>{\node [anchor=north,fill=ugreen,minimum height=1.2em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+\visible<9>{\node [anchor=north,fill=ugreen,minimum height=1.5em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+\visible<10->{\node [anchor=north,fill=ugreen,minimum height=1.3em,minimum width=1.5em] (w2) at (1.25,-1.5) {};}
+
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+
+}
+
+\visible<5->{
+\begin{center}
+\begin{tabular}{c<{\onslide<5->}c<{\onslide<6->}c<{\onslide<7->}c<{\onslide<8->}c<{\onslide<9->}c<{\onslide<10->}c<{\onslide}}
+实验 & 1 & 2 & 3 & 4 & ... & 10k \\
+结果 & 失败 & 成功 & 失败 & 失败 & ... & 成功
+\end{tabular}
+\end{center}
+}
+
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%% 感知机 - 一个例子 - 总结
+\begin{frame}{一个例子 - 总结}
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------