\documentclass{beamer}
\usetheme{metropolis}
\usepackage{hyperref}
\usepackage[utf8]{inputenc} % this is needed for german umlauts
\usepackage[english]{babel} % this is needed for german umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{positioning}
\usetikzlibrary{decorations.text}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{shapes.multipart, calc}

\begin{document}

\title{Convolutional Neural Networks (CNNs)}
\subtitle{Theory and Applications}
\author{Martin Thoma}
\date{22. February 2019}
\subject{Machine Learning, AI, Neural Networks, Convolutional Neural Networks}

\frame{\titlepage}

% \section{Neural Network Basics}
% \subsection{}
\begin{frame}{Artificial Neuron (Perceptron)}
    $$f: \mathbb{R}^n \rightarrow \mathbb{R}$$
    \begin{figure}[ht]
        \centering
        \includegraphics[width=0.8\paperwidth, height=0.7\paperheight, keepaspectratio]{graphics/artificial-neuron.pdf}
    \end{figure}
    % $$f(x) = ax^2 + bx + c \text{ with } f(0) = 3, f(1) = 2, f(-1) = 6$$
    % \begin{align*}
    %     \onslide<2->{f(0) &= a \cdot 0^2 + b \cdot 0 + c = 3} &\onslide<3->{\Rightarrow c &= 3\\}
    %     \onslide<4->{f(1) &= a \cdot 1^2 + b \cdot 1 + 3 = 2} &\onslide<5->{\Rightarrow a &= -1-b\\}
    %     \onslide<6->{f(-1) &= a \cdot {(-1)}^2 - b + 3 = 6\\}
    %     \onslide<7->{\Leftrightarrow 3&=a - b\\}
    %     \onslide<8->{\Leftrightarrow 3&= (-1-b) - b\\}
    %     \onslide<9->{\Leftrightarrow b&= -2\\}
    %     \onslide<10>{\Rightarrow \quad f(x) &= x^2 -2 x + 3\\}
    % \end{align*}
%     \only<1>{$$f: \mathbb{R}^n \rightarrow \mathbb{R}^m$$}
%     \only<2>{$$f: \mathbb{R}^2 \rightarrow \mathbb{R}$$
% # 2x - 1
% # (x-1)^2 + 1
%     Examples:
%         \begin{itemize}
%             \item $1 \rightarrow 1$: $f(x) = x$
%             \item $2 \rightarrow 3$: $f(x) = $
%             % \item $3 \rightarrow 3$
%         \end{itemize}
%     }
\end{frame}

\begin{frame}{Multi-Layer Perceptron (MLP)}
    $$f: \mathbb{R}^n \rightarrow \mathbb{R}^m$$
    \begin{figure}[ht]
        \centering
        \includegraphics[width=0.8\paperwidth, height=0.7\paperheight, keepaspectratio]{graphics/perceptron-notation.pdf}
    \end{figure}
\end{frame}

\begin{frame}{}
    \begin{itemize}[<+->]
        \item Predict housing prices: (bed rooms, size, age) $\rightarrow$ Price
        \item Product categorization: (weight, volume, price) $\rightarrow$ \{shoe, handbag, shirt\}
        \item Image classification: List of pixel colors $\rightarrow$ \{cat, dog\}
    \end{itemize}
\end{frame}

\begin{frame}{}
    \begin{center}
    \Huge Data
    \end{center}
\end{frame}

\begin{frame}{Necessary Data}
    \begin{itemize}
        \item $f(x) = w_0$
        \item $f(x) = w_1 \cdot x + w_0$
        \item $f(x) = w_2^2 \cdot x^2 + w_1^2 \cdot x + w_0$
        \item sin, cos, tan, \dots
    \end{itemize}
\end{frame}

\begin{frame}{Convolution}
\begin{figure}[ht]
    \centering
    \includegraphics[width=0.8\paperwidth]{graphics/convolution-linear.pdf}
\end{figure}
\end{frame}

\begin{frame}{Convolutional Layer}
\begin{figure}[ht]
    \centering
    \input{graphics/convolution-layer}
\end{figure}
\end{frame}

\begin{frame}{Max Pooling}
\begin{figure}[ht]
    \centering
    \includegraphics[width=0.8\paperwidth]{graphics/max-pooling.pdf}
\end{figure}
\end{frame}

\section{Applications}
\begin{frame}{Symbol recognizer}
    \begin{center}
        \href{http://write-math.com}{write-math.com}
    \end{center}
\end{frame}

\begin{frame}{Symbol recognizer}
GANs
\end{frame}

\end{document}