figure-the-whole-of-LSTM.tex 6.78 KB
Newer Older
曹润柘 committed
1 2
  
  
曹润柘 committed
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156



%--------------------------------------------------------------------------------
\begin{tikzpicture}
\setlength{\base}{0.6cm}

\tikzstyle{wordnode} = [font=\scriptsize]
\tikzstyle{auxnode} = [inner sep=0pt,outer sep=0pt,opacity=0,draw=red,fill=red,circle,minimum size=3pt]
\tikzstyle{opnode} = [inner sep=0pt,outer sep=0pt,draw,fill=green!30!white,font=\scriptsize,minimum size=10pt]
\tikzstyle{standard} = [rounded corners=5pt,thick]
\tikzstyle{emph} = [rounded corners=5pt,thick,draw=red]
\tikzstyle{formulanode} = [font=\scriptsize,align=left,draw=red,rectangle,fill=red!10!white,rounded corners=2pt,drop shadow]

% Skeleton
\begin{scope}[every label/.append style={label distance=1pt,font=\tiny,inner sep=0pt,opacity=0}]
\coordinate (aux12) at (0,0);
\node[auxnode,label={-45:12}] () at (aux12) {};

\coordinate (aux22) at ([yshift=\base]aux12);
\node[auxnode,label={-45:22}] () at (aux22) {};
\coordinate (aux21) at ([xshift=-2\base]aux22);
\node[auxnode,label={-45:21}] () at (aux21) {};
\coordinate (aux23) at ([xshift=\base]aux22);
\node[auxnode,label={-45:23}] () at (aux23) {};
\coordinate (aux24) at ([xshift=\base]aux23);
\node[auxnode,label={-45:24}] () at (aux24) {};
\coordinate (aux25) at ([xshift=\base]aux24);
\node[auxnode,label={-45:25}] () at (aux25) {};
\coordinate (aux26) at ([xshift=\base]aux25);
\node[auxnode,label={-45:26}] () at (aux26) {};
\coordinate (aux27) at ([xshift=\base]aux26);
\node[auxnode,label={-45:27}] () at (aux27) {};
\coordinate (aux28) at ([xshift=\base]aux27);
\node[auxnode,label={-45:28}] () at (aux28) {};
\coordinate (aux29) at ([xshift=2\base]aux28);
\node[auxnode,label={-45:29}] () at (aux29) {};

\coordinate (aux33) at ([yshift=\base]aux23);
\node[auxnode,label={-45:33}] () at (aux33) {};
\coordinate (aux34) at ([yshift=\base]aux24);
\node[auxnode,label={-45:34}] () at (aux34) {};
\coordinate (aux35) at ([yshift=\base]aux25);
\node[auxnode,label={-45:35}] () at (aux35) {};
\coordinate (aux37) at ([yshift=\base]aux27);
\node[auxnode,label={-45:37}] () at (aux37) {};

\coordinate (aux45) at ([yshift=\base]aux35);
\node[auxnode,label={-45:45}] () at (aux45) {};

\coordinate (aux55) at ([yshift=\base]aux45);
\node[auxnode,label={-45:55}] () at (aux55) {};
\ExtractX{$(aux21)$}
\ExtractY{$(aux55)$}
\coordinate (aux51) at (\XCoord,\YCoord);
\node[auxnode,label={-45:51}] () at (aux51) {};
\ExtractX{$(aux23)$}
\ExtractY{$(aux55)$}
\coordinate (aux53) at (\XCoord,\YCoord);
\node[auxnode,label={-45:53}] () at (aux53) {};
\ExtractX{$(aux28)$}
\ExtractY{$(aux55)$}
\coordinate (aux58) at (\XCoord,\YCoord);
\node[auxnode,label={-45:58}] () at (aux58) {};
\ExtractX{$(aux29)$}
\ExtractY{$(aux55)$}
\coordinate (aux59) at (\XCoord,\YCoord);
\node[auxnode,label={-45:59}] () at (aux59) {};

\coordinate (aux68) at ([yshift=\base]aux58);
\node[auxnode,label={-45:68}] () at (aux68) {};
\end{scope}

\begin{scope}
\node[opnode,circle,opacity=0] (f53) at (aux53) {};
\node[opnode,circle,opacity=0] (u55) at (aux55) {};
% forget gate
{
\draw[emph] (aux21) -- (aux23) -- (aux33);
\draw[-latex,emph] (aux12) -- (aux22) -- (aux23) -- (f53);
\node[opnode,circle,draw=red,thick] () at (aux33) {$\sigma$};
}
{
\draw[standard] (aux21) -- (aux23) -- (aux33);
\draw[-latex,standard] (aux12) -- (aux22) -- (aux23) -- (f53);
\node[opnode,circle] () at (aux33) {$\sigma$};
}
% input gate
{
\node[opnode,circle] (i45) at (aux45) {};
\draw[-latex,emph] (aux21) -- (aux24) |- (i45);
\draw[-latex,emph] (aux21) -- (aux25) -- (u55);
\draw[emph] (aux12) -- (aux22) -- (aux23);
\node[opnode,circle,draw=red,thick] () at (aux34) {$\sigma$};
\node[opnode,rectangle,rounded corners=2pt,inner sep=2pt,draw=red,thick] () at (aux35) {$\mathrm{tanh}$};
\node[opnode,circle,draw=red,thick] (i45) at (aux45) {X};
}
{
\node[opnode,circle] (i45) at (aux45) {};
\draw[-latex,standard] (aux21) -- (aux24) |- (i45);
\draw[-latex,standard] (aux21) -- (aux25) -- (u55);
\node[opnode,circle] () at (aux34) {$\sigma$};
\node[opnode,rectangle,rounded corners=2pt,inner sep=2pt] () at (aux35) {$\mathrm{tanh}$};
\node[opnode,circle] (i45) at (aux45) {X};
}
% cell update
{
\draw[-latex,emph] (aux51) -- (aux59);
\node[opnode,circle,draw=red,thick] (f53) at (aux53) {X};
\node[opnode,circle,draw=red,thick] (u55) at (aux55) {\textbf{+}};
}
{
\draw[-latex,standard] (aux51) -- (aux59);
\node[opnode,circle] (f53) at (aux53) {X};
\node[opnode,circle] (u55) at (aux55) {\textbf{+}};
}
% output gate
{
\node[opnode,circle,draw=red,thick] (o27) at (aux27) {X};
\draw[-latex,emph] (u55) -| (o27);
\draw[-latex,emph] (aux21) -- (o27);
\draw[emph] (aux12) -- (aux22) -- (aux23);
\node[opnode,circle,draw=red,thick] () at (aux26) {$\sigma$};
\node[opnode,rectangle,rounded corners=2pt,inner sep=2pt,draw=red,thick] () at (aux37) {$\mathrm{tanh}$};

\draw[-latex,emph] (o27) -- (aux29);
\draw[-latex,emph] (o27) -| (aux68);
}
{
\node[opnode,circle] (o27) at (aux27) {X};
\draw[-latex,standard] (u55) -| (o27);
\draw[-latex,standard] (aux21) -- (o27);
\node[opnode,circle] () at (aux26) {$\sigma$};
\node[opnode,rectangle,rounded corners=2pt,inner sep=2pt] () at (aux37) {$\mathrm{tanh}$};

\draw[-latex,standard] (o27) -- (aux29);
\draw[-latex,standard] (o27) -| (aux68);
}
\end{scope}

\begin{scope}
\node[wordnode,anchor=south] () at ([xshift=0.5\base]aux21) {$\mathbf{h}_{t-1}$};
\node[wordnode,anchor=west] () at (aux12) {$\mathbf{x}_t$};
\node[wordnode,anchor=south] () at ([xshift=0.5\base]aux51) {$\mathbf{c}_{t-1}$};
{
\node[wordnode,anchor=south] () at ([xshift=-0.5\base]aux59) {$\mathbf{c}_{t}$};
}
{
\node[wordnode,anchor=east] () at (aux68) {$\mathbf{h}_{t}$};
\node[wordnode,anchor=south] () at ([xshift=-0.5\base]aux29) {$\mathbf{h}_{t}$};
}
\end{scope}

\begin{pgfonlayer}{background}
曹润柘 committed
157
\node[draw,very thick,rectangle,fill=blue!10!white,rounded corners=5pt,inner sep=4pt,fit=(aux22) (aux58) (u55) (o27)] (LSTM) {};
曹润柘 committed
158 159 160 161 162
\end{pgfonlayer}

\begin{scope}
{
% forget gate formula
曹润柘 committed
163
\node[formulanode,anchor=south east,text width=10em] () at ([shift={(4\base,1.5\base)}]aux51) {遗忘门\\$\mathbf{f}_t=\sigma(\mathbf{W}_f[\mathbf{h}_{t-1},\mathbf{x}_t]+\mathbf{b}_f)$};
曹润柘 committed
164 165 166
}
{
% input gate formula
曹润柘 committed
167
\node[formulanode,anchor=north east,text width=10em] () at ([shift={(4\base,-1.5\base)}]aux21) {输入门\\$\mathbf{i}_t=\sigma(\mathbf{W}_i[\mathbf{h}_{t-1},\mathbf{x}_t]+\mathbf{b}_i)$\\$\hat{\mathbf{c}}_t=\mathrm{tanh}(\mathbf{W}_c[\mathbf{h}_{t-1},\mathbf{x}_t]+\mathbf{b}_c)$};
曹润柘 committed
168 169 170
}
{
% cell update formula
曹润柘 committed
171
\node[formulanode,anchor=south west,text width=10em] () at ([shift={(-4\base,1.5\base)}]aux59) {记忆更新\\$\mathbf{c}_{t}=\mathbf{f}_t\cdot \mathbf{c}_{t-1}+\mathbf{i}_t\cdot \hat{\mathbf{c}}_t$};
曹润柘 committed
172 173 174
}
{
% output gate formula
曹润柘 committed
175
\node[formulanode,anchor=north west,text width=10em] () at ([shift={(-4\base,-1.5\base)}]aux29) {输出门\\$\mathbf{o}_t=\sigma(\mathbf{W}_o[\mathbf{h}_{t-1},\mathbf{x}_t]+\mathbf{b}_o)$\\$\mathbf{h}_{t}=\mathbf{o}_t\cdot \mathrm{tanh}(\mathbf{c}_{t})$};
曹润柘 committed
176 177 178 179
}
\end{scope}
\end{tikzpicture}