fiture sigmoid added

paper/src/chapters/figures/sigmoid_softmax_gap.tex

@@ -0,0 +1,38 @@
+\begin{tikzpicture}
+\begin{axis}[
+  width=8.8cm,
+  height=5.2cm,
+  xmin=-4.6,
+  xmax=4.6,
+  ymin=-0.02,
+  ymax=1.06,
+  axis lines=left,
+  xlabel={$\Delta_H - \Delta_A$},
+  xlabel style={yshift=-1.5pt},
+  ylabel={$f(\tau')$},
+  xtick={-4,-2,0,2,4},
+  ytick={0,0.5,1},
+  tick label style={font=\small},
+  label style={font=\small},
+  line width=0.6pt,
+  clip=false,
+  enlarge x limits=false,
+]
+\addplot[
+  thick,
+  domain=-4.6:4.6,
+  samples=201,
+  smooth,
+] {1/(1+exp(-x))};
+\draw[dashed, line width=0.45pt, black!38]
+  (axis cs:-2.15,0) -- (axis cs:-2.15,{1/(1+exp(2.15))});
+\draw[dashed, line width=0.45pt, black!38]
+  (axis cs:2.15,0) -- (axis cs:2.15,{1/(1+exp(-2.15))});
+\addplot[only marks, mark=*, mark size=2.2pt, forget plot, draw=black!55, fill=black!55]
+  coordinates {(-2.15, {1/(1+exp(2.15))})};
+\addplot[only marks, mark=*, mark size=2.2pt, forget plot, draw=black, fill=black]
+  coordinates {(2.15, {1/(1+exp(-2.15))})};
+\node[font=\footnotesize, anchor=south, inner sep=11pt] at (axis cs:-2.15,{1/(1+exp(2.15))}) {$\Delta_H<\Delta_A$};
+\node[font=\footnotesize, anchor=south, inner sep=6pt] at (axis cs:2.15,{1/(1+exp(-2.15))}) {$\Delta_H>\Delta_A$};
+\end{axis}
+\end{tikzpicture}