From 997dc9351f9f0ee4f4462c5480d08fbb3f23a283 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Tue, 24 Jan 2023 18:37:20 +0100 Subject: [PATCH] Added visualization of gradients to appendix --- latex/presentations/midterm/presentation.tex | 39 + latex/presentations/midterm/res/2d_grad_L.csv | 901 ++++++++++++++++++ .../presentations/midterm/res/2d_grad_rep.csv | 901 ++++++++++++++++++ .../midterm/sections/appendix.tex | 79 ++ 4 files changed, 1920 insertions(+) create mode 100644 latex/presentations/midterm/res/2d_grad_L.csv create mode 100644 latex/presentations/midterm/res/2d_grad_rep.csv diff --git a/latex/presentations/midterm/presentation.tex b/latex/presentations/midterm/presentation.tex index 19d2844..7a96c57 100644 --- a/latex/presentations/midterm/presentation.tex +++ b/latex/presentations/midterm/presentation.tex @@ -33,6 +33,45 @@ +\pgfplotsset{ + /pgfplots/colormap/mako/.style={ + colormap={mako}{ + rgb=(0.18195582, 0.11955283, 0.23136943) + rgb=(0.25307401, 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+ + \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}