.gitignore

@@ -7,3 +7,6 @@
 *.snm
 *.blg
 *.bbl
+!report/articles/*.pdf
+.DS_Store
+*.synctex.gz

diapo_gnn/diapo_gnn.tex

+\documentclass[]{beamer}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage[francais]{babel}     
+\usepackage{siunitx}
+% \usepackage[caption=false]{subfig}
+\usepackage{caption}
+\usepackage{subcaption}
+\usepackage{etoolbox}
+\usepackage{marvosym} %scorpion, capricorn
+\newcommand{\scorp}{\text{\Scorpio}}
+\newcommand{\capri}{\text{\Capricorn}}
+
+\usepackage{cancel} % Barer des équations
+
+\usepackage{tikz}
+\usetikzlibrary{shapes.geometric,arrows}
+\usetikzlibrary{mindmap,backgrounds,positioning}
+\usetikzlibrary{automata,positioning,fit,backgrounds}
+\usetikzlibrary{positioning,arrows}
+\usetikzlibrary{matrix,chains,positioning,decorations.pathreplacing,arrows}
+\usepackage{pgfplots}
+
+
+% \usepackage{subcaption}
+\usetheme{Warsaw}
+% \usepackage{aas_macros}
+\graphicspath{{pictures/}} % on change la racine des images
+
+
+
+
+\usepackage{thmtools}
+% \declaretheorem[name=Definition]{definition}
+% \declaretheorem[name=Theorem]{theorem}
+% \declaretheorem[name=Lemma,sibling=theorem]{lemma}
+
+
+% \usetheme{Ilmenau}
+% \usecolortheme{seahorse}
+% \usepackage{apacite}
+
+% Thème général du diaporama - quasi obligatoire
+% \usetheme{Malmoe}
+% \usetheme{Copenhagen}
+% Nous verrons apres ce que cela veut dire
+% \usecolortheme[named=blue]{structure}
+% \usepackage[citestyle=verbose]{biblatex}
+
+% \setbeamercolor{itemize item}{fg=white!80!black}
+% \setbeamercolor{itemize subitem}{fg=white!80!black}
+
+\AtBeginSection[]
+{
+  \begin{frame}<beamer>
+    \frametitle{Plan}
+    \tableofcontents[currentsection]
+  \end{frame}
+}
+
+\defbeamertemplate*{footline}{shadow theme}{%
+  \leavevmode%
+  \hbox{\begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm plus1fil,rightskip=.3cm]{author in head/foot}%
+      \usebeamerfont{author in head/foot}\hfill\insertshortauthor
+    \end{beamercolorbox}%
+
+    \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
+      \usebeamerfont{title in head/foot}\insertshorttitle\hfill%
+      \insertframenumber\,/\,\inserttotalframenumber
+    \end{beamercolorbox}}%
+  \vskip0pt%
+}
+% \addtobeamertemplate{navigation symbols}{}{%
+% \usebeamerfont{footline}%
+% \usebeamercolor[fg]{footline}%
+% \hspace{1em}%
+% \insertframenumber/\inserttotalframenumber
+% }
+
+\title[Projet Réseau]{Présentation du Projet Réseau}
+\author{Colisson Léo \and Jeanmaire Paul}
+\institute{École Normale Supérieure Paris Saclay, Département Informatique \\Initiation à la recherche}
+
+\begin{document}
+% ==================================================
+
+\begin{frame}
+  \titlepage
+\end{frame}
+% ==================================================
+
+\begin{frame}
+  \tableofcontents
+\end{frame}
+
+% ==================================================
+\section{Réseau de neurone}
+% TODO : Paul
+
+\section{Rétro-propagation du gradient}
+% TODO : Léo
+
+\begin{frame}[fragile]
+  \frametitle{Rétro-propagation du gradient}
+  \begin{figure}[H]
+  \begin{tikzpicture}[
+    plain/.style={
+      draw=none,
+      fill=none,
+    },
+    net/.style={
+      matrix of nodes,
+      nodes={
+        draw,
+        circle,
+        inner sep=10pt
+      },
+      nodes in empty cells,
+      column sep=2cm,
+      row sep=-9pt
+    },
+    >=latex
+    ]
+    \matrix[net] (mat)
+    {
+      |[plain]| \parbox{1cm}{} & |[plain]| \parbox{1cm}{} & |[plain]| \parbox{1cm}{} \\
+      & |[plain]| \\
+      |[plain]| & \\
+      & |[plain]| \\
+      |[plain]| & |[plain]| \\
+      & & \\
+      |[plain]| & |[plain]| \\
+      & |[plain]| \\
+      |[plain]| & \\
+      & |[plain]| \\
+    };
+    \foreach \ai [count=\mi ]in {2,4,...,10}
+    \draw[<-] (mat-\ai-1) -- node[above] {Input \mi} +(-2cm,0);
+    \foreach \ai in {2,4,...,10}
+    {\foreach \aii in {3,6,9}
+      \draw[->] (mat-\ai-1) -- (mat-\aii-2);
+    }
+    \foreach \ai in {3,6,9}
+    \draw[->] (mat-\ai-2) -- (mat-6-3);
+    \draw[->] (mat-6-3) -- node[above] {Ouput} +(2cm,0);
+  \end{tikzpicture}
+\end{figure}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Rétro-propagation du gradient}
+  \begin{block}{Cas général : algorithme du gradient}
+    Minimiser une fonction $f(x)$ via l'algorithme du gradient :
+    \begin{enumerate}
+    \item Calcul du gradient $\nabla f(x_k)$
+    \item On s'arrête si $\nabla f(x_k) \leq \varepsilon$
+    \item On calcule $x_{k+1} = x_k - \lambda \nabla f(x_k)$ pour un $\lambda$ bien choisit
+    \item On recommence
+    \end{enumerate}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Rétro-propagation du gradient}
+  \begin{exampleblock}{Cas des neurones}
+    \begin{itemize}
+    \item $\mathcal{N}_\omega(x) =$ fonction issue du réseau de neurone ($\omega = $ poids, $x = $ entrées)
+    \item $\mathcal{E}_x = $ valeur idéale de $\mathcal{N}_\omega$ dans la base d'entraînement.
+    \end{itemize}
+    But : trouver ``les meilleurs poids'' $\Rightarrow$ minimiser pour un $x$ fixé la fonction
+    $$f: \omega \rightarrow \mathcal{N}_\omega(x) - \mathcal{E}_x$$
+    Problème : on ne sait pas calculer $\nabla f$ en un seul bloc
+    
+    Solution :  rétro-propagation locale.
+  \end{exampleblock}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Rétro-propagation du gradient}
+  \begin{figure}[H]
+  \begin{tikzpicture}[
+    plain/.style={
+      draw=none,
+      fill=none,
+    },
+    net/.style={
+      matrix of nodes,
+      nodes={
+        draw,
+        circle,
+        inner sep=10pt
+      },
+      nodes in empty cells,
+      column sep=2cm,
+      row sep=-9pt
+    },
+    >=latex
+    ]
+    \matrix[net] (mat)
+    {
+      |[plain]| \parbox{1cm}{} & |[plain]| \parbox{1cm}{} & |[plain]| \parbox{1cm}{} \\
+      & |[plain]| \\
+      |[plain]| & \\
+      & |[plain]| \\
+      |[plain]| & |[plain]| \\
+      & & \\
+      |[plain]| & |[plain]| \\
+      & |[plain]| \\
+      |[plain]| & \\
+      & |[plain]| \\
+    };
+    \foreach \ai [count=\mi ]in {2,4,...,10}
+    \draw[<-] (mat-\ai-1) -- node[above] {Input \mi} +(-2cm,0);
+    \foreach \ai in {2,4,...,10}
+    {\foreach \aii in {3,6,9}
+      \draw[<-] (mat-\ai-1) -- (mat-\aii-2);
+    }
+    \foreach \ai in {3,6,9}
+    \draw[<-] (mat-\ai-2) -- (mat-6-3);
+    \draw[<-] (mat-6-3) -- node[above] {Ouput} +(2cm,0);
+  \end{tikzpicture}
+\end{figure}
+\end{frame}
+
+
+\section{Graph Neural Network (GNN)}
+
+\begin{frame}
+  \frametitle{Graph Neural Network (GNN)}
+  \begin{block}{GNN}
+    \begin{itemize}
+    \item Idée : pouvoir appliquer un réseau de neurone sur un graph
+    \end{itemize}
+  \end{block}
+\end{frame}
+
+\tikzstyle{vertex}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt]
+\tikzstyle{selected vertex} = [vertex, fill=red!24]
+\tikzstyle{edge} = [draw,thick,-]
+\tikzstyle{weight} = [font=\small]
+\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
+\tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20]
+\begin{frame}
+  \frametitle{Graph Neural Network (GNN)}
+  \begin{figure}[H]
+    \centering
+  \begin{tikzpicture}[scale=1.8, auto,swap]
+    % Draw a 7,11 network
+    % First we draw the vertices
+    \foreach \pos/\name/\nname in {{(0,2)/a/45}, {(2,1)/b/12}, {(4,1)/c/8},
+      {(0,0)/d/16}, {(3,0)/e/1}, {(2,-1)/f/7}, {(4,-1)/g/-5}}
+    \node[vertex] (\name) at \pos {$\nname$};
+    % Connect vertices with edges and draw weights
+    \foreach \source/ \dest /\weight in {b/a/7, c/b/8,d/a/5,d/b/9,
+      e/b/7, e/c/5,e/d/15,
+      f/d/6,f/e/8,
+      g/e/9,g/f/11}
+    \path[edge] (\source) -- node[weight] {$\weight$} (\dest);
+    % % Start animating the vertex and edge selection. 
+    % \foreach \vertex / \fr in {d/1,a/2,f/3,b/4,e/5,c/6,g/7}
+    % \path<\fr-> node[selected vertex] at (\vertex) {$\vertex$};
+    % For convenience we use a background layer to highlight edges
+    % This way we don't have to worry about the highlighting covering
+    % weight labels. 
+    % \begin{pgfonlayer}{background}
+    %   \pause
+    %   \foreach \source / \dest in {d/a,d/f,a/b,b/e,e/c,e/g}
+    %   \path<+->[selected edge] (\source.center) -- (\dest.center);
+    %   \foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
+    %   \path<\fr->[ignored edge] (\source.center) -- (\dest.center);
+    % \end{pgfonlayer}
+  \end{tikzpicture}
+  \end{figure}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Graph Neural Network (GNN)}
+  \begin{figure}[H]
+    \centering
+  \begin{tikzpicture}[scale=1.8, auto,swap]
+    % Draw a 7,11 network
+    % First we draw the vertices
+    \foreach \pos/\name/\nname in {{(0,2)/a/45}, {(2,1)/b/12}, {(4,1)/c/8}, {(3,0)/e/1}, {(2,-1)/f/7}, {(4,-1)/g/-5}}
+    \node[vertex] (\name) at \pos {$\nname$};
+    \node[selected vertex] (d) at (0,0) {$f_\omega$};
+    % Connect vertices with edges and draw weights
+    \foreach \source/ \dest /\weight in {b/a/7, c/b/8,d/a/5,d/b/9,
+      e/b/7, e/c/5,e/d/15,
+      f/d/6,f/e/8,
+      g/e/9,g/f/11}
+    \path[edge] (\source) -- node[weight] {$\weight$} (\dest);
+    % % Start animating the vertex and edge selection. 
+    % \foreach \vertex / \fr in {d/1,a/2,f/3,b/4,e/5,c/6,g/7}
+    % \path<\fr-> node[selected vertex] at (\vertex) {$\vertex$};
+    % For convenience we use a background layer to highlight edges
+    % This way we don't have to worry about the highlighting covering
+    % weight labels. 
+    % \begin{pgfonlayer}{background}
+    %   \pause
+    %   \foreach \source / \dest in {d/a,d/f,a/b,b/e,e/c,e/g}
+    %   \path<+->[selected edge] (\source.center) -- (\dest.center);
+    %   \foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
+    %   \path<\fr->[ignored edge] (\source.center) -- (\dest.center);
+    % \end{pgfonlayer}
+  \end{tikzpicture}
+  \end{figure}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Graph Neural Network (GNN)}
+  \begin{block}{Idée}
+    \begin{itemize}
+    \item $f_\omega$ est une contraction $\Rightarrow $ itération converge (Théorème de Banach).
+    \item On peut par exemple encoder $f_\omega$ dans un réseau de neurone récurrent.
+    \item Apprentissage : on chaîne les $f_\omega$, puis propagation du gradient.
+    \end{itemize}
+    
+    
+  \end{block}
+\end{frame}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:

report/Makefile

+DEFAULT:
+	pdflatex report.tex
+
+all:
+	pdflatex report.tex
+	bibtex report.aux
+	pdflatex report.tex
+	pdflatex report.tex