Added visualization of gradients to appendix

2023-01-24 18:37:20 +01:00
parent 238cbcf17c
commit 997dc9351f
4 changed files with 1920 additions and 0 deletions
--- a/latex/presentations/midterm/sections/appendix.tex
+++ b/latex/presentations/midterm/sections/appendix.tex
@@ -40,3 +40,82 @@
              }

 \end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+    \frametitle{Proximal Decoding: Visualization of Gradients}
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{subfigure}[c]{0.5\textwidth}
+
+            \centering
+
+            \begin{tikzpicture}[scale=0.8]
+                \begin{axis}[xmin = -1.25, xmax=1.25,
+                             ymin = -1.25, ymax=1.25,
+                             xlabel={$x_1$}, ylabel={$x_2$},
+                             grid=major, grid style={dotted},
+                             view={0}{90}]
+                    \addplot3[point meta=\thisrow{grad_norm},
+                              point meta min=1,
+                              point meta max=3,
+                              quiver={u=\thisrow{grad_0},
+                                      v=\thisrow{grad_1},
+                                      scale arrows=.05,
+                                      every arrow/.append style={%
+                                        line width=.3+\pgfplotspointmetatransformed/1000,
+                                        -{Latex[length=0pt 5,width=0pt 3]}
+                                      },
+                                  },
+                                quiver/colored = {mapped color},
+                                colormap/rocket,
+                                -stealth,
+                              ]
+                                table[col sep=comma] {res/2d_grad_L.csv};
+                \end{axis}
+            \end{tikzpicture}
+
+            \caption{$\nabla L \left(\boldsymbol{y} \mid \boldsymbol{x} \right) $ for a repetition code with $n=2$
+                \footnotemark}
+        \end{subfigure}%
+        \begin{subfigure}[c]{0.5\textwidth}
+            \centering
+
+            \begin{tikzpicture}[scale=0.8]
+                \begin{axis}[xmin = -1.25, xmax=1.25,
+                             ymin = -1.25, ymax=1.25,
+                             xlabel={$x_1$}, ylabel={$x_2$},
+                             grid=major, grid style={dotted},
+                             view={0}{90}]
+                    \addplot3[point meta=\thisrow{grad_norm},
+                              point meta min=1,
+                              point meta max=4,
+                              quiver={u=\thisrow{grad_0},
+                                      v=\thisrow{grad_1},
+                                      scale arrows=.03,
+                                      every arrow/.append style={%
+                                        line width=.3+\pgfplotspointmetatransformed/1000,
+                                        -{Latex[length=0pt 5,width=0pt 3]}
+                                      },
+                                  },
+                                quiver/colored = {mapped color},
+                                colormap/rocket,
+                                -stealth,
+                              ]
+                                table[col sep=comma] {res/2d_grad_rep.csv};
+                \end{axis}
+            \end{tikzpicture}
+
+            \caption{$\nabla h \left( \boldsymbol{x} \right) $ for a repetition code with $n=2$}
+        \end{subfigure}%
+    \end{figure}
+
+    \footnotetext{In an AWGN Channel $L\left( \boldsymbol{y} \mid \boldsymbol{x} \right)
+                \propto \frac{1}{2} \left| \boldsymbol{x} - \boldsymbol{y} \right|^2
+                \Rightarrow \nabla L\left( \boldsymbol{y} \mid \boldsymbol{x}\right)
+                    \propto \left( \boldsymbol{x} - \boldsymbol{y} \right) $}
+
+\end{frame}