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Cuts are pictured as solid coloured blocks running from one intersection point to another at finite. @@ -599,8 +598,7 @@ We choose $\bart = 1$ in what follows. \begin{figure}[tbp] \centering - \def\svgwidth{0.35\linewidth} - \import{img}{threebranes_plane.pdf_tex} + \import{tikz}{threebranes_plane.pgf} \caption{% Fixing the \SL{2}{\R} invariance for $N_B = 3$ and $\bart = 1$ leads to a cut structure with all the cuts defined on the real axis towards $\omega_{\bart} = \infty$.} \label{fig:hypergeometric_cuts} @@ -2111,23 +2109,41 @@ Here we compute the parameter $\vec{n}_{1}$ given two Abelian rotation in $\omeg Results are shown in~\Cref{tab:Abelian_composition}. \begin{figure}[tbp] + \centering + \begin{subfigure}[b]{0.45\linewidth} \centering - \def\svgwidth{0.8\textwidth} - \import{img}{abelian_angles_case1.pdf_tex} - \caption{% - The Abelian limit when the triangle has all acute angles. - This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.} - \label{fig:Abelian_angles_1} + \import{tikz}{abelian_angles_case1_a.pgf} + \caption{Case 1.} + \end{subfigure} + \hfill + \begin{subfigure}[b]{0.45\linewidth} + \centering + \import{tikz}{abelian_angles_case1_b.pgf} + \caption{Case 2.} + \end{subfigure} + \caption{% + The Abelian limit when the triangle has all acute angles. + This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.} + \label{fig:Abelian_angles_1} \end{figure} \begin{figure}[tbp] + \centering + \begin{subfigure}[b]{0.45\linewidth} \centering - \def\svgwidth{0.8\textwidth} - \import{img}{abelian_angles_case2.pdf_tex} - \caption{% - The Abelian limit when the triangle has one obtuse angle. - This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.} - \label{fig:Abelian_angles_2} + \import{tikz}{abelian_angles_case2_a.pgf} + \caption{Case 1.} + \end{subfigure} + \hfill + \begin{subfigure}[b]{0.45\linewidth} + \centering + \import{tikz}{abelian_angles_case2_b.pgf} + \caption{Case 2.} + \end{subfigure} + \caption{% + The Abelian limit when the triangle has one obtuse angle. + This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.} + \label{fig:Abelian_angles_2} \end{figure} Under the parity transformation $P_2$ the previous four cases are grouped @@ -2151,8 +2167,17 @@ when all $m = 0$. \begin{figure}[tbp] \centering - \def\svgwidth{0.8\textwidth} - \import{img}{usual_abelian_angles.pdf_tex} + \begin{subfigure}[b]{0.45\linewidth} + \centering + \import{tikz}{usual_abelian_angles_a.pgf} + \caption{Case 1.} + \end{subfigure} + \hfill + \begin{subfigure}[b]{0.45\linewidth} + \centering + \import{tikz}{usual_abelian_angles_b.pgf} + \caption{Case 2.} + \end{subfigure} \caption{% The geometrical angles used in the usual geometrical approach to the Abelian configuration do not distinguish among the possible branes orientations. In fact we have $0 \le \alpha < 1$ and $0 < \varepsilon < 1$. @@ -2552,8 +2577,7 @@ Each term of the action can be interpreted again as an area of a triangle where \begin{figure}[tbp] \centering - \def\svgwidth{0.35\textwidth} - \import{img/}{brane3d.pdf_tex} + \import{tikz}{brane3d.pgf} \caption{% Pictorial $3$-dimensional representation of two D2-branes intersecting in the Euclidean space $\R^3$ along a line (in $\R^4$ the intersection is a point since the co-dimension of each D-brane is 2): since it is no longer constrained on a bi-dimensional plane, the string must be deformed in order to stretch between two consecutive D-branes. Its action can be larger than the planar area. diff --git a/sec/part1/fermions.tex b/sec/part1/fermions.tex index 411b626..e59c9a8 100644 --- a/sec/part1/fermions.tex +++ b/sec/part1/fermions.tex @@ -95,7 +95,7 @@ Their solutions are the ``holomorphic'' functions $\psi_{+}^i(\xi_+)$ and $\psi_ } \begin{figure}[tbp] \centering - \includegraphics[width=0.4\linewidth]{img/point-like-defects} + \import{tikz}{defects.pgf} \caption{Propagation of the string in the presence of the worldsheet defects.} \label{fig:point-like-defects} \end{figure} @@ -838,7 +838,7 @@ Finally we get the anti-commutation relations as \begin{figure}[tbp] \centering - \includegraphics[width=0.5\linewidth]{img/complex-plane} + \import{tikz}{complex_plane_defects.pgf} \caption{% Fields are glued on the $x < 0$ semi-axis with non trivial discontinuities for $x_{(t)} < x < x_{(t-1)}$ for $t = 1,\, 2,\, \dots,\, N$ and where $x_{(t)} = \exp( \htau_{E,\, (t)} )$. } @@ -1636,7 +1636,7 @@ Moreover notice that for $\rL \le -1$ both $b^{(\rE)}_{\rL \le n \le 0}$ and $b^ \begin{figure}[tbp] \centering - \includegraphics[width=0.5\linewidth]{img/in-annihilators.pdf} + \import{tikz}{inconsistent_theories.pgf} \caption{As a consistency condition, we have to exclude the values of $\rL$ for which both $b^{( E)}_n$ and $b^{*\, ( \brE )}_{\rL + 1 - n}$ are in-annihilators diff --git a/sec/part3/introduction.tex b/sec/part3/introduction.tex index b9e2fa4..925f8c5 100644 --- a/sec/part3/introduction.tex +++ b/sec/part3/introduction.tex @@ -59,7 +59,7 @@ Thus getting also \hodge{2}{1} from \ml techniques is an important first step to Finally regression is also more useful for extrapolating results: a classification approach assumes that we already know all the possible values of the Hodge numbers and has difficulties to predict labels which do not appear in the training set. This is necessary when we move to a dataset for which not all topological quantities have been computed, for instance CY constructed from the Kreuzer--Skarke list of polytopes~\cite{Kreuzer:2000:CompleteClassificationReflexive}. -The data analysis and \ml are programmed in Python using open-source packages: \texttt{pandas}~\cite{WesMcKinney:2010:DataStructuresStatistical}, \texttt{matplotlib}~\cite{Hunter:2007:Matplotlib2DGraphics}, \texttt{seaborn}~\cite{Waskom:2020:MwaskomSeabornV0}, \texttt{scikit-learn}~\cite{Pedregosa:2011:ScikitlearnMachineLearning}, \texttt{scikit-optimize}~\cite{Head:2020:ScikitoptimizeScikitoptimize}, \texttt{tensorflow}~\cite{Abadi:2015:TensorFlowLargescaleMachine} (and its high level API \emph{Keras}). +The data analysis and \ml are programmed in Python using known open-source packages such as \texttt{pandas}~\cite{WesMcKinney:2010:DataStructuresStatistical}, \texttt{matplotlib}~\cite{Hunter:2007:Matplotlib2DGraphics}, \texttt{seaborn}~\cite{Waskom:2020:MwaskomSeabornV0}, \texttt{scikit-learn}~\cite{Pedregosa:2011:ScikitlearnMachineLearning}, \texttt{scikit-optimize}~\cite{Head:2020:ScikitoptimizeScikitoptimize}, \texttt{tensorflow}~\cite{Abadi:2015:TensorFlowLargescaleMachine} (and its high level API \emph{Keras}). Code is available on \href{https://thesfinox.github.io/ml-cicy/}{Github}. @@ -192,14 +192,14 @@ Below we show a list of the \cicy properties and of their configuration matrices \begin{figure}[tbp] \centering - \begin{subfigure}[c]{.45\linewidth} + \begin{subfigure}[b]{.45\linewidth} \centering \includegraphics[width=\linewidth, trim={0 0.45in 6in 0}, clip]{img/label-distribution_orig} \caption{\hodge{1}{1}} \label{fig:data:hist-h11} \end{subfigure} \hfill - \begin{subfigure}[c]{.45\linewidth} + \begin{subfigure}[b]{.45\linewidth} \centering \includegraphics[width=\linewidth, trim={6in 0.45in 0 0}, clip]{img/label-distribution_orig} \caption{\hodge{2}{1}} diff --git a/sec/part3/ml.tex b/sec/part3/ml.tex index 2c61ab8..249c623 100644 --- a/sec/part3/ml.tex +++ b/sec/part3/ml.tex @@ -1020,7 +1020,7 @@ Using the same network we also achieve \SI{97}{\percent} of accuracy in the favo \centering \begin{subfigure}[c]{0.475\linewidth} \centering - \includegraphics[width=\linewidth]{img/fc} + \import{tikz}{fc.pgf} \caption{Architecture of the network.} \label{fig:nn:dense} \end{subfigure} @@ -1099,7 +1099,7 @@ The convolution layers have $180$, $100$, $40$ and $20$ units each. \begin{figure}[tbp] \centering - \includegraphics[width=0.75\linewidth]{img/ccnn} + \import{tikz}{ccnn.pgf} \caption{% Pure convolutional neural network for redicting \hodge{1}{1}. It is made of $4$ modules composed by convolutional layer, ReLU activation, batch normalisation (in this order), followed by a dropout layer, a flatten layer and the output layer (in this order). @@ -1204,7 +1204,7 @@ The callbacks helped to contain the training time (without optimisation) under 5 \begin{figure}[tbp] \centering - \includegraphics[width=0.9\linewidth]{img/icnn} + \resizebox{\linewidth}{!}{\import{tikz}{icnn.pgf}} \caption{% In each concatenation module (here shown for the ``old'' dataset) we operate with separate convolution operations over rows and columns, then concatenate the results. The overall architecture is composed of 3 ``inception'' modules made by two separate convolutions, a concatenation layer and a batch normalisation layer (strictly in this order), followed by a dropout layer, a flatten layer and the output layer with ReLU activation (in this order). @@ -1374,7 +1374,7 @@ Another reason is that the different algorithms may perform similarly well in th \begin{figure}[tbp] \centering - \includegraphics[width=0.65\linewidth]{img/stacking} + \resizebox{0.65\linewidth}{!}{\import{tikz}{stacking.pgf}} \caption{Stacking ensemble learning with two level learning.} \label{fig:stack:def} \end{figure} diff --git a/thesis.pdf b/thesis.pdf index 17b5576..dcb98f8 100644 Binary files a/thesis.pdf and b/thesis.pdf differ diff --git a/tikz/abelian_angles_case1_a.pgf b/tikz/abelian_angles_case1_a.pgf new file mode 100644 index 0000000..d64bc8d --- /dev/null +++ b/tikz/abelian_angles_case1_a.pgf @@ -0,0 +1,20 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (0.2cm, -0.3cm) -- (4.1cm, 3.1cm) node[anchor=west] {$D_{(1)}$}; +\draw[thick] (4.5cm, -0.4cm) -- (1cm, 2.4cm) node[anchor=east] {$D_{(2)}$}; +\draw[thick] (0cm, 0cm) -- (5cm, 0cm) node[anchor=north west] {$D_{(3)}$}; + +% draw angles +\draw[dashed, ->] (1.25cm, 0cm) arc (0:45:0.6cm); +\draw[dashed, <-] (4.5cm, 0cm) arc (0:130:0.6cm); +\draw[dashed, ->] (2.6cm, 1.85cm) arc (45:135:0.6cm); + +% draw names +\node[anchor=north] at (1.25, 0cm) {$n_{0}^3 > 0$}; +\node[anchor=south west] at (4.5cm, 0cm) {$n_{1}^3 < 0$}; +\node[anchor=north west] at (2.9cm, 1.85cm) {$n_{\infty}^3 > 0$}; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/abelian_angles_case1_b.pgf b/tikz/abelian_angles_case1_b.pgf new file mode 100644 index 0000000..7d4e212 --- /dev/null +++ b/tikz/abelian_angles_case1_b.pgf @@ -0,0 +1,20 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (0.2cm, -0.3cm) -- (4.1cm, 3.1cm) node[anchor=west] {$D_{(1)}$}; +\draw[thick] (4.5cm, -0.4cm) -- (1cm, 2.4cm) node[anchor=east] {$D_{(2)}$}; +\draw[thick] (0cm, 0cm) -- (5cm, 0cm) node[anchor=north west] {$D_{(3)}$}; + +% draw angles +\draw[dashed, ->] (1.25cm, 0cm) arc (0:45:0.6cm); +\draw[dashed, <-] (4.4cm, -0.3cm) arc (320:360:0.6cm); +\draw[dashed, <-] (2.7cm, 1.05cm) arc (-50:50:0.6cm); + +% draw names +\node[anchor=north] at (1.25, 0cm) {$n_{0}^3 > 0$}; +\node[anchor=south west] at (4.5cm, 0cm) {$n_{1}^3 < 0$}; +\node[anchor=north west] at (2.9cm, 1.85cm) {$n_{\infty}^3 > 0$}; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/abelian_angles_case2_a.pgf b/tikz/abelian_angles_case2_a.pgf new file mode 100644 index 0000000..853cf7f --- /dev/null +++ b/tikz/abelian_angles_case2_a.pgf @@ -0,0 +1,20 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (-0.1cm, -0.6cm) -- (5.4cm, 3.5cm) node[anchor=south] {$D_{(1)}$}; +\draw[thick] (3cm, -0.4cm) -- (5cm, 4.4cm) node[anchor=east] {$D_{(2)}$}; +\draw[thick] (-0.5cm, 0cm) -- (5cm, 0cm) node[anchor=north west] {$D_{(3)}$}; + +% draw angles +\draw[dashed, ->] (3.75cm, 0cm) arc (0:65:0.6cm); +\draw[dashed, <-] (-0.1cm, 0cm) arc (180:225:0.6cm); +\draw[dashed, ->] (4.5cm, 3.35cm) arc (75:220:0.6cm); + +% draw names +\node[anchor=north] at (4.5, 1cm) {$n_{0}^3 > 0$}; +\node[anchor=south west] at (-0.5cm, 0.2cm) {$n_{1}^3 < 0$}; +\node[anchor=north west] at (2cm, 3.25cm) {$n_{\infty}^3 > 0$}; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/abelian_angles_case2_b.pgf b/tikz/abelian_angles_case2_b.pgf new file mode 100644 index 0000000..0458f05 --- /dev/null +++ b/tikz/abelian_angles_case2_b.pgf @@ -0,0 +1,20 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (-0.1cm, -0.6cm) -- (5.4cm, 3.5cm) node[anchor=south] {$D_{(1)}$}; +\draw[thick] (3cm, -0.4cm) -- (5cm, 4.4cm) node[anchor=east] {$D_{(2)}$}; +\draw[thick] (-0.5cm, 0cm) -- (5cm, 0cm) node[anchor=north west] {$D_{(3)}$}; + +% draw angles +\draw[dashed, ->] (3.75cm, 0cm) arc (0:65:0.6cm); +\draw[dashed, <-] (1.5cm, 0cm) arc (0:45:0.6cm); +\draw[dashed, <-] (4.9cm, 3.15cm) arc (25:67:0.6cm); + +% draw names +\node[anchor=north] at (4.5, 1cm) {$n_{0}^3 > 0$}; +\node[anchor=south west] at (-0.5cm, 0.2cm) {$n_{1}^3 > 0$}; +\node[anchor=north west] at (2cm, 3.25cm) {$n_{\infty}^3 < 0$}; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/branchcuts.pgf b/tikz/branchcuts.pgf new file mode 100644 index 0000000..74e5791 --- /dev/null +++ b/tikz/branchcuts.pgf @@ -0,0 +1,32 @@ +\usetikzlibrary{decorations.pathreplacing} +\usetikzlibrary{decorations.pathmorphing} + +\begin{tikzpicture} + +% draw axis +\draw[thick, ->] (-3cm, 0cm) -- (3cm, 0cm) node[anchor=south] {$x$}; +\draw[thick, ->] (-0.4cm, -1cm) -- (-0.4cm, 3cm) node[anchor=east] {$y$}; + +% draw branching cuts +\filldraw[fill=black!50, draw=black, dashed] (-2cm, 3pt) rectangle (2.5cm, -3pt); +\filldraw[fill=black!30, draw=black, dashed] (-0.75cm, 2pt) rectangle (2.5cm, -2pt); +\filldraw[fill=black!10, draw=black, dashed] (1cm, 1pt) rectangle (2.5cm, -1pt); + +% draw branching points +\filldraw[fill=white, draw=black] (2.5cm, 0cm) circle (2pt) node[anchor=north, below=3pt] (x1) {$x_{(1)}$}; +\filldraw[fill=white, draw=black] (1cm, 0cm) circle (2pt) node[anchor=north, below=3pt] (x2) {$x_{(2)}$}; +\filldraw[fill=white, draw=black] (-0.75cm, 0cm) circle (2pt) node[anchor=north, below=3pt] (x3) {$x_{(3)}$}; +\filldraw[fill=white, draw=black] (-2cm, 0cm) circle (2pt) node[anchor=north, below=3pt] (x4) {$x_{(4)}$}; + +% assign the D-branes +\draw[thin, decorate, decoration={brace}] (1cm, 0.3cm) -- (2.5cm, 0.3cm) node[midway, anchor=south] {$D_{(2)}$}; +\draw[thin, decorate, decoration={brace}] (-0.75cm, 0.3cm) -- (1cm, 0.3cm) node[midway, anchor=south] {$D_{(3)}$}; +\draw[thin, decorate, decoration={brace}] (-2cm, 0.3cm) -- (-0.75cm, 0.3cm) node[midway, anchor=south] {$D_{(4)}$}; + +% draw the remaining D-brane +\draw[thin, ->, dash pattern=on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 1cm] (-2cm, 2pt) -- (-2cm, 1cm)-- (-2.75cm, 1cm) node[midway, anchor=south] {$D_{(1)}$} ; +\draw[thin, ->, dash pattern=on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 1cm] (2.5cm, 2pt) -- (2.5cm, 1cm)-- (3cm, 1cm) node[midway, anchor=south] {$D_{(1)}$} ; + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file diff --git a/tikz/brane3d.pgf b/tikz/brane3d.pgf new file mode 100644 index 0000000..910701a --- /dev/null +++ b/tikz/brane3d.pgf @@ -0,0 +1,25 @@ +\usetikzlibrary{decorations.pathmorphing} + +\begin{tikzpicture} + +% draw branes +\draw[thick] (-0.35cm, 0cm) -- (-3cm, -2cm) -- (-3cm, 3cm) -- (1cm, 5cm) -- (1cm, 4cm); +\draw[dashed] (1cm, 4cm) -- (1cm, 1cm) -- (-0.35cm, 0cm); + +\draw[thick] (-3cm, 2cm) -- (-4cm, 4cm) -- (1.5cm, 4cm) -- (3.5cm, 0cm) -- (-0.35cm, 0cm); +\draw[dashed] (-3cm, 2cm) -- (-2cm, 0cm) -- (-0.35cm, 0cm); + +\draw[dotted] (-0.35cm, 0cm) -- (-1cm, 4.01cm); + +% draw names +\node[anchor=base] at (0.15cm, 5cm) {$D_{(t)}$}; +\node[anchor=base] at (2.5cm, -0.5cm) {$D_{(t+1)}$}; + +% draw string +\draw[thick, decorate, decoration={snake, segment length=1cm}] (1.5cm, 2cm) .. controls (1.1cm, 1.1cm) and (-1cm, 0.1cm) .. (-1.8cm, 0.3cm); +\filldraw[fill=black, draw=black] (1.5cm, 2cm) circle (2pt); +\filldraw[fill=black, draw=black] (-1.8cm, 0.3cm) circle (2pt); + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file diff --git a/tikz/branesangles.pgf b/tikz/branesangles.pgf index 7429bed..56cf643 100644 --- a/tikz/branesangles.pgf +++ b/tikz/branesangles.pgf @@ -28,7 +28,7 @@ \draw[thin, <-] (2.6cm, -2.12cm) arc (0:30:0.4cm) node[anchor=south] {$\pi \alpha_{(1)}$}; \draw[thin, <-] (-2.1cm, -1.5cm) arc (250:360:0.4cm) node[anchor=south west] {$\pi \alpha_{(2)}$}; -\draw[thin, <-] (1.1cm, 2.4cm) arc (0:100:0.4cm) node[anchor=south] {$\pi \alpha_{(3)}$}; +\draw[thin, ->] (1.1cm, 2.4cm) arc (0:100:0.4cm) node[anchor=south] {$\pi \alpha_{(3)}$}; \end{tikzpicture} diff --git a/tikz/ccnn.pgf b/tikz/ccnn.pgf new file mode 100644 index 0000000..fe6ab5d --- /dev/null +++ b/tikz/ccnn.pgf @@ -0,0 +1,96 @@ +%\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=texft=texft=texft=texft=texx \ No newline at end of file diff --git a/tikz/complex_plane.pgf b/tikz/complex_plane.pgf index 1514022..7d51db9 100644 --- a/tikz/complex_plane.pgf +++ b/tikz/complex_plane.pgf @@ -1,22 +1,19 @@ -\usetikzlibrary{decorations.markings} -\usetikzlibrary{arrows} - -\begin{tikzpicture} +\begin{tikzpicture} % draw axis \draw[thick, ->] (-3cm, 0cm) -- (3cm, 0cm) node[anchor=south] {$\Re z$}; \draw[thick, ->] (0cm, -3cm) -- (0cm, 3cm) node[anchor=east] {$\Im z$}; % draw closed loops -\draw[dotted, decorate, decoration={markings, mark=at position 0.0 with {\arrow{latex}}}] (0cm, 0cm) circle [radius=1.0cm]; -\draw[dotted, decorate, decoration={markings, mark=at position 0.0 with {\arrow{latex}}}] (0cm, 0cm) circle [radius=2.5cm]; +\draw[dotted, -latex] (1cm, 0cm) arc (0:360:1cm); +\draw[dotted, -latex] (2.5cm, 0cm) arc (0:360:2.5cm); % draw arrows -\draw[-latex] (0,0) -- (1.75cm, 1.75cm) node[anchor=south west] (z1) {$\abs{z_{(1)}} = e^{\tau_{E\, (1)}}$}; -\draw[-latex] (0,0) -- (0.45cm, -0.9cm) node[anchor=north west] (z0) {$\abs{z_{(0)}} = e^{\tau_{E\, (0)}}$}; +\draw[-latex] (0,0) -- (1.75cm, 1.75cm) node[anchor=south] (z1) {$\abs{z_{(1)}} = e^{\tau_{E\, (1)}}$}; +\draw[-latex] (0,0) -- (0.45cm, -0.9cm) node[anchor=north] (z0) {$\abs{z_{(0)}} = e^{\tau_{E\, (0)}}$}; % draw isolated point -\draw[fill] (-1.5cm, 1.1cm) circle [radius=2pt] node[anchor=south west] (w) {$w$}; +\draw[fill] (-1.5cm, 1.1cm) circle (2pt) node[anchor=south west] (w) {$w$}; % draw the names of the paths (use $\mathcal{C}$ instead of $\ccC$ if it does not compile) \node (c0) at (-0.7cm, -1.2cm) {$\ccC_{(0)}$}; diff --git a/tikz/complex_plane_defects.pgf b/tikz/complex_plane_defects.pgf new file mode 100644 index 0000000..04683fa --- /dev/null +++ b/tikz/complex_plane_defects.pgf @@ -0,0 +1,21 @@ +\begin{tikzpicture} + +% draw axis +\draw[thick, ->] (-3cm, 0cm) node[anchor=north] {$0$} -- (2.5cm, 0cm) node[anchor=south] {$x$}; +\draw[thick, ->] (-2.75cm, -1cm) -- (-2.75cm, 3cm) node[anchor=east] {$y$}; + +% draw branching cuts +\filldraw[fill=black!30, draw=black, dashed] (-2cm, 2pt) rectangle (2.25cm, -2pt); +\filldraw[fill=black!10, draw=black, dashed] (0.25cm, 1pt) rectangle (2.25cm, -1pt); + +% draw branching points +\filldraw[fill=white, draw=black] (-2cm, 0cm) circle (2pt) node[anchor=north] {$x_{(t+1)}$}; +\filldraw[fill=white, draw=black] (0.25cm, 0cm) circle (2pt) node[anchor=north] {$x_{(t)}$}; +\filldraw[fill=white, draw=black] (2.25cm, 0cm) circle (2pt) node[anchor=north] {$x_{(t-1)}$}; + +% draw closed loop +\draw[dotted, ->] (1cm, 2pt) arc (0:350:0.75cm); + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file diff --git a/tikz/defects.pgf b/tikz/defects.pgf new file mode 100644 index 0000000..f9635b0 --- /dev/null +++ b/tikz/defects.pgf @@ -0,0 +1,29 @@ +\usetikzlibrary{decorations.pathmorphing} + +\begin{tikzpicture} + +% draw axis +\draw[thick, ->] (-3cm, 0cm) -- (3cm, 0cm) node[anchor=south] {$\tau$}; +\draw[thick, ->] (-0.75cm, -1cm) -- (-0.75cm, 3cm) node[anchor=east] {$\sigma$}; + +% draw defects +\filldraw[fill=white, draw=black] (-2cm, 0cm) circle (2pt) node[anchor=north] {$\htau_{(t+1)}$}; +\filldraw[fill=white, draw=black] (0.25cm, 0cm) circle (2pt) node[anchor=north] {$\htau_{(t)}$}; +\filldraw[fill=white, draw=black] (2.25cm, 0cm) circle (2pt) node[anchor=north] {$\htau_{(t-1)}$}; + +% draw the endlines +\draw[dotted] (-2cm, 2pt) -- (-2cm, 2cm); +\draw[dotted] (0.25cm, 2pt) -- (0.25cm, 2cm); +\draw[dotted] (2.25cm, 2pt) -- (2.25cm, 2cm); + +% draw the second D-brane +\draw[dashed] (-3cm, 2cm) -- (3cm, 2cm); +\node[anchor=south west] at (-0.75cm, 2cm) {$\pi$}; + +% draw the string +\draw[decorate, decoration={snake, segment length=0.75cm}] (1cm, 0cm) -- (1cm, 2cm); +\draw[->] (1.1cm, 1cm) -- (1.6cm, 1cm); + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/fc.pgf b/tikz/fc.pgf new file mode 100644 index 0000000..e728d86 --- /dev/null +++ b/tikz/fc.pgf @@ -0,0 +1,160 @@ +\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 \ No newline at end of file diff --git a/tikz/icnn.pgf b/tikz/icnn.pgf new file mode 100644 index 0000000..2ae093e --- /dev/null +++ b/tikz/icnn.pgf @@ -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} + +% vim: ft=texft=texft=texft=texft=tex \ No newline at end of file diff --git a/tikz/inconsistent_theories.pgf b/tikz/inconsistent_theories.pgf new file mode 100644 index 0000000..d3e55f8 --- /dev/null +++ b/tikz/inconsistent_theories.pgf @@ -0,0 +1,29 @@ +\usetikzlibrary{patterns} + +\begin{tikzpicture} + +% fill the overlap area +\draw[black!0, pattern=north east lines, pattern color=black!15] (0cm, 0cm) rectangle (2cm, 2cm); +\node[anchor=base, text width=2cm, align=center] at (1cm, 1.4cm) {\textsc{Overlap Region}}; +\node[anchor=base, text width=3cm, align=center, scale=0.5] at (1cm, 0.5cm) {\textsc{inconsistent theories}}; + +% draw the horizontal axis +\draw[thick, ->] (-3cm, 0cm) -- (4cm, 0cm) node[anchor=south west] {$n$}; + +% draw points +\node[anchor=north] at (-3cm, 0cm) {$\cdots$}; +\filldraw[fill=white, draw=black] (-2cm,0cm) circle (2pt) node[anchor=north] {$-1$}; +\filldraw[fill=white, draw=black] (-1cm,0cm) circle (2pt) node[anchor=north] {$0$}; +\filldraw[fill=white, draw=black] (0cm,0cm) circle (2pt) node[anchor=north] {$1$}; +\node[anchor=north] at (1cm, 0cm) {$\cdots$}; +\filldraw[fill=white, draw=black] (2cm,0cm) circle (2pt) node[anchor=north] {$\rL$}; +\filldraw[fill=white, draw=black] (3cm,0cm) circle (2pt) node[anchor=north] {$\rL+1$}; +\node[anchor=north] at (4cm, 0cm) {$\cdots$}; + +% draw limits +\draw[->] (0cm, 2pt) -- (0cm, 2cm) -- (4cm, 2cm) node[midway, anchor=south west] {in-annihilators} node[anchor=north east] {$b_{n}$}; +\draw[->] (2cm, 2pt) -- (2cm, 1.8cm) -- (-3cm, 1.8cm) node[midway, anchor=south east] {out-annihilators} node[anchor=north west] {$b^*_{\rL + 1 - n}$}; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/radial_ordering.pgf b/tikz/radial_ordering.pgf index 98a1dbb..464c364 100644 --- a/tikz/radial_ordering.pgf +++ b/tikz/radial_ordering.pgf @@ -1,17 +1,14 @@ -\usetikzlibrary{decorations.markings} -\usetikzlibrary{arrows} - -\begin{tikzpicture} +\begin{tikzpicture} % draw axis \draw[thick, ->] (-3cm, 0cm) -- (3cm, 0cm) node[anchor=south] (ascissa) {$\Re z$}; \draw[thick, ->] (0cm, -3cm) -- (0cm, 3cm) node[anchor=east] (ordinata) {$\Im z$}; % draw isolated point -\draw[fill] (-1.5cm, 1.1cm) circle [radius=2pt] node[anchor=south west] (w) {$w$}; +\draw[fill] (-1.5cm, 1.1cm) circle (2pt) node[anchor=south west] (w) {$w$}; % draw closed loops -\draw[dotted, decorate, decoration={markings, mark=at position 0.0 with {\arrow{latex}}}] (-1.5cm, 1.1cm) circle [radius=0.6cm]; +\draw[dotted, -latex] (-0.9cm, 1.1cm) arc (0:360:0.6cm); % draw the names of the paths (use $\mathcal{C}$ instead of $\ccC$ if it does not compile) \node (c0) at (-2.1cm, 0.3cm) {$\ccC_{(w)}$}; diff --git a/tikz/stacking.pgf b/tikz/stacking.pgf new file mode 100644 index 0000000..7b82c93 --- /dev/null +++ b/tikz/stacking.pgf @@ -0,0 +1,43 @@ +\begin{tikzpicture} + +% draw first level +\filldraw[thick, fill=cyan!20, draw=black] (0cm, 0cm) -- (7cm, 0cm) node[midway, anchor=south, align=center, text width=3cm, above=5pt] {training set} -- (7cm, 1cm) -- (0cm, 1cm) -- cycle; +\filldraw[thick, fill=orange!20, draw=black] (7.1cm, 0cm) -- (10cm, 0cm) node[midway, anchor=south, align=center, text width=2cm, above=8pt] {test set} -- (10cm, 1cm) -- (7.1cm, 1cm) -- cycle; + +\draw[-latex] (3.5cm, 0cm) -- (1.75cm, -0.8cm); +\draw[-latex] (3.5cm, 0cm) -- (5.25cm, -0.8cm); + +% draw second level +\filldraw[thick, fill=cyan!20, draw=black] (0cm, -2cm) -- (3.45cm, -2cm) node[midway, anchor=south, align=center, text width=3cm, above=5pt] {training set 1} -- (3.45cm, -1cm) -- (0cm, -1cm) -- cycle; +\filldraw[thick, fill=cyan!20, draw=black] (3.55cm, -2cm) -- (7cm, -2cm) node[midway, anchor=south, align=center, text width=3cm, above=5pt] {training set 2} -- (7cm, -1cm) -- (3.55cm, -1cm) -- cycle; +\filldraw[thick, fill=orange!20, draw=black] (7.1cm, -2cm) -- (10cm, -2cm) node[midway, anchor=south, align=center, text width=2cm, above=8pt] {test set} -- (10cm, -1cm) -- (7.1cm, -1cm) -- cycle; + +\draw[-latex] (1.75cm, -2cm) -- (1.75cm, -2.65cm) node[anchor=south west] {training}; + +% 1st level trainers +\filldraw[thick, fill=green!20, draw=black] (1.725cm, -3.5cm) ellipse [x radius=1.5cm,y radius=0.75cm] node[anchor=center, align=center, text width=3cm] {1st level learners}; + +\draw[-latex] (5.25cm, -2cm) -- (5.25cm, -4.85cm) node[anchor=south west] {predictions}; +\draw[-latex] (8.5cm, -2cm) -- (8.5cm, -4.85cm) node[anchor=south west] {predictions}; + +\filldraw (3.25cm, -3.5cm) -- (8.5cm, -3.5cm) circle (2pt); +\draw (1.75cm, -4.25cm) -- (1.75cm, -4.45cm) -- (5.25cm, -4.45cm); +\filldraw (5.25cm, -4.45cm) circle (2pt); + +% 1st level labels +\filldraw[thick, fill=red!20, draw=black] (3.55cm, -6cm) -- (7cm, -6cm) node[midway, anchor=south, align=center, scale=0.8] {\begin{tabular}{c} test set 2 \\ (1st level labels) \\ \end{tabular}} -- (7cm, -5cm) -- (3.55cm, -5cm) -- cycle; +\filldraw[thick, fill=blue!20, draw=black] (7.1cm, -6cm) -- (10cm, -6cm) node[midway, anchor=south, align=center, scale=0.8] {\begin{tabular}{c} test set 1 \\ (1st level labels) \\ \end{tabular}} -- (10cm, -5cm) -- (7.1cm, -5cm) -- cycle; + +\draw[-latex] (5.25cm, -6cm) -- (5.25cm, -6.65cm); +\draw[-latex] (8.5cm, -6cm) -- (8.5cm, -8.85cm) node[anchor=south west] {predictions}; +\filldraw (6.75cm, -7.5cm) -- (8.5cm, -7.5cm) circle (2pt); + +% 2nd level trainers +\filldraw[thick, fill=black!20, draw=black] (5.25cm, -7.5cm) ellipse [x radius=1.5cm,y radius=0.75cm] node[anchor=center, align=center, text width=3cm] {meta learner}; + +% final predictions +\filldraw[thick, fill=yellow!20, draw=black] (7.1cm, -10cm) -- (10cm, -10cm) node[midway, anchor=south, align=center, scale=0.8] {\begin{tabular}{c} test set 1 \\ (1st level labels) \\ \end{tabular}} -- (10cm, -9cm) -- (7.1cm, -9cm) -- cycle; + +\end{tikzpicture} + +% vim: ft=tex diff --git a/tikz/threebranes_plane.pgf b/tikz/threebranes_plane.pgf new file mode 100644 index 0000000..d7e3f12 --- /dev/null +++ b/tikz/threebranes_plane.pgf @@ -0,0 +1,21 @@ +\usetikzlibrary{decorations.pathreplacing} +\usetikzlibrary{decorations.pathmorphing} + +\begin{tikzpicture} + +% draw axis +\draw[thick, ->] (-0.5cm, 0cm) -- (5cm, 0cm) node[anchor=south] {$\Re \omega$}; +\draw[thick, ->] (0cm, -1cm) -- (0cm, 3cm) node[anchor=east] {$\Im \omega$}; + +% draw branching cuts +\filldraw[fill=black!30, draw=black, dashed] (0cm, 2pt) rectangle (4.8cm, -2pt); +\filldraw[fill=black!10, draw=black, dashed] (1cm, 1pt) rectangle (4.8cm, -1pt); + +% draw branching points +\filldraw[fill=white, draw=black] (4.8cm, 0cm) circle (2pt) node[anchor=north] (x1) {$\infty$}; +\filldraw[fill=white, draw=black] (1cm, 0cm) circle (2pt) node[anchor=north] (x2) {$1$}; +\filldraw[fill=white, draw=black] (0cm, 0cm) circle (2pt) node[anchor=north east] (x3) {$0$}; + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file diff --git a/tikz/usual_abelian_angles_a.pgf b/tikz/usual_abelian_angles_a.pgf new file mode 100644 index 0000000..68e77fd --- /dev/null +++ b/tikz/usual_abelian_angles_a.pgf @@ -0,0 +1,15 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (-0.5cm, -0.5cm) -- (4cm, 2cm) node[anchor=west] {$D_{(t)}$}; +\draw[thick] (0cm, -1cm) -- (1.7cm, 4cm) node[anchor=west] {$D_{(t+1)}$}; + +% draw baseline and angles +\draw[dotted] (-1cm, -0.05cm) -- (5cm, -0.05cm); +\draw[->] (1.5cm, -0.05cm) node[anchor=north] {$\alpha_{(t)}$} arc (0:22:1.6cm); +\draw[->] (2.5cm, -0.05cm) node[anchor=north] {$\alpha_{(t+1)}$} arc (0:62:2.6cm); +\draw[->] (3.5cm, 1.7cm) arc (22:76:2.9cm) node[anchor=east] {$\varepsilon_{(t)}$}; + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file diff --git a/tikz/usual_abelian_angles_b.pgf b/tikz/usual_abelian_angles_b.pgf new file mode 100644 index 0000000..85d0974 --- /dev/null +++ b/tikz/usual_abelian_angles_b.pgf @@ -0,0 +1,15 @@ +\begin{tikzpicture} + +% draw D-branes +\draw[thick] (0cm, -1cm) -- (1.7cm, 4cm) node[anchor=west] {$D_{(t)}$}; +\draw[thick] (-0.5cm, -0.5cm) -- (4cm, 2cm) node[anchor=west] {$D_{(t+1)}$}; + +% draw baseline and angles +\draw[dotted] (-1cm, -0.05cm) -- (5cm, -0.05cm); +\draw[->] (2.5cm, -0.05cm) node[anchor=north] {$\alpha_{(t)}$} arc (0:62:2.6cm); +\draw[->] (1.5cm, -0.05cm) node[anchor=north] {$\alpha_{(t+1)}$} arc (0:22:1.6cm); +\draw[->] (0.55cm, 0.6cm) node[anchor=south east] {$\varepsilon_{(t)}$} arc (76:210:0.6cm); + +\end{tikzpicture} + +% vim: ft=tex \ No newline at end of file