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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
Riccardo
2020-11-12 18:24:15 +01:00
parent 3aef870c4d
commit 77139f0386
17 changed files with 1474 additions and 31 deletions
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%\newlength{\layer}
\newlength{\layerheight}
\newlength{\perspective}
\newlength{\filters}
%\newlength{\unit}
\setlength{\layer}{3cm}
\setlength{\layerheight}{3cm}
\setlength{\perspective}{1cm}
\setlength{\filters}{0.01cm}
\setlength{\unit}{0.225cm}
\begin{tikzpicture}
% first layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, 0cm) -- (\layer + 180 * \filters, 0cm) -- (\layer + 180 * \filters + \perspective, \perspective) -- (\layer + \perspective, \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer + \perspective, \perspective) -- (\layer + 180 * \filters + \perspective, \perspective) -- (\layer + 180 * \filters + \perspective, \perspective + \layerheight) -- (\layer + \perspective, \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, 0cm) -- (\layer + \perspective, \perspective) -- (\layer + \perspective, \perspective + \layerheight) -- (\layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, 0cm) -- (\layer + 180 * \filters, 0cm) -- (\layer + 180 * \filters, \layerheight) -- (\layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer + 180 * \filters, 0cm) -- (\layer + 180 * \filters + \perspective, \perspective) -- (\layer + 180 * \filters + \perspective, \perspective + \layerheight) -- (\layer + 180 * \filters, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \layerheight) -- (\layer + 180 * \filters, \layerheight) -- (\layer + 180 * \filters + \perspective, \perspective + \layerheight) -- (\layer + \perspective, \perspective + \layerheight) -- cycle;
\node[anchor=north west, scale=0.65] at (\layer, 0cm) {$180 @ 12 \times 15$};
% second layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, 0cm) -- (2 * \layer + 100 * \filters, 0cm) -- (2 * \layer + 100 * \filters + \perspective, \perspective) -- (2 * \layer + \perspective, \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer + \perspective, \perspective) -- (2 * \layer + 100 * \filters + \perspective, \perspective) -- (2 * \layer + 100 * \filters + \perspective, \perspective + \layerheight) -- (2 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, 0cm) -- (2 * \layer + \perspective, \perspective) -- (2 * \layer + \perspective, \perspective + \layerheight) -- (2 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, 0cm) -- (2 * \layer + 100 * \filters, 0cm) -- (2 * \layer + 100 * \filters, \layerheight) -- (2 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters, 0cm) -- (2 * \layer + 100 * \filters + \perspective, \perspective) -- (2 * \layer + 100 * \filters + \perspective, \perspective + \layerheight) -- (2 * \layer + 100 * \filters, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, \layerheight) -- (2 * \layer + 100 * \filters, \layerheight) -- (2 * \layer + 100 * \filters + \perspective, \perspective + \layerheight) -- (2 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\node[anchor=north west, scale=0.65] at (2 * \layer, 0cm) {$100 @ 12 \times 15$};
% third layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, 0cm) -- (3 * \layer + 40 * \filters, 0cm) -- (3 * \layer + 40 * \filters + \perspective, \perspective) -- (3 * \layer + \perspective, \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + \perspective, \perspective) -- (3 * \layer + 40 * \filters + \perspective, \perspective) -- (3 * \layer + 40 * \filters + \perspective, \perspective + \layerheight) -- (3 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, 0cm) -- (3 * \layer + \perspective, \perspective) -- (3 * \layer + \perspective, \perspective + \layerheight) -- (3 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, 0cm) -- (3 * \layer + 40 * \filters, 0cm) -- (3 * \layer + 40 * \filters, \layerheight) -- (3 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters, 0cm) -- (3 * \layer + 40 * \filters + \perspective, \perspective) -- (3 * \layer + 40 * \filters + \perspective, \perspective + \layerheight) -- (3 * \layer + 40 * \filters, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \layerheight) -- (3 * \layer + 40 * \filters, \layerheight) -- (3 * \layer + 40 * \filters + \perspective, \perspective + \layerheight) -- (3 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\node[anchor=north west, scale=0.65] at (3 * \layer, 0cm) {$40 @ 12 \times 15$};
% fourth layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, 0cm) -- (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- (4 * \layer + \perspective, \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer + \perspective, \perspective) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- (4 * \layer + 20 * \filters + \perspective, \perspective + \layerheight) -- (4 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, 0cm) -- (4 * \layer + \perspective, \perspective) -- (4 * \layer + \perspective, \perspective + \layerheight) -- (4 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, 0cm) -- (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 20 * \filters, \layerheight) -- (4 * \layer, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- (4 * \layer + 20 * \filters + \perspective, \perspective + \layerheight) -- (4 * \layer + 20 * \filters, \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, \layerheight) -- (4 * \layer + 20 * \filters, \layerheight) -- (4 * \layer + 20 * \filters + \perspective, \perspective + \layerheight) -- (4 * \layer + \perspective, \perspective + \layerheight) -- cycle;
\node[anchor=north west, scale=0.65] at (4 * \layer, 0cm) {$20 @ 12 \times 15$};
% flatten layer
\foreach \x in {2,...,7} {
\filldraw[fill=cyan!10, draw=black] (4 * \layer + 3cm, 0.5cm * \x) circle (\unit);
\draw (4 * \layer + 3cm + \unit, 0.5cm * \x) -- (5 * \layer + 2cm - \unit, 2.5cm);
};
\node[anchor=north, scale=0.5, below=15pt, align=center] at (4 * \layer + 3cm, 1cm) {flatten};
% output layer
\filldraw[fill=cyan!10, draw=black] (5 * \layer + 2cm, 2.5cm - \unit) -- (5 * \layer + 2cm, 2.5cm) circle (\unit) -- (5 * \layer + 2cm, 2.5cm + \unit);
\draw (5 * \layer + 2cm + 0.05cm, 2.5cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (5 * \layer + 2cm + 0.10cm, 2.5cm) -- (5 * \layer + 2cm + 0.15cm, 2.5cm + 0.05cm);
% draw first convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (\layer + 180 * \filters, \layerheight) -- (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- (\layer + 180 * \filters, \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (2 * \layer, 0.8 * \layerheight) -- (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (\layer + 180 * \filters, \layerheight - 0.3 * \layerheight) -- (2 * \layer, 0.8 * \layerheight) -- (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (\layer + 180 * \filters, \layerheight) -- (2 * \layer, 0.8 * \layerheight) -- (\layer + 180 * \filters, \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (\layer + 180 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (2 * \layer, 0.8 * \layerheight) -- (\layer + 180 * \filters, \layerheight) -- cycle;
% draw second convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters, 0.4 * \layerheight) -- (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective) -- (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- (2 * \layer + 100 * \filters, 0.4 * \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective) -- (3 * \layer, 0.2 * \layerheight) -- (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters, 0.4 * \layerheight - 0.3 * \layerheight) -- (3 * \layer, 0.2 * \layerheight) -- (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters, 0.4 * \layerheight) -- (3 * \layer, 0.2 * \layerheight) -- (2 * \layer + 100 * \filters, 0.4 * \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (2 * \layer + 100 * \filters + 0.4 * \perspective, 0.4 * \layerheight + 0.4 * \perspective) -- (3 * \layer, 0.2 * \layerheight) -- (2 * \layer + 100 * \filters, 0.4 * \layerheight) -- cycle;
% draw third convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters, 0.6 * \layerheight) -- (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective) -- (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- (3 * \layer + 40 * \filters, 0.6 * \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective) -- (4 * \layer, 0.3 * \layerheight) -- (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters, 0.6 * \layerheight - 0.3 * \layerheight) -- (4 * \layer, 0.3 * \layerheight) -- (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters, 0.6 * \layerheight) -- (4 * \layer, 0.3 * \layerheight) -- (3 * \layer + 40 * \filters, 0.6 * \layerheight - 0.3 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective) -- (4 * \layer, 0.3 * \layerheight) -- (3 * \layer + 40 * \filters, 0.6 * \layerheight) -- cycle;
% draw the "flatenisation"
\draw[dashed] (4 * \layer + 20 * \filters, \layerheight) -- (4 * \layer + 3 cm, 3.5cm + \unit) -- (4 * \layer + 20 * \filters + \perspective, \layerheight + \perspective) -- cycle;
\draw[dashed] (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 3 cm, 1cm - \unit) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- cycle;
% hidden layer labels
\node[anchor=base, align=center, text width=3.9cm, scale=0.75] (c) at (11cm, 5.5cm) {convolutional layers ($5 \times 5$ kernel, ReLU activation)};
\draw[->] (c) -- (\layer + 180 * \filters + \perspective, \layerheight + \perspective + \unit);
\draw[->] (c) -- (2 * \layer + 100 * \filters + \perspective, \layerheight + \perspective + \unit);
\draw[->] (c) -- (3 * \layer + 40 * \filters + \perspective, \layerheight + \perspective + \unit);
\draw[->] (c) -- (4 * \layer + 0.5 * \perspective, \layerheight + \perspective + \unit);
\end{tikzpicture}
% vim: ft=tex

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\newlength{\unit}
\newlength{\layer}
\setlength{\unit}{0.225cm}
\setlength{\layer}{1cm}
\begin{tikzpicture}
% draw the first layer
\filldraw[fill=cyan!10, draw=black] (\layer, -0.75cm - \unit) -- (\layer, -0.75cm) circle (\unit) -- (\layer, -0.75cm + \unit);
\draw (\layer + 0.05cm, -0.75cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [876 units]} -- (\layer + 0.10cm, -0.75cm) -- (\layer + 0.15cm, -0.75cm + 0.05cm);
\node[anchor=base, scale=0.35] at (\layer, -0.75cm + 1.25 * \unit) {$\vdots$};
\foreach \x in {0,...,5} {
\filldraw[fill=cyan!10, draw=black] (\layer, 0.5cm * \x - \unit) -- (\layer, 0.5cm * \x) circle (\unit) -- (\layer, 0.5cm * \x + \unit);
\draw (\layer + 0.05cm, 0.5cm * \x) -- (\layer + 0.10cm, 0.5cm * \x) -- (\layer + 0.15cm, 0.5cm * \x + 0.05cm);
};
\filldraw[fill=cyan!10, draw=black] (\layer, 3.25cm - \unit) -- (\layer, 3.25cm) circle (\unit) -- (\layer, 3.25cm + \unit);
\draw (\layer + 0.05cm, 3.25cm) -- (\layer + 0.10cm, 3.25cm) -- (\layer + 0.15cm, 3.25cm + 0.05cm);
\node[anchor=base, scale=0.35] at (\layer, 3.25cm - 2\unit) {$\vdots$};
% draw the second layer
\filldraw[fill=cyan!10, draw=black] (2 * \layer, -\unit) -- (2 * \layer, 0cm) circle (\unit) -- (2 * \layer, \unit);
\draw (2 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [461 units]} -- (2 * \layer + 0.10cm, 0cm) -- (2 * \layer + 0.15cm, 0.05cm);
\node[anchor=base, scale=0.35] at (2 * \layer, 1.25 * \unit) {$\vdots$};
\foreach \x in {1.5,...,3.5} {
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 0.5cm * \x - \unit) -- (2 * \layer, 0.5cm * \x) circle (\unit) -- (2 * \layer, 0.5cm * \x + \unit);
\draw (2 * \layer + 0.05cm, 0.5cm * \x) -- (2 * \layer + 0.10cm, 0.5cm * \x) -- (2 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
};
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 2.5cm - \unit) -- (2 * \layer, 2.5cm) circle (\unit) -- (2 * \layer, 2.5cm + \unit);
\draw (2 * \layer + 0.05cm, 2.5cm) -- (2 * \layer + 0.10cm, 2.5cm) -- (2 * \layer + 0.15cm, 2.5cm + 0.05cm);
\node[anchor=base, scale=0.35] at (2 * \layer, 2.5cm - 2\unit) {$\vdots$};
% draw the third layer
\filldraw[fill=cyan!10, draw=black] (3 * \layer, -\unit) -- (3 * \layer, 0cm) circle (\unit) -- (3 * \layer, \unit);
\draw (3 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [437 units]} -- (3 * \layer + 0.10cm, 0cm) -- (3 * \layer + 0.15cm, 0.05cm);
\node[anchor=base, scale=0.35] at (3 * \layer, 1.25 * \unit) {$\vdots$};
\foreach \x in {1.5,...,3.5} {
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 0.5cm * \x - \unit) -- (3 * \layer, 0.5cm * \x) circle (\unit) -- (3 * \layer, 0.5cm * \x + \unit);
\draw (3 * \layer + 0.05cm, 0.5cm * \x) -- (3 * \layer + 0.10cm, 0.5cm * \x) -- (3 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
};
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 2.5cm - \unit) -- (3 * \layer, 2.5cm) circle (\unit) -- (3 * \layer, 2.5cm + \unit);
\draw (3 * \layer + 0.05cm, 2.5cm) -- (3 * \layer + 0.10cm, 2.5cm) -- (3 * \layer + 0.15cm, 2.5cm + 0.05cm);
\node[anchor=base, scale=0.35] at (3 * \layer, 2.5cm - 2\unit) {$\vdots$};
% draw the fourth layer
\filldraw[fill=cyan!10, draw=black] (4 * \layer, -0.75cm - \unit) -- (4 * \layer, -0.75cm) circle (\unit) -- (4 * \layer, -0.75cm + \unit);
\draw (4 * \layer + 0.05cm, -0.75cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [929 units]} -- (4 * \layer + 0.10cm, -0.75cm) -- (4 * \layer + 0.15cm, -0.75cm + 0.05cm);
\node[anchor=base, scale=0.35] at (4 * \layer, -0.75cm + 1.25 * \unit) {$\vdots$};
\foreach \x in {0,...,5} {
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 0.5cm * \x - \unit) -- (4 * \layer, 0.5cm * \x) circle (\unit) -- (4 * \layer, 0.5cm * \x + \unit);
\draw (4 * \layer + 0.05cm, 0.5cm * \x) -- (4 * \layer + 0.10cm, 0.5cm * \x) -- (4 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
};
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 3.25cm - \unit) -- (4 * \layer, 3.25cm) circle (\unit) -- (4 * \layer, 3.25cm + \unit);
\draw (4 * \layer + 0.05cm, 3.25cm) -- (4 * \layer + 0.10cm, 3.25cm) -- (4 * \layer + 0.15cm, 3.25cm + 0.05cm);
\node[anchor=base, scale=0.35] at (4 * \layer, 3.25cm - 2\unit) {$\vdots$};
% draw the fifth layer
\filldraw[fill=cyan!10, draw=black] (5 * \layer, -\unit) -- (5 * \layer, 0cm) circle (\unit) -- (5 * \layer, \unit);
\draw (5 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [404 units]} -- (5 * \layer + 0.10cm, 0cm) -- (5 * \layer + 0.15cm, 0.05cm);
\node[anchor=base, scale=0.35] at (5 * \layer, 1.25 * \unit) {$\vdots$};
\foreach \x in {1.5,...,3.5} {
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 0.5cm * \x - \unit) -- (5 * \layer, 0.5cm * \x) circle (\unit) -- (5 * \layer, 0.5cm * \x + \unit);
\draw (5 * \layer + 0.05cm, 0.5cm * \x) -- (5 * \layer + 0.10cm, 0.5cm * \x) -- (5 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
};
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 2.5cm - \unit) -- (5 * \layer, 2.5cm) circle (\unit) -- (5 * \layer, 2.5cm + \unit);
\draw (5 * \layer + 0.05cm, 2.5cm) -- (5 * \layer + 0.10cm, 2.5cm) -- (5 * \layer + 0.15cm, 2.5cm + 0.05cm);
\node[anchor=base, scale=0.35] at (5 * \layer, 2.5cm - 2\unit) {$\vdots$};
% draw the output layer
\filldraw[fill=cyan!10, draw=black] (6 * \layer, 1.25cm - \unit) -- (6 * \layer, 1.25cm) circle (\unit) -- (6 * \layer, 1.25cm + \unit);
\draw (6 * \layer + 0.05cm, 1.25cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (6 * \layer + 0.10cm, 1.25cm) -- (6 * \layer + 0.15cm, 1.25cm + 0.05cm);
% draw weights 1 --> 2 and 4 --> 5
\foreach \x in {\layer, 4 * \layer} {
\foreach \y in {-0.75cm, 3.25cm} {
\foreach \z in {0cm, 2.5cm} {
\draw (\x + \unit, \y) -- (\x + \layer - \unit, \z);
};
};
\foreach \y in {0,...,5} {
\foreach \z in {1.5,...,3.5} {
\draw (\x + \unit, 0.5cm * \y) -- (\x + \layer - \unit, 0.5cm * \z);
};
\foreach \z in {0cm, 2.5cm} {
\draw (\x + \unit, 0.5 * \y) -- (\x + \layer - \unit, \z);
};
};
\foreach \y in {1.5,...,3.5} {
\draw (\x + \unit, 3.25cm) -- (\x + \layer - \unit, 0.5cm * \y);
\draw (\x + \unit, -0.75cm) -- (\x + \layer - \unit, 0.5cm * \y);
};
};
% draw weights 2 --> 3
\foreach \y in {0cm, 2.5cm} {
\foreach \z in {0cm, 2.5cm} {
\draw (2 * \layer + \unit, \y) -- (2 * \layer + \layer - \unit, \z);
};
};
\foreach \y in {1.5,...,3.5} {
\foreach \z in {1.5,...,3.5} {
\draw (2 * \layer + \unit, 0.5cm * \y) -- (2 * \layer + \layer - \unit, 0.5cm * \z);
};
\foreach \z in {0cm, 2.5cm} {
\draw (2 * \layer + \unit, 0.5cm * \y) -- (2 * \layer + \layer - \unit, \z);
};
};
\foreach \y in {1.5,...,3.5} {
\draw (2 * \layer + \unit, 2.5cm) -- (2 * \layer + \layer - \unit, 0.5cm * \y);
\draw (2 * \layer + \unit, 0cm) -- (2 * \layer + \layer - \unit, 0.5cm * \y);
};
% draw weights 3 --> 4
\foreach \y in {0cm, 2.5cm} {
\foreach \z in {-0.75cm, 3.25cm} {
\draw (3 * \layer + \unit, \y) -- (3 * \layer + \layer - \unit, \z);
};
};
\foreach \y in {1.5,...,3.5} {
\foreach \z in {0,...,5} {
\draw (3 * \layer + \unit, 0.5cm * \y) -- (3 * \layer + \layer - \unit, 0.5cm * \z);
};
\foreach \z in {0cm, 2.5cm} {
\draw (3 * \layer + \unit, 0.5cm * \y) -- (3 * \layer + \layer - \unit, \z);
};
};
\foreach \y in {0,...,5} {
\draw (3 * \layer + \unit, 2.5cm) -- (3 * \layer + \layer - \unit, 0.5cm * \y);
\draw (3 * \layer + \unit, 0cm) -- (3 * \layer + \layer - \unit, 0.5cm * \y);
};
% draw weights 5 --> output
\foreach \y in {0cm, 2.5cm} {
\draw (5 * \layer + \unit, \y) -- (5 * \layer + \layer - \unit, 1.25cm);
};
\foreach \y in {1.5,...,3.5} {
\draw (5 * \layer + \unit, 0.5cm * \y) -- (5 * \layer + \layer - \unit, 1.25cm);
};
% draw hidden layers legend
\node[anchor=base, align=center, text width=3.5cm, scale=0.5] (h) at (4cm, 4.5cm) {hidden layers (ReLU activation)};
\draw[->] (h) -- (\layer + \unit, 3.6cm);
\draw[->] (h) -- (2 * \layer + \unit, 2.85cm);
\draw[->] (h) -- (3 * \layer + 0.5 * \unit, 2.85cm);
\draw[->] (h) -- (4 * \layer, 3.6cm);
\draw[->] (h) -- (5 * \layer - 0.5 * \unit, 2.85cm);
\end{tikzpicture}
% vim: ft=tex

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img/icnn.pgf Normal file
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@@ -0,0 +1,193 @@
%\newlength{\layer}
%\newlength{\layerheight}
%\newlength{\perspective}
%\newlength{\filters}
%\newlength{\unit}
\newlength{\upperlevel}
\newlength{\bottomlevel}
\newlength{\concatheight}
\setlength{\layer}{3cm}
\setlength{\layerheight}{3cm}
\setlength{\perspective}{1cm}
\setlength{\filters}{0.01cm}
\setlength{\unit}{0.225cm}
\setlength{\upperlevel}{2.25cm}
\setlength{\bottomlevel}{-2.25cm}
\setlength{\concatheight}{0cm}
\usetikzlibrary{decorations.pathreplacing}
\begin{tikzpicture}
% input layer
\filldraw[fill=cyan!20, draw=black, fill opacity=0.5] (1cm, 0cm) -- (1cm + \perspective, \perspective) -- (1cm + \perspective, \perspective + \layerheight) -- (1cm, \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (1cm, \layerheight) {$1 @ 12 \times 15$};
\node[anchor=north west, scale=0.65] at (1cm, 0cm) {input layer};
% first layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \upperlevel) -- (\layer + 32 * \filters, \upperlevel) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (\layer + \perspective, \upperlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer + \perspective, \upperlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (\layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \upperlevel) -- (\layer + \perspective, \upperlevel + \perspective) -- (\layer + \perspective, \upperlevel + \perspective + \layerheight) -- (\layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \upperlevel) -- (\layer + 32 * \filters, \upperlevel) -- (\layer + 32 * \filters, \upperlevel + \layerheight) -- (\layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer + 32 * \filters, \upperlevel) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (\layer + 32 * \filters, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \upperlevel + \layerheight) -- (\layer + 32 * \filters, \upperlevel + \layerheight) -- (\layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (\layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (\layer, \upperlevel + \layerheight) {$32 @ 12 \times 15$};
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \bottomlevel) -- (\layer + 32 * \filters, \bottomlevel) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (\layer + \perspective, \bottomlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer + \perspective, \bottomlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (\layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \bottomlevel) -- (\layer + \perspective, \bottomlevel + \perspective) -- (\layer + \perspective, \bottomlevel + \perspective + \layerheight) -- (\layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \bottomlevel) -- (\layer + 32 * \filters, \bottomlevel) -- (\layer + 32 * \filters, \bottomlevel + \layerheight) -- (\layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer + 32 * \filters, \bottomlevel) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (\layer + 32 * \filters, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (\layer, \bottomlevel + \layerheight) -- (\layer + 32 * \filters, \bottomlevel + \layerheight) -- (\layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (\layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (\layer, \bottomlevel + \layerheight) {$32 @ 12 \times 15$};
% first concatenation
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, \concatheight) -- (2 * \layer + 64 * \filters, \concatheight) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (2 * \layer + \perspective, \concatheight + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer + \perspective, \concatheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (2 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, \concatheight) -- (2 * \layer + \perspective, \concatheight + \perspective) -- (2 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- (2 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, \concatheight) -- (2 * \layer + 64 * \filters, \concatheight) -- (2 * \layer + 64 * \filters, \concatheight + \layerheight) -- (2 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer + 64 * \filters, \concatheight) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (2 * \layer + 64 * \filters, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (2 * \layer, \concatheight + \layerheight) -- (2 * \layer + 64 * \filters, \concatheight + \layerheight) -- (2 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (2 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (2 * \layer, \concatheight + \layerheight) {$64 @ 12 \times 15$};
\draw (\layer + 32 * \filters + 1.2 * \perspective, \upperlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective, \upperlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.2 * \perspective, \bottomlevel + 0.5 * \layerheight);
\filldraw[fill=red!20, draw=black] (\layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
\draw[-latex] (\layer + 32 * \filters + 1.7 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
% second layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \upperlevel) -- (3 * \layer + 64 * \filters, \upperlevel) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective) -- (3 * \layer + \perspective, \upperlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + \perspective, \upperlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (3 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \upperlevel) -- (3 * \layer + \perspective, \upperlevel + \perspective) -- (3 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- (3 * \layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \upperlevel) -- (3 * \layer + 64 * \filters, \upperlevel) -- (3 * \layer + 64 * \filters, \upperlevel + \layerheight) -- (3 * \layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + 64 * \filters, \upperlevel) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (3 * \layer + 64 * \filters, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \upperlevel + \layerheight) -- (3 * \layer + 64 * \filters, \upperlevel + \layerheight) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (3 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (3 * \layer, \upperlevel + \layerheight) {$64 @ 12 \times 15$};
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \bottomlevel) -- (3 * \layer + 64 * \filters, \bottomlevel) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective) -- (3 * \layer + \perspective, \bottomlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + \perspective, \bottomlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (3 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \bottomlevel) -- (3 * \layer + \perspective, \bottomlevel + \perspective) -- (3 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- (3 * \layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \bottomlevel) -- (3 * \layer + 64 * \filters, \bottomlevel) -- (3 * \layer + 64 * \filters, \bottomlevel + \layerheight) -- (3 * \layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer + 64 * \filters, \bottomlevel) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (3 * \layer + 64 * \filters, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \bottomlevel + \layerheight) -- (3 * \layer + 64 * \filters, \bottomlevel + \layerheight) -- (3 * \layer + 64 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (3 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (3 * \layer, \bottomlevel + \layerheight) {$64 @ 12 \times 15$};
% second concatenation
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, \concatheight) -- (4 * \layer + 128 * \filters, \concatheight) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective) -- (4 * \layer + \perspective, \concatheight + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer + \perspective, \concatheight + \perspective) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (4 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, \concatheight) -- (4 * \layer + \perspective, \concatheight + \perspective) -- (4 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- (4 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, \concatheight) -- (4 * \layer + 128 * \filters, \concatheight) -- (4 * \layer + 128 * \filters, \concatheight + \layerheight) -- (4 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer + 128 * \filters, \concatheight) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (4 * \layer + 128 * \filters, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (4 * \layer, \concatheight + \layerheight) -- (4 * \layer + 128 * \filters, \concatheight + \layerheight) -- (4 * \layer + 128 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (4 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (4 * \layer, \concatheight + \layerheight) {$128 @ 12 \times 15$};
\draw (3 * \layer + 64 * \filters + 1.1 * \perspective, \upperlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective, \upperlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.1 * \perspective, \bottomlevel + 0.5 * \layerheight);
\filldraw[fill=red!20, draw=black] (3 * \layer + 64 * \filters + 1.6 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
\draw[-latex] (3 * \layer + 64 * \filters + 1.6 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
% third layer
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \upperlevel) -- (5 * \layer + 32 * \filters, \upperlevel) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (5 * \layer + \perspective, \upperlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer + \perspective, \upperlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (5 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \upperlevel) -- (5 * \layer + \perspective, \upperlevel + \perspective) -- (5 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- (5 * \layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \upperlevel) -- (5 * \layer + 32 * \filters, \upperlevel) -- (5 * \layer + 32 * \filters, \upperlevel + \layerheight) -- (5 * \layer, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer + 32 * \filters, \upperlevel) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (5 * \layer + 32 * \filters, \upperlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \upperlevel + \layerheight) -- (5 * \layer + 32 * \filters, \upperlevel + \layerheight) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective + \layerheight) -- (5 * \layer + \perspective, \upperlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (5 * \layer, \upperlevel + \layerheight) {$32 @ 12 \times 15$};
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \bottomlevel) -- (5 * \layer + 32 * \filters, \bottomlevel) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (5 * \layer + \perspective, \bottomlevel + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer + \perspective, \bottomlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (5 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \bottomlevel) -- (5 * \layer + \perspective, \bottomlevel + \perspective) -- (5 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- (5 * \layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \bottomlevel) -- (5 * \layer + 32 * \filters, \bottomlevel) -- (5 * \layer + 32 * \filters, \bottomlevel + \layerheight) -- (5 * \layer, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer + 32 * \filters, \bottomlevel) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (5 * \layer + 32 * \filters, \bottomlevel + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \bottomlevel + \layerheight) -- (5 * \layer + 32 * \filters, \bottomlevel + \layerheight) -- (5 * \layer + 32 * \filters + \perspective, \bottomlevel + \perspective + \layerheight) -- (5 * \layer + \perspective, \bottomlevel + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (5 * \layer, \bottomlevel + \layerheight) {$32 @ 12 \times 15$};
% third concatenation
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer, \concatheight) -- (6 * \layer + 64 * \filters, \concatheight) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (6 * \layer + \perspective, \concatheight + \perspective) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer + \perspective, \concatheight + \perspective) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (6 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer, \concatheight) -- (6 * \layer + \perspective, \concatheight + \perspective) -- (6 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- (6 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer, \concatheight) -- (6 * \layer + 64 * \filters, \concatheight) -- (6 * \layer + 64 * \filters, \concatheight + \layerheight) -- (6 * \layer, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer + 64 * \filters, \concatheight) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (6 * \layer + 64 * \filters, \concatheight + \layerheight) -- cycle;
\filldraw[thick, fill=orange!20, draw=black, fill opacity=0.5] (6 * \layer, \concatheight + \layerheight) -- (6 * \layer + 64 * \filters, \concatheight + \layerheight) -- (6 * \layer + 64 * \filters + \perspective, \concatheight + \perspective + \layerheight) -- (6 * \layer + \perspective, \concatheight + \perspective + \layerheight) -- cycle;
\node[anchor=south west, scale=0.65, rotate=45] at (6 * \layer, \concatheight + \layerheight) {$64 @ 12 \times 15$};
\draw (5 * \layer + 32 * \filters + 1.2 * \perspective, \upperlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective, \upperlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.2 * \perspective, \bottomlevel + 0.5 * \layerheight);
\filldraw[fill=red!20, draw=black] (5 * \layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
\draw[-latex] (5 * \layer + 32 * \filters + 1.7 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
% flatten layer
\foreach \x in {0,...,4} {
\filldraw[fill=cyan!10, draw=black] (6 * \layer + 3cm, \concatheight + \unit + 0.75 * \x cm) circle (\unit);
\draw (6 * \layer + 3cm + \unit, \concatheight + \unit + 0.75 * \x cm) -- (7 * \layer + 2cm - \unit, \concatheight + \unit + 0.5 * \layerheight);
};
\node[anchor=north, scale=0.5, below=15pt, align=center] at (6 * \layer + 3cm, \concatheight + \unit) {flatten};
% draw the "flatenisation"
\draw[dashed] (6 * \layer + 64 * \filters, \layerheight) -- (6 * \layer + 3 cm, 3cm + 2 * \unit) -- (6 * \layer + 64 * \filters + \perspective, \layerheight + \perspective) -- cycle;
\draw[dashed] (6 * \layer + 64 * \filters, 0cm) -- (6 * \layer + 3 cm, 0cm) -- (6 * \layer + 64 * \filters + \perspective, \perspective) -- cycle;
% output layer
\filldraw[fill=cyan!10, draw=black] (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight - \unit) -- (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight) circle (\unit) -- (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight + \unit);
\draw (7 * \layer + 2cm + 0.05cm, \concatheight + \unit + 0.5 * \layerheight) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (7 * \layer + 2cm + 0.10cm, \concatheight + \unit + 0.5 * \layerheight) -- (7 * \layer + 2cm + 0.15cm, \concatheight + \unit + 0.5 * \layerheight + 0.05cm);
% draw the first convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0.9 * \layerheight) -- (1cm + \perspective, 0.9 * \layerheight + \perspective) -- (1cm + \perspective, \layerheight + \perspective) -- (1cm, \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0.9 * \layerheight) -- (\layer, \upperlevel + 0.9 * \layerheight) -- (1cm + \perspective, 0.9 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, \layerheight) -- (\layer, \upperlevel + 0.9 * \layerheight) -- (1cm + \perspective, \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm + \perspective, 0.9 * \layerheight + \perspective) -- (\layer, \upperlevel + 0.9 * \layerheight) -- (1cm + \perspective, \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0.9 * \layerheight) -- (\layer, \upperlevel + 0.9 * \layerheight) -- (1cm, \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0cm) -- (1cm + 0.2 * \perspective, 0.2 * \perspective) -- (1cm + 0.2 * \perspective, \layerheight + 0.2 * \perspective) -- (1cm, \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0cm) -- (\layer, \bottomlevel + 0.9 * \layerheight) -- (1cm + 0.2 * \perspective, 0.2 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm + 0.2 * \perspective, 0.2 * \perspective) -- (\layer, \bottomlevel + 0.9 * \layerheight) -- (1cm + 0.2 * \perspective, \layerheight + 0.2 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm + 0.2 * \perspective, \layerheight + 0.2 * \perspective) -- (\layer, \bottomlevel + 0.9 * \layerheight) -- (1cm, \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0cm) -- (\layer, \bottomlevel + 0.9 * \layerheight) -- (1cm, \layerheight) -- cycle;
% draw the second convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
% draw the second convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters, 0.4 * \layerheight) -- (3 * \layer, \upperlevel + 0.6 * \layerheight) -- (2 * \layer + 64 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (2 * \layer + 64 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (3 * \layer, \bottomlevel + 0.9 * \layerheight) -- (2 * \layer + 64 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
% draw the third convolution
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters, 0.4 * \layerheight) -- (4 * \layer + 128 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (4 * \layer + 128 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- (4 * \layer + 128 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters, 0.4 * \layerheight) -- (5 * \layer, \upperlevel + 0.6 * \layerheight) -- (4 * \layer + 128 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters, 0.5 * \layerheight) -- (5 * \layer, \upperlevel + 0.6 * \layerheight) -- (4 * \layer + 128 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + \perspective, 0.4 * \layerheight + \perspective) -- (5 * \layer, \upperlevel + 0.6 * \layerheight) -- (4 * \layer + 128 * \filters + \perspective, 0.5 * \layerheight + \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters, 0.4 * \layerheight) -- (5 * \layer, \upperlevel + 0.6 * \layerheight) -- (4 * \layer + 128 * \filters, 0.5 * \layerheight) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (4 * \layer + 128 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (4 * \layer + 128 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (4 * \layer + 128 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (5 * \layer, \bottomlevel + 0.9 * \layerheight) -- (4 * \layer + 128 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + 0.4 * \perspective, 0.4 * \perspective) -- (5 * \layer, \bottomlevel + 0.9 * \layerheight) -- (4 * \layer + 128 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + 0.4 * \perspective, \layerheight + 0.4 * \perspective) -- (5 * \layer, \bottomlevel + 0.9 * \layerheight) -- (4 * \layer + 128 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (4 * \layer + 128 * \filters + 0.3 * \perspective, 0.3 * \perspective) -- (5 * \layer, \bottomlevel + 0.9 * \layerheight) -- (4 * \layer + 128 * \filters + 0.3 * \perspective, \layerheight + 0.3 * \perspective) -- cycle;
% hidden layer labels
\draw[decorate, decoration={brace}] (\layer, \upperlevel + 1.25 * \layerheight + \perspective) -- (2 * \layer + 64 * \filters + \perspective, \upperlevel + 1.25 * \layerheight + \perspective) node[midway, anchor=south, above=2cm, align=center] {concatenation module 1} node[midway, anchor=south, above=0.8cm, align=center, text width=4cm] {hor: $1 \times 15$ kernel ver: $12 \times 1$ kernel} node[midway, anchor=south] {(ReLU activation)};
\draw[decorate, decoration={brace}] (3 * \layer, \upperlevel + 1.25 * \layerheight + \perspective) -- (4 * \layer + 128 * \filters + \perspective, \upperlevel + 1.25 * \layerheight + \perspective) node[midway, anchor=south, above=2cm, align=center] {concatenation module 2} node[midway, anchor=south, above=0.8cm, align=center, text width=4cm] {hor: $1 \times 15$ kernel ver: $12 \times 1$ kernel} node[midway, anchor=south] {(ReLU activation)};
\draw[decorate, decoration={brace}] (5 * \layer, \upperlevel + 1.25 * \layerheight + \perspective) -- (6 * \layer + 64 * \filters + \perspective, \upperlevel + 1.25 * \layerheight + \perspective) node[midway, anchor=south, above=2cm, align=center] {concatenation module 3} node[midway, anchor=south, above=0.8cm, align=center, text width=4cm] {hor: $1 \times 15$ kernel ver: $12 \times 1$ kernel} node[midway, anchor=south] {(ReLU activation)};
\end{tikzpicture}
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634
thesis.tex
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@@ -1,4 +1,4 @@
\documentclass[10pt, aspectratio=169]{beamer}
\documentclass[10pt, aspectratio=169, compress]{beamer}
\usepackage[utf8]{inputenc}
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\end{center}
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@@ -601,7 +601,7 @@
\end{frame}
\begin{frame}{Doubling Trick and Spinor Representation}
\begin{block}{Doubling Trick}
\begin{equationblock}{Doubling Trick}
\begin{equation*}
\partial_z \mathcal{X}( z )
=
@@ -628,12 +628,12 @@
}
\end{equation*}
where $\mathscr{H}_{\gtrless}^{(t)} = \qty{z \in \mathds{C} \mid \Im z \gtrless 0~\text{or}~z \in D_{(t)} }$ and $\updelta_{\pm} = \upeta \pm i 0^+$.
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@@ -700,8 +700,7 @@
\frac{1}{\Upgamma( c_n )}\,
\tensor[_2]{F}{_1}( a_n,\, b_n;\, c_n;\, \upomega_z )
\\
\qty( -\upomega_z )^{1 - c_n}\,
\frac{1}{\Upgamma( 2 - c_n )}\,
\frac{\qty( -\upomega_z )^{1 - c_n}}{\Upgamma( 2 - c_n )}\,
\tensor[_2]{F}{_1}( a_n + 1 - c_n,\, b_n + 1 - c_n;\, 2 - c_n;\, \upomega_z )
)
\end{equation*}
@@ -1177,13 +1176,586 @@
\subsection[NBO]{Null Boost Orbifold}
\begin{frame}{Null Boost Orbifold}
Start from $\qty( x^+,\, x^-,\, x^2,\, \vec{x} ) \in \mathscr{M}^{1,\, D-1}$:
\begin{equation*}
\begin{cases}
u & = x^-
\\
z & = \frac{x^2}{\Updelta\, x^-}
\\
v & = x^+ - \frac{1}{2} \frac{\qty( x^2 )^2}{x^-}
\end{cases}
\qquad
\Rightarrow
\qquad
\dd{s}^2 = -2 \dd{u} \dd{v} + \qty( \Updelta\, u )^2\, \dd{z}^2 + \updelta_{ij} \dd{x}^i \dd{x}^j
\end{equation*}
\pause
\begin{equationblock}{Killing Vector and Null Boost Oribfold}
\begin{equation*}
\upkappa = -i \qty( 2 \uppi \Updelta ) J_{+2} = 2 \uppi \partial_z
\Rightarrow
z \sim z + 2 \uppi n
\end{equation*}
\end{equationblock}
\pause
Consider \highlight{scalar QED:}
\begin{equation*}
\upphi_{\qty{ k_+,\, l,\, \vec{k},\, r}}\qty( u,\, v,\, z,\, \vec{x} )
=
e^{i \qty( k_+ v + l z + \vec{k} \cdot \vec{x} )}\,
\widetilde{\upphi}_{\qty{ k_+,\, l,\, \vec{k},\, r}}\qty( u )
=
\frac{e^{i \qty( k_+ v + l z + \vec{k} \cdot \vec{x} )}}{\sqrt{\qty( 2 \uppi )^D\, \abs{2 \Updelta k_+ u}}}\,
e^{-i \frac{l^2}{2 \Updelta^2 k_+} \frac{1}{u} + i \frac{\norm{\vec{k}}^2 + r}{2 k_+} u}
\end{equation*}
\end{frame}
\begin{frame}{Scalar QED Interactions}
Scalar--photon interactions:
\begin{equation*}
S_{\text{sQED}}^{\text{(int)}}
=
\int\limits_{\Upomega} \dd[D]{x} \sqrt{- g }\,
\qty(%
-i\, e\, g^{\upalpha\upbeta} a_{\upalpha} \qty( \upphi^*\, \partial_{\upbeta} \upphi - \partial_{\upbeta} \upphi^*\, \upphi )
+ e^2\, g^{\upalpha\upbeta} a_{\upalpha} a_{\upbeta} \abs{\upphi}^2
- \frac{g_4}{4}\, \abs{\upphi}^4
)
\end{equation*}
\pause
Terms involved:
\begin{equation*}
\begin{split}
\mathcal{I}^{\qty[\upnu]}_{\qty{N}}
& =
\int\limits_{-\infty}^{+\infty} \dd{u}
\abs{\Updelta\, u} u^{\upnu}
\prod\limits_{i = 1}^N
\widetilde{\upphi}_{\qty{ k_{+\, (i)},\, l_{(i)},\, \vec{k}_{(i)},\, r_{(i)}}}\qty( u )
\\
\mathcal{J}^{\qty[\upnu]}_{\qty{N}}
& =
\int\limits_{-\infty}^{+\infty} \dd{u}
\abs{\Updelta} \abs{u}^{1 + \upnu}
\prod\limits_{i = 1}^N
\widetilde{\upphi}_{\qty{ k_{+\, (i)},\, l_{(i)},\, \vec{k}_{(i)},\, r_{(i)}}}\qty( u )
\end{split}
\end{equation*}
\pause
\begin{center}
\it
most terms \textbf{do not converge} and cannot be recovered even with a \textbf{distributional interpretions} due to the term $\propto u^{-1}$ in the exponentatial
\end{center}
\end{frame}
\begin{frame}{String and Field Theory}
So far:
\begin{itemize}
\item field theory presents \textbf{divergences}
\pause
\item issues are \textbf{still present} in sQED (eikonal?)
\pause
\item divergences are \textbf{not (only) gravitational}
\end{itemize}
\pause
\begin{equationblock}{Massive String States}
\begin{equation*}
V_M\qty( x;\, k,\, S,\, \upxi )
=
\colon
\qty(%
\frac{i}{\sqrt{2 \upalpha'}}\,
\upxi \cdot \partial^2_x X( x,\, x )
+
\qty( \frac{i}{\sqrt{2 \upalpha'}} )^2\,
S_{\upalpha\upbeta}
\partial_x X^{\upalpha}( x,\, x )
\partial_x X^{\upbeta}( x,\, x )
)
e^{i k \cdot X( x,\, x )}
\colon
\end{equation*}
\end{equationblock}
\pause
\begin{center}
\it
string theory cannot do \textbf{better than field theory} (EFT) if the latter \textbf{does not exist} (even a Wilson line around $z$ does not prevent such behaviour)
\end{center}
\end{frame}
\begin{frame}{Resolution and Motivation}
Introduce the \highlight{generalised NBO:}
\begin{equation*}
\begin{cases}
u & = x^-
\\
z & = \frac{1}{2 x^-} \qty( \frac{x^2}{\Updelta_2} + \frac{x^3}{\Updelta_3} )
\\
w & = \frac{1}{2 x^-} \qty( \frac{x^2}{\Updelta_2} - \frac{x^3}{\Updelta_3} )
\\
v & = x^+ - \frac{1}{2 x^-} \qty( \qty( x^2 )^2 + \qty( x^3 )^2 )
\end{cases}
\qquad
\Rightarrow
\qquad
\upkappa
=
-2 \uppi i \qty( \Updelta_2 J_{+2} + \Updelta_3 J_{+3} )
=
2 \uppi \partial_z
\end{equation*}
\pause
\begin{equationblock}{Distributional Interpretation}
\begin{equation*}
\widetilde{\upphi}_{\qty{ k_+,\, p,\, l,\, \vec{k},\, r}}\qty( u )
=
\frac{1}{2 \sqrt{\qty(2 \uppi)^D \abs{\Updelta_2 \Updelta_3 k_+}}}
\frac{1}{\abs{u}}
e^{-i\, \qty( \frac{1}{8 k_+ u} \qty[ \frac{(l + p)^2}{\Updelta_2^2} + \frac{(l - p)^2}{\Updelta_3^2} ] - \frac{\norm{\vec{k}}^2 + r}{2 k_+} u )}
\end{equation*}
\end{equationblock}
\end{frame}
\begin{frame}{On the Divergences and Their Nature}
\begin{itemize}
\item divergences are present in sQED and \textbf{open string} sector
\pause
\item singularities $\Rightarrow$ \textbf{massive states} are no longer spectators
\pause
\item vanishing volume (\textbf{compact orbifold directions}) $\Rightarrow$ particles ``cannot escape''
\pause
\item \textbf{non compact} orbifold directions $\Rightarrow$ interpretation of \textbf{amplitudes as distributions}
\pause
\item issue not restricted to NBO/GNBO but also BO, null brane, etc. (it is a \textbf{general issues} connected to the geometry of the underlying space)
\end{itemize}
\pause
\vspace{2em}
\begin{center}
\it
spacetime singularities are \textbf{hidden into contact terms} and interactions with \textbf{massive states} (the gravitational eikonal deals with massless interactions)
\end{center}
\begin{tikzpicture}[remember picture, overlay]
\draw[line width=4pt, red] (0em, 4.5em) rectangle (40em, 1em);
\end{tikzpicture}
\end{frame}
\section[Deep Learning]{Deep Learning the Geometry of String Theory}
\begin{frame}{CCC}
c
\subsection[Introduction]{Machine Learning and Deep Learning}
\begin{frame}{The Simplest Calabi--Yau}
Focus on Calabi--Yau \highlight{3-folds:}
\begin{equation*}
h^{r,\, s} = \dim\limits_{\mathds{C}} H_{\overline{\partial}}^{r,\, s}\qty( M,\, \mathds{C} )
\qquad
\Rightarrow
\qquad
\begin{cases}
h^{0,\, 0} & = h^{3,\, 0} = 1
\\
h^{r,\, 0} & = 0 \quad \text{if} \quad r \neq 3
\\
h^{r,\, s} & = h^{3 - r,\, 3 - s}
\\
h^{1,\, 1},\, h^{2,\, 1} \in \mathds{N}
\end{cases}
\end{equation*}
\pause
\begin{block}{Complete Intersection Calabi--Yau Manifolds}
Intersection of hypersurfaces in
\begin{equation*}
\mathcal{A} = \mathds{P}^{n_1} \times \dots \times \mathds{P}^{n_m}
\end{equation*}
where
\begin{equation*}
\mathds{P}^n\colon
\qquad
\begin{cases}
p_a\qty( Z^0,\, \dots,\, Z^n ) & = P_{I_1 \dots I_a} Z^{I_1} \dots Z^{I_a} = 0
\\
p_a\qty( \uplambda Z^0,\, \dots,\, \uplambda Z^n ) & = \uplambda^a p_a\qty( Z^0,\, \dots,\, Z^n )
\end{cases}
\end{equation*}
\end{block}
\end{frame}
\begin{frame}{Representation of the Output}
CICY can be generalised to \highlight{$m$ projective spaces and $k$ equations.}
The problem is thus mapped to:
\begin{equation*}
\begin{tabular}{@{}lccc@{}}
$\mathscr{R}\colon$
&
$\mathds{Z}^{m \times k}$
&
$\longrightarrow$
&
$\mathds{N}$
\\[1em]
&
$\qty[%
\begin{tabular}{@{}c|ccc@{}}
$\mathds{P}^{n_1}$ & $a_1^1$ & $\dots$ & $a_k^1$
\\
$\vdots$ & $\vdots$ & $\ddots$ & $\vdots$
\\
$\mathds{P}^{n_m}$ & $a_1^m$ & $\dots$ & $a_k^m$
\end{tabular}
]$
&
$\longrightarrow$
&
$h^{1,\, 1} \quad \text{or} \quad h^{2,\, 1}$
\end{tabular}
\end{equation*}
\pause
\begin{block}{Machine Learning Approach}
What is $\mathscr{R}$?
\begin{equation*}
\mathscr{R}( M ) \longrightarrow \mathscr{R}_n( M;\, w )
\qquad
\text{s.t.}
\qquad
\lim\limits_{n \to \infty} f( M;\, w ) = \lim\limits_{n \to \infty} \abs{\mathscr{R}( M ) - \mathscr{R}_n( M;\, w )} = 0
\end{equation*}
\end{block}
\end{frame}
\begin{frame}{Machine Learning}
\begin{itemize}
\item exchange \textbf{analytical solution} with \textbf{optimisation problem}
\pause
\item use \textbf{various algorithms} and exploit \textbf{large datasets}
\pause
\item learn a \textbf{representation} rather than a \textbf{solution}
\pause
\item effectively use knowledge from \textbf{computer science, mathematics and physics} to solve problems
\end{itemize}
\pause
\begin{center}
\includegraphics[width=0.7\linewidth]{img/label-distribution_orig}
\end{center}
\end{frame}
\subsection[Machine Learning]{Machine Learning for String Theory}
\begin{frame}{Exploratory Data Analysis}
Machine Learning \highlight{pipeline:}
\begin{center}
\textbf{exploratory} data analysis
$\rightarrow$
feature \textbf{selection}
$\rightarrow$
Hodge numbers
\end{center}
\pause
\begin{columns}
\begin{column}{0.5\linewidth}
\centering
\includegraphics[width=0.9\columnwidth]{img/corr-matrix_orig}
\end{column}
\hfill
\begin{column}{0.5\linewidth}
\centering
\includegraphics[width=0.9\columnwidth, trim={0 0 6in 0}, clip]{img/scalar-features_orig}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Dataset}
\begin{itemize}
\item $7890$ CICY manifolds (full dataset)
\pause
\item \textbf{dataset pruning}: no product spaces, no ``very far'' outliers (reduction of $0.49\%$)
\pause
\item $h^{1,\, 1} \in \qty[ 1,\, 16 ]$ and $h^{2,\, 1} \in \qty[ 15,\, 86 ]$
\pause
\item $80\%$ training, $10\%$ validation, $10\%$ test
\pause
\item choose \textbf{regression}, but evaluate using \textbf{accuracy} (round the result)
\end{itemize}
\pause
\begin{center}
\includegraphics[width=0.7\linewidth]{img/label-distribution-compare_orig}
\end{center}
\end{frame}
\begin{frame}{Machine Learning}
\centering
\includegraphics[width=0.85\linewidth]{img/ml_map}
\pause
\begin{tikzpicture}[remember picture, overlay]
\draw[line width=10pt, red, -latex] (-18em,1em) -- (-14.5em, 6em);
\draw[line width=10pt, red, -latex] (19em, 7em) -- (14em, 4em);
\end{tikzpicture}
\pause
\begin{tikzpicture}[remember picture, overlay]
\draw[line width=4pt, red] (12em,12em) ellipse (2cm and 1.5cm);
\end{tikzpicture}
\end{frame}
\begin{frame}{A Word on PCA}
\begin{columns}
\begin{column}{0.4\linewidth}
What is PCA for a $X \in \mathds{R}^{n \times p}$?
\begin{itemize}
\item find new coordinates to \textbf{``put the variance in order''}
\item \highlight{equivalently} compute the \textbf{eigenvectors} of $X X^T$ or the \textbf{singular values} of $X$
\item isolate \textbf{the signal} from the \textbf{background}
\item ease the machine learning job of finding a better representation of the input
\end{itemize}
\end{column}
\hfill
\begin{column}{0.6\linewidth}
\centering
\includegraphics[width=0.5\columnwidth]{img/marchenko-pastur}
\includegraphics[width=\columnwidth]{img/svd_orig}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Machine Learning Results}
\begin{columns}
\begin{column}{0.5\linewidth}
\centering
\textbf{Configuration Matrix Only}
\includegraphics[width=0.8\columnwidth, trim={0 0 3.3in 0}, clip]{img/cicy_matrix_plots}
\end{column}
\hfill\pause
\begin{column}{0.5\linewidth}
\centering
\textbf{Best Training Set}
\includegraphics[width=0.8\columnwidth, trim={0 0 3.3in 0}, clip]{img/cicy_best_plots}
\end{column}
\end{columns}
\end{frame}
\subsection[Deep Learning]{AI Implementations for Geometry and Strings}
\begin{frame}{Artificial Intelligence and Neural Networks}
\begin{columns}
\begin{column}{0.6\linewidth}
\begin{itemize}
\item use \textbf{gradient descent} to optimise \textbf{weights}
\item learn highly \textbf{non linear} representations of the input
\item can be \highlight{``large''} to have enough parameters
\item can be \highlight{``deep''} to to learn \textbf{complicated functions}
\end{itemize}
\begin{block}{Neural Networks}
\vspace{0.5em}
\begin{tabular}{@{}lc@{}}
fully connected:
&
$a^{\qty(i)\, \qty{l+1}} = \upphi\qty( a^{\qty(i)\, \qty{l}} \cdot W^{\qty{l}} + b^{\qty{l}} \mathds{1} )$
\\
convolutional:
&
$a^{\qty(i)\, \qty{l+1}} = \upphi\qty( a^{\qty(i)\, \qty{l}}\, *\, W^{\qty{l}} + b^{\qty{l}} \mathds{1} )$
\end{tabular}
\end{block}
Non linearity ensured by:
\begin{equation*}
\upphi( z ) = \mathrm{ReLU}\qty( z ) = \max\qty(0,\, z)
\end{equation*}
\end{column}
\hfill
\begin{column}{0.4\linewidth}
\centering
\resizebox{\columnwidth}{!}{\import{img}{fc.pgf}}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Convolutional Neural Networks}
Why convolutional?
\begin{columns}
\begin{column}{0.4\linewidth}
\begin{itemize}[<+->]
\item retain \textbf{spacial awareness}
\item smaller \textbf{no.\ of parameters} ($\approx 2 \times 10^5$ vs.\ $\approx 2 \times 10^6$)
\item weights are \textbf{shared}
\item CNN can isolate \textbf{``defining features''}
\item find patterns as in \textbf{computer vision}
\end{itemize}
\end{column}
\hfill
\begin{column}{0.6\linewidth}
\centering
\only<1>{\includegraphics[width=0.75\columnwidth, trim={12in 10in 0 0}, clip]{img/input_mat}}
\only<2>{\includegraphics[width=0.75\columnwidth, trim={12in 5in 0 5in}, clip]{img/input_mat}}
\only<3>{\includegraphics[width=0.75\columnwidth, trim={12in 0 0 10in}, clip]{img/input_mat}}
\only<4->{\resizebox{\columnwidth}{!}{\import{img}{ccnn.pgf}}}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Inception Neural Networks}
Recent development by Google's deep learning teams led to:
\begin{itemize}
\item neural networks with \textbf{better generalisation properties}
\item smaller networks (both parameters and depth)
\item different \textbf{concurrent kernels} (e.g.\ one over \textbf{equations} one over \textbf{coordinates})
\end{itemize}
\pause
\begin{center}
\resizebox{0.75\linewidth}{!}{\import{img}{icnn.pgf}}
\end{center}
\end{frame}
\begin{frame}{Deep Learning Results and Generalisation Properties}
\begin{columns}
\begin{column}{0.5\linewidth}
\centering
\textbf{Best Training Set}
\includegraphics[width=\columnwidth]{img/cicy_best_plots}
\end{column}
\hfill
\begin{column}{0.5\linewidth}
\centering
\includegraphics[width=0.75\columnwidth]{img/inc_nn_learning_curve_h11}
\includegraphics[width=0.75\columnwidth]{img/inc_nn_learning_curve}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{A Few Comments and Future Directions}
Why \highlight{deep learning in physics?}
\begin{itemize}
\item reliable \textbf{predictive method} \pause (provided good data analysis)
\pause
\item reliable \textbf{source of inspiration} \pause (provided good data analysis)
\pause
\item reliable \textbf{generalisation method} \pause (provided good data analysis)
\pause
\item \textbf{CNNs are powerful tools} (this is the \emph{first time in physics!})
\pause
\item interdisciplinary approach $=$ win-win situation!
\end{itemize}
\pause
What now?
\begin{itemize}
\item representation learning $\Rightarrow$ what is the best way to represent CICYs?
\pause
\item study invariances $\Rightarrow$ invariances should not influence the result (graph representations?)
\pause
\item higher dimensions $\Rightarrow$ what about CICY 4-folds?
\pause
\item geometric deep learning $\Rightarrow$ explain the geometry of the ``AI'' behind deep learning!
\pause
\item reinforcement learning $\Rightarrow$ give the rules, not the result!
\end{itemize}
\end{frame}
{%
\setbeamertemplate{footline}{}
\usebackgroundtemplate{%
\transparent{0.1}
\includegraphics[width=\paperwidth]{img/torino.png}
}
\addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{}
\begin{frame}[noframenumbering]{The End?}
\begin{center}
\Huge
THANK YOU!
\end{center}
\end{frame}
}
\end{document}