\documentclass{beamer}
%Information to be included in the title page:
\title{Project of Advanced Machine Learning :\\Neural Networks Fail to Learn Periodic Functions\\and How to Fix It}
\author{Virgile Batto, Émilien Marolleau, Doriand Petit, Émile Siboulet}
\institute{Machine Learning Avancé (2021-2022)}
\date{2021}
\usetheme{Darmstadt}
\usepackage{amssymb,amsmath,epsfig}
\usepackage{caption}
\usepackage{subcaption}
\DeclareMathOperator{\relu}{relu}
\DeclareMathOperator{\snake}{snake}

\logo{
\includegraphics[width=2.5cm]{images/Logo_Sorbonne_Universite.png}
}

\begin{document}


\begin{frame}
\maketitle    
\end{frame}

\section{Introduction}
\begin{frame}
\begin{block}{Fonction d'activation snake}
$$snake_a(x) = x +\frac{1}{a} \sin^2(ax)$$
\end{block}

\begin{figure}[H]
  \centering
  \includegraphics[width = 0.4\textwidth]{snake_plot.PNG}
  \caption{Tracé des fonctions Snake}
  \label{fig:snake_plot}
\end{figure}

\end{frame}

\section{Classical activation function}
\begin{frame}
\begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_x2_ReLU.png}
         \caption{ReLU}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_x2_swish.png}
         \caption{swish}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_x2_tanh.png}
         \caption{tanh}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{tanh.png}
         \caption{tanh avec base de données asymétrique}
     \end{subfigure}
        \caption{Prediction d'un signal carré avec différentes fonctions d'activations}
    \label{fig:classique_x2}
\end{figure}
\end{frame}
\begin{frame}
    \begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_ReLU.png}
         \caption{ReLU}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_swish.png}
         \caption{swish}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_tanh.png}
         \caption{tanh}
     \end{subfigure}
        \caption{Prediction d'un signal sinus avec différentes fonctions d'activations}
    \label{fig:classique_sinus}
\end{figure}
\end{frame}
\begin{frame}
    \begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{prediction_x2_snake_v2.png}
         \caption{$\snake(x)$}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{prediction_x2_x+sin.png}
         \caption{$x+\sin(x)$}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_x2_sin.png}
         \caption{$\sin(x)$}
     \end{subfigure}
        \caption{Prediction d'un signal carré avec différentes fonctions d'activations}
    \label{fig:custom_carre}
\end{figure}
\end{frame}




\begin{frame}
    \begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_snake.png}
         \caption{$\snake(x)$}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_sin.png}
         \caption{$x+\sin(x)$}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{img_partie_1/prediction_sinus_sin.png}
         \caption{$\sin(x)$}
     \end{subfigure}
        \caption{Prédiction d'un signal sinus avec les différentes fonctions d'activations}
    \label{fig:custom_sinus}
\end{figure}
\end{frame}

\begin{frame}
        \begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{sinus_quasi_fonctionnelle.png}
         \caption{$\sin(x)$}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{snake_quasi_fonctionnelle.png}
         \caption{$\snake(x)$}
     \end{subfigure}
        \caption{Prédiction par des réseaux de neurones avec des fonctions d'activations périodiques ou pseudo-périodique}
    \label{fig:custom_sinus}
\end{figure}
\end{frame}

\section{Ciphar-10}

\begin{frame}
\begin{figure}[H]
  \centering
  \includegraphics[width = 0.8\textwidth]{ciphar-10.jpeg}
  \caption{Exemple de la base de données ciphar-10}
  \label{fig:ciphar-10}
\end{figure}
\end{frame}

\begin{frame}
\begin{figure}[H]
  \centering
  \includegraphics[width = 0.9\textwidth]{resnet.png}
  \caption{Architecture du réseau de neurone convolutionnel ResNet-18}
  \label{fig:resnet}
\end{figure}
\end{frame}


\begin{frame}
    \begin{figure}
     \centering
     \begin{subfigure}[b]{0.60\textwidth}
         \centering
         \includegraphics[width=\textwidth]{snake.png}
         \caption{Prédiction de snake (a = 1) sur la base de données Ciphar-10}
         \label{snake_ciphar}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.60\textwidth}
         \centering
         \includegraphics[width=\textwidth]{reLu.png}
         \caption{Prédiction de ReLu sur la base de données Ciphar-10}
     \end{subfigure}
     \caption{Comparaison de l'efficacité de Snake\\ par rapport à ReLu sur un tache de classification d'image}
\end{figure}
\end{frame}


\section{Wilshire 5000}
\begin{frame}
    \begin{figure}[H]
  \centering
  \includegraphics[width = 1\textwidth]{a_plot.png}
  \caption{Prédictions pour différentes valeurs de a}
  \label{fig:snake_plot}
\end{figure}
\end{frame}

\begin{frame}
    \begin{figure}[H]
  \centering
  \includegraphics[width = 1\textwidth]{30aSnake.png}
  \caption{Prédiction pour a = 30}
  \label{fig:snake_plot}
\end{figure}
\end{frame}

\section{LSTM}
\begin{frame}
    \begin{figure}
     \centering
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{images/rnn/164_126_fig2.png}
         \caption{Prédiction des températures par réseau récurent}
         \label{meteornn1}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.40\textwidth}
         \centering
         \includegraphics[width=\textwidth]{images/rnn/164_126_fig4.png}
         \caption{Vérificaiton de la staibilité de la prédiction}
     \end{subfigure}
     \caption{Prédiction par des réseaux utilisant des couches LSTM}
\end{figure}
\end{frame}

\begin{frame}
    \begin{figure}[H]
  \centering
  \includegraphics[width = 0.8\textwidth]{images/rnn/256_32_fig2.png}
  \caption{Prédiction de l'évolution du wilshire5000}
\end{figure}
\end{frame}

\section{Conclusion}
\begin{frame}
\begin{center}
\Huge{ Merci pour votre attention !}
\end{center}
\end{frame}

\end{document}