warp.tex

   1 %% -*- mode: latex; mode: reftex; mode: flyspell; coding: utf-8; tex-command: "pdflatex.sh" -*-
   2
   3 %% Any copyright is dedicated to the Public Domain.
   4 %% https://creativecommons.org/publicdomain/zero/1.0/
   5
   6 %% Written by Francois Fleuret <francois@fleuret.org>
   7
   8 \documentclass[11pt,a4paper,twoside]{article}
   9 \usepackage[a4paper,top=2.5cm,bottom=2cm,left=2.5cm,right=2.5cm]{geometry}
  10 \usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue,citecolor=blue]{hyperref}
  11 \usepackage{amsmath}
  12 \usepackage{amssymb}
  13 \usepackage{dsfont}
  14 \usepackage{tikz}
  15 \usetikzlibrary{arrows,arrows.meta,calc}
  16 \usetikzlibrary{patterns,backgrounds}
  17 \usetikzlibrary{positioning,fit}
  18 \usetikzlibrary{shapes.geometric,shapes.multipart}
  19 \usetikzlibrary{patterns.meta,decorations.pathreplacing,calligraphy}
  20 \usetikzlibrary{tikzmark}
  21 \usetikzlibrary{decorations.pathmorphing}
  22 \usepackage{pgfplots}
  23 \usepgfplotslibrary{patchplots,colormaps}
  24 \pgfplotsset{compat = newest}
  25
  26
  27 \begin{document}
  28
  29 \definecolor{blue}{rgb}{0.3,0.5,0.85}
  30 \definecolor{red}{rgb}{0.65,0.0,0.0}
  31
  32 \begin{figure}
  33
  34   \immediate\write18{./warp.py --result_dir=.}
  35
  36   \newcommand{\warp}[1]{%
  37     \begin{tikzpicture}
  38       \begin{axis}[ticks=none,width=7.0cm, height=7.0cm,xmin=-1.2,xmax=1.2,ymin=-1.2,ymax=1.2]
  39         \input{#1}
  40       \end{axis}
  41     \end{tikzpicture}
  42   }
  43
  44   \center
  45
  46   \begin{tikzpicture}[warp/.style={inner sep=1pt,minimum width=5.0cm,minimum height=5.0cm}]
  47     \node[warp]                 (W0) {\warp{warp_0.tex}};
  48     \node[warp,right=2pt of W0] (W1) {\warp{warp_1.tex}};
  49     \node[warp,right=2pt of W1] (W2) {\warp{warp_2.tex}};
  50     \node[warp,below=20pt of W0] (W3) {\warp{warp_3.tex}};
  51     \node[warp,right=2pt of W3] (W4) {\warp{warp_4.tex}};
  52     \node[warp,right=2pt of W4] (W5) {\warp{warp_5.tex}};
  53     \node[warp,below=20pt of W3] (W6) {\warp{warp_6.tex}};
  54     \node[warp,right=2pt of W6] (W7) {\warp{warp_7.tex}};
  55     \node[warp,right=2pt of W7] (W8) {\warp{warp_8.tex}};
  56     \node[inner sep=0pt,below=4pt of W0] (lW0) {\footnotesize Input};
  57     \foreach \n in {1,...,8}{
  58       \node[inner sep=0pt,below=4pt of W\n] (lW\n) {\footnotesize Layer \#\n};
  59     };
  60
  61   \end{tikzpicture}
  62
  63   \caption[Feature warping]{Each plot shows the deformation of the space
  64     and the resulting distribution of the training points in
  65     $\mathbb{R}^2$ corresponding to the output of each layer, starting
  66     with the input in the top-left square. The thick oblique line in the
  67     bottom-right plot shows the final affine decision.}\label{fig:warp}
  68
  69 \end{figure}
  70
  71 \end{document}