From 77139f038636edc2a79e9f8ab29ca954de15c92b Mon Sep 17 00:00:00 2001 From: Riccardo Finotello Date: Thu, 12 Nov 2020 18:24:15 +0100 Subject: [PATCH] Finish writing Signed-off-by: Riccardo Finotello --- img/ccnn.pgf | 96 ++++ img/cicy_best_plots.pdf | Bin 0 -> 19600 bytes img/cicy_matrix_plots.pdf | Bin 0 -> 19576 bytes img/corr-matrix_orig.pdf | Bin 0 -> 23712 bytes img/fc.pgf | 160 ++++++ img/icnn.pgf | 193 ++++++++ img/inc_nn_learning_curve.pdf | Bin 0 -> 14150 bytes img/inc_nn_learning_curve_h11.pdf | Bin 0 -> 12926 bytes img/input_mat.png | Bin 0 -> 54004 bytes img/label-distribution-compare_orig.pdf | Bin 0 -> 16771 bytes img/label-distribution_orig.pdf | Bin 0 -> 13837 bytes img/marchenko-pastur.nb | 422 ++++++++++++++++ img/marchenko-pastur.pdf | Bin 0 -> 12494 bytes img/ml_map.png | Bin 0 -> 774895 bytes img/scalar-features_orig.pdf | Bin 0 -> 19512 bytes img/svd_orig.pdf | Bin 0 -> 23797 bytes thesis.tex | 634 ++++++++++++++++++++++-- 17 files changed, 1474 insertions(+), 31 deletions(-) create mode 100644 img/ccnn.pgf create mode 100644 img/cicy_best_plots.pdf create mode 100644 img/cicy_matrix_plots.pdf create mode 100644 img/corr-matrix_orig.pdf create mode 100644 img/fc.pgf create mode 100644 img/icnn.pgf create mode 100644 img/inc_nn_learning_curve.pdf create mode 100644 img/inc_nn_learning_curve_h11.pdf create mode 100644 img/input_mat.png create mode 100644 img/label-distribution-compare_orig.pdf create mode 100644 img/label-distribution_orig.pdf create mode 100644 img/marchenko-pastur.nb create mode 100644 img/marchenko-pastur.pdf create mode 100644 img/ml_map.png create mode 100644 img/scalar-features_orig.pdf create mode 100644 img/svd_orig.pdf diff --git a/img/ccnn.pgf b/img/ccnn.pgf new file mode 100644 index 0000000..bbeb13b --- /dev/null +++ b/img/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=tex diff --git a/img/cicy_best_plots.pdf b/img/cicy_best_plots.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7b21b63e214f520e1a9a3493826ceb69b8833875 GIT binary patch literal 19600 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zmV_cMc&35r;|4`$?A?Ds6+GL;G`T~u8gu6f19dELM~sc!7zl+qlJOwOeD}@Jsgg=S z!LhUd=e(hnzi*GM0QT@nS~5(Qjt@*l!2m|*g{ z`fZ#bdGXkmc0oG1AM#8K;i}8j))&zt+j{|Pk!7965$AuGG`Ea9tP-q_xf! zza`63cUG-f6{#V7>mIpjMy3M=CHY*$Mp4yc*y+aHC&EH;G9ztUvkQGDGWlcPiCiQ0^QZH{p_6KS`?xBfPL-WD=sZl7aV}Twc*wc4 z$#hf?dav9gyJhOH&mAh~FrB!5ouHxRVYk{XTI2Kl7j0YNs=+)H{4V^H3eV!k2s3mW zCEql^Id3zSp+zf|jkrxl!FgTI5zq9dtgOgCelG)_OAU8W$&Zm3zA-jqK23XtVP~zF zwr)^6h3YsfuUmHan(j^Vv$=Qr@0IJ&QAMQBoR0mldp~YRn^x8Ej`pB7I|EgCh;fTt zyytOeK85569yHM%a;4mtc&5dAi%R6W+{_w&F4t!V&o2g@K0$7&ws)13Rn)Pz^edH- zne*r!5&cCqa@{A~6I`*8w;t)nUN?s1#_N_Y6Z1s)@LkIF<5sz8XR>u0zb;YnInaG!V5h7|68D-RO2&X7nrUKf$Sz|=VuVo6V zW+J0r(%jLeyE45Dgn!|B0gV8VHkd29Go$)!!uTBDtk*=zG<)MB6W}mhA*ye{KVRp?+P1pI;ClpI`eS_!&ubE(%16U)lr#;Q6&p z2#PMh^g{t~`AZvM?YDjiBgR)FN+#Sb*{dU 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/img/icnn.pgf b/img/icnn.pgf new file mode 100644 index 0000000..62ebb18 --- /dev/null +++ b/img/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=tex diff --git a/img/inc_nn_learning_curve.pdf 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zzvLg;3;g?hAO!!N{}5n0{YQR+D9D`u#WNBKW|;rvxjGwL*_u0JKTob;ZviYl5D?_u oXgWARwhf!svbt&xj00paTwINvU9si@31)wOB34#eH94aH4}K^cWB>pF literal 0 HcmV?d00001 diff --git a/thesis.tex b/thesis.tex index 9b5232a..872b9f2 100644 --- a/thesis.tex +++ b/thesis.tex @@ -1,4 +1,4 @@ -\documentclass[10pt, aspectratio=169]{beamer} +\documentclass[10pt, aspectratio=169, compress]{beamer} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} @@ -119,30 +119,30 @@ \end{center} } -% \setbeamertemplate{footline}{% -% \usebeamerfont{footnote} -% \usebeamercolor{footnote} -% \hfill -% \insertframenumber{}~/~\inserttotalframenumber{} -% \hspace{1em} -% \vspace{1em} -% \par -% } +\setbeamertemplate{footline}{% + \usebeamerfont{footnote} + \usebeamercolor{footnote} + \hfill + \insertframenumber{}~/~\inserttotalframenumber{} + \hspace{1em} + \vspace{1em} + \par +} -% \AtBeginSection[] -% {% -% {% -% \setbeamertemplate{footline}{} -% \usebackgroundtemplate{% -% \transparent{0.1} -% \includegraphics[width=\paperwidth]{img/torino.png} -% } -% \addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{} -% \begin{frame}[noframenumbering]{\contentsname} -% \tableofcontents[currentsection] -% \end{frame} -% } -% } +\AtBeginSection[] +{% + {% + \setbeamertemplate{footline}{} + \usebackgroundtemplate{% + \transparent{0.1} + \includegraphics[width=\paperwidth]{img/torino.png} + } + \addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{} + \begin{frame}[noframenumbering]{\contentsname} + \tableofcontents[currentsection] + \end{frame} + } +} \begin{document} @@ -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 $\updelta_{\pm} = \upeta \pm i 0^+$. - \end{block} + \end{equationblock} \pause \begin{tikzpicture}[remember picture, overlay] - \draw[line width=4pt, red] (31em,6em) ellipse (0.8cm and 1.2cm); + \draw[line width=4pt, red] (31em,6em) ellipse (0.8cm and 1cm); \end{tikzpicture} \pause @@ -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}