--- /dev/null
+\documentclass[11pt,a4paper,twoside]{article}
+\usepackage{amsmath,amssymb,dsfont}
+\usepackage[pdftex]{graphicx}
+
+\usepackage{tikz}
+\usetikzlibrary{arrows,arrows.meta,calc}
+\usetikzlibrary{patterns}
+
+\tikzset{>={Straight Barb[angle'=80,scale=1.2]}}
+\tikzset{axes/.style={
+ samples=1000,
+ smooth,
+ scale=0.8,
+ }
+}
+
+\usepackage{pgfplots}
+\usepgfplotslibrary{patchplots,colormaps}
+\pgfplotsset{compat = newest}
+
+ \def\nbsamplesgd{31}
+ \def\nbsamplesgdlevelcurves{51}
+
+\begin{document}
+
+\begin{figure}
+\center
+
+\begin{tikzpicture}[axes,scale=0.95]
+\begin{axis} [
+ width=8cm, height=8cm,
+ view={0}{90},
+ domain=0:6,
+ xmin=0, xmax=6, ymin=0, ymax=6, clip=true,
+ trig format plots=rad,
+ xtick style={draw=none},
+ ytick style={draw=none},
+ ztick style={draw=none},
+ xticklabel = \empty,
+ yticklabel = \empty,
+ zticklabel = \empty,
+ zmin=-2,
+ xlabel = $w$, ylabel = \empty, zlabel = $\mathcal{L}(w)$,
+ ylabel style = { rotate=-90 },
+ point meta max=50,
+ point meta min=0,
+]
+\addplot3 [
+ samples=\nbsamplesgdlevelcurves,
+ samples y=\nbsamplesgdlevelcurves,
+ contour gnuplot={
+ number=31,%levels={-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9},
+ labels=false,
+ draw color=black!40,
+ handler/.style=smooth,
+ },
+] {
+ y*y + (x-3.1415926)*(x-3.1415926)
+ + 18*exp(-0.5*((x-5)*(x-5)+(y-1)*(y-1)))
+ + 12*exp(-0.5*((x-1.5)*(x-1.5)+(y-3)*(y-3)))
+ - 3 *exp(-1.5*((x-3)*(x-3)+(y-1)*(y-1)))
+};
+\immediate\write18{src/gradient.py --fig=2 --filename=src/gradient_field.tex}
+%\input{src/gradient_field.tex}
+\addplot[blue,very thin,quiver={u=\thisrow{u},v=\thisrow{v}},-stealth]
+table
+{
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+5.938642397522926 4.619497179985046 0.17271539568901062 0.28469014167785645
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+5.938510067760944 5.231664568185806 0.17298005521297455 0.3235132098197937
+5.9385011196136475 5.537946492433548 0.17299795150756836 0.342528760433197
+5.938498705625534 5.844252943992615 0.17300277948379517 0.3614943027496338
+};
+
+%% \input{src/gradient_descent.tex}
+\end{axis}
+\end{tikzpicture}
+
+\medskip
+
+\begin{tikzpicture}[axes,scale=0.9]
+\draw[draw=none] (-1,-0.4) rectangle (8,5.7);
+\begin{axis} [
+ trig format plots=rad,
+ xtick style={draw=none},
+ ytick style={draw=none},
+ ztick style={draw=none},
+ xticklabel = \empty,
+ yticklabel = \empty,
+ zticklabel = \empty,
+ zmin=-2,
+ xlabel = $w$, ylabel = \empty, zlabel = $\mathcal{L}(w)$,
+ zlabel style = { rotate=-90 },
+]
+\addplot3 [
+ surf,
+ colormap={bw}{color=(black!50) color=(black!50)},
+ color=white,
+ very thin,
+ domain=0:6,
+ samples=\nbsamplesgd,
+] {
+ y*y + (x-3.1415926)*(x-3.1415926)
+ + 18*exp(-0.5*((x-5)*(x-5)+(y-1)*(y-1)))
+ + 12*exp(-0.5*((x-1.5)*(x-1.5)+(y-3)*(y-3)))
+ - 3 *exp(-1.5*((x-3)*(x-3)+(y-1)*(y-1)))
+};
+\immediate\write18{src/gradient.py --fig=1 --filename=src/gradient_descent.tex}
+%\input{src/gradient_descent.tex}
+\coordinate (w0) at (1.5,5.699999809265137,35.4982795715332);
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+\end{axis}
+\end{tikzpicture}
+\end{figure}
+
+\begin{figure}
+\newcommand{\fillcubexyz}[7]{%
+\draw[draw=none,fill=#7] (#1,#2,#3)--++(#4,0,0)--++(0,0,#6)--++(0,#5,0)--++(-#4,0,0)--++(0,0,-#6)--cycle;
+}
+\newcommand{\cubexyz}[6]{%
+\draw (#1,#2,#3) --++(0,0,#6)--++(0,#5,0)--++(0,0,-#6)--cycle;
+\draw (#1,#2,#3)++(#4,0,0)--++(0,0,#6)--++(0,#5,0)--++(0,0,-#6)--cycle;
+\draw (#1,#2,#3)--++(#4,0,0);
+\draw (#1,#2,#3)++(0,#5,0)--++(#4,0,0);
+\draw (#1,#2,#3)++(0,#5,#6)--++(#4,0,0);
+\draw (#1,#2,#3)++(0,0,#6)--++(#4,0,0);
+}
+\center
+\begin{tikzpicture}[
+ very thin, line join=bevel,
+ x={(0:0.15cm)},
+ y={(90:0.215cm)},
+ z={(50:0.08cm)}
+]
+
+\begin{scope}[shift={(0,0,0)}]
+ \fillcubexyz{0}{1}{1}{4}{5}{3}{blue}
+ \cubexyz{0}{0}{0}{4}{10}{8} % 4x10x8
+ \cubexyz{0}{1}{1}{4}{5}{3} % 4x5x3
+ \fillcubexyz{10}{3}{2}{6}{1}{1}{red}
+ \cubexyz{10}{2}{1}{6}{6}{6} % 6x6x6
+ \cubexyz{10}{3}{2}{6}{1}{1}
+ \draw[->,thick] (0,1,1)++(4.8,2.5,1.5)--++(4.6,0,0) node[midway,above] {$\phi$};
+ \node[every text node part/.style={align=center}] at (9,-4) {\it 2d convolution};
+\end{scope}
+
+\begin{scope}[shift={(24,0,0)}]
+ \fillcubexyz{13}{1}{1}{4}{5}{3}{red}
+ \cubexyz{13}{0}{0}{4}{10}{8}
+ \cubexyz{13}{1}{1}{4}{5}{3}
+ \fillcubexyz{0}{3}{2}{6}{1}{1}{blue}
+ \cubexyz{0}{2}{1}{6}{6}{6}
+ \cubexyz{0}{3}{2}{6}{1}{1}
+ \draw[->,thick] (0,1,1)++(6.6,2.5,1.5)--++(5.2,0,0) node[midway,above] {$\psi$};
+ \node[every text node part/.style={align=center}] at (9,-4)
+ {\it 2d transposed\\ \it convolution};
+\end{scope}
+
+\end{tikzpicture}
+
+\end{figure}
+
+
+\end{document}
projects / tex.git / commitdiff