From 1950a500e9336d7f0b990ce8ddec615bad7692e1 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 13:50:17 +0100 Subject: [PATCH 01/13] Removed image files for which we now have tikz files. --- docs/src/images/adam_optimizer.png | Bin 58818 -> 0 bytes docs/src/images/general_optimization.pdf | Bin 59754 -> 0 bytes docs/src/images/general_optimization.png | Bin 42854 -> 0 bytes .../general_optimization_with_boundary.png | Bin 102813 -> 0 bytes docs/src/images/sympnet_pendulum_test.png | Bin 76278 -> 0 bytes 5 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 docs/src/images/adam_optimizer.png delete mode 100644 docs/src/images/general_optimization.pdf delete mode 100644 docs/src/images/general_optimization.png delete mode 100644 docs/src/images/general_optimization_with_boundary.png delete mode 100644 docs/src/images/sympnet_pendulum_test.png diff --git a/docs/src/images/adam_optimizer.png b/docs/src/images/adam_optimizer.png deleted file mode 100644 index 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z?<`*_G}&6ax!nMKH`3VLhU|_22 zgDVHc{rWN*5Qkz0M!XW#b#Gz z+96MTcclN1!GE zTHO4eSCiAzlxX3gE&xoGWO)6j+#nGWz!Y?71m_g+xS$pZ6UhO_;Xp;{r8|iopbGAM zx*tA3B@OaB?R+gL*akH#&^`k?OW~rVXyM>2APxDL4H$D(p-n)i2WV&{vt!}lH2OSx z0Oy~a525g{13;<|e3F2E5a8>9r{jAf24q<{Z040UH31Yc30!Vf)zl=!#lK1Z0M2(8 z`!geRa~hp^VqRVkKtiU+=*H^_gtL)!Zm=AIqzE`lC#0p_-<%pDARw4if#H5~iJ~U% z?0gBjx_B}&6BAW6GyoN6Z)b;kO;nW`gj1l)MN1peZw$&u_t9+OhIiRkGv)S;+D6Re z53B3IC%Lk+a(&$pIGh8HW?&rQ%O0|kNf7)eDg8HZ{-@BaC6L_mL5F+u`58)1c!~OH0cumoOXm*CHE)SMvC{BIx8L zMgdx5V6=>m0wFWt1`b}Nu{&Ujf^0NE6YK{1MF&fgub;ZHAU^=(pjk`DLJDw65D+SF no Date: Tue, 12 Dec 2023 13:59:54 +0100 Subject: [PATCH 03/13] Added the tikz for symplectic autoencoders. --- docs/src/tikz/Makefile | 2 + docs/src/tikz/symplectic_autoencoders.tex | 128 ++++++++++++++++++++++ 2 files changed, 130 insertions(+) create mode 100644 docs/src/tikz/symplectic_autoencoders.tex diff --git a/docs/src/tikz/Makefile b/docs/src/tikz/Makefile index 0c271f439..814cf0cef 100644 --- a/docs/src/tikz/Makefile +++ b/docs/src/tikz/Makefile @@ -7,6 +7,7 @@ pdf: xelatex -shell-escape sympnet_architecture xelatex -shell-escape structs_visualization xelatex -shell-escape logo + xelatex -shell-escape symplectic_autoencoders png: pdftocairo -png -r 150 -transp -singlefile adam_optimizer.pdf adam_optimizer @@ -17,6 +18,7 @@ png: pdftocairo -png -r 150 -transp -singlefile sympnet_architecture.pdf sympnet_architecture pdftocairo -png -r 150 -transp -singlefile structs_visualization.pdf structs_visualization pdftocairo -png -r 150 -transp -singlefile logo.pdf logo + pdftocairo -png -r 150 -transp -singlefile symplectic_autoencoders.pdf symplectic_autoencoders logo: xelatex -shell-escape logo_with_name diff --git a/docs/src/tikz/symplectic_autoencoders.tex b/docs/src/tikz/symplectic_autoencoders.tex new file mode 100644 index 000000000..4197d996c --- /dev/null +++ b/docs/src/tikz/symplectic_autoencoders.tex @@ -0,0 +1,128 @@ +\documentclass[tikz]{standalone} + +\definecolor{morange}{RGB}{255,127,14} +\definecolor{mblue}{RGB}{31,119,180} +\definecolor{mred}{RGB}{214,39,40} +\definecolor{mpurple}{RGB}{148,103,189} +\definecolor{mgreen}{RGB}{44,160,44} + +\newcommand*{\colIn}{morange}% +\newcommand*{\colEnc}{mpurple}% +\newcommand*{\colIntr}{mred}% +\newcommand*{\colDec}{mpurple}% +\newcommand*{\colOut}{mgreen}% +\newcommand*{\colSym}{mblue}% + +\newcommand*{\arrowLength}{1}% + +\newcommand*{\xMin}{1}% +\newcommand*{\xMax}{8}% +\newcommand*{\xMaxEnc}{4}% +\newcommand*{\xMaxIntr}{2}% +\newcommand*{\xMaxDec}{4}% + +\newcommand*{\xin}{0}% +\newcommand*{\xinsym}{\xin+\arrowLength+2}% +\newcommand*{\xenc}{\xinsym+\arrowLength+2}% +\newcommand*{\xencsym}{\xenc+\arrowLength+2}% +\newcommand*{\xintr}{\xencsym+\arrowLength+2}% +\newcommand*{\xdecsym}{\xintr+\arrowLength+2}% +\newcommand*{\xdec}{\xdecsym+\arrowLength+2}% +\newcommand*{\xoutsym}{\xdec+\arrowLength+2}% +\newcommand*{\xout}{\xoutsym+\arrowLength+2}% + + +\begin{document} +\begin{tikzpicture}[scale=0.5] + + \begin{scope} + \foreach \i in {\xMin,...,\xMax} { + \draw [rectangle, draw, fill=\colIn] (\xin,\xMax/2-\i) rectangle (\xin+1,\xMax/2-\i+1) node [pos=.5] {$x_\i$}; + } + \end{scope} + + \path [draw,->] (\xin+1.5,0) -- (\xinsym-0.5,0) node [pos=0.5,above,align=left] {$\psi_1$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMax} { + \draw [rectangle, draw, fill=\colSym] (\xinsym,\xMax/2-\i) rectangle (\xinsym+1,\xMax/2-\i+1) node [pos=.5] {}; + } + \end{scope} + + \path [draw,->] (\xinsym+1.5,0) -- (\xenc-0.5,0) node [pos=0.5,above,align=left] {$A_1$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMaxEnc} { + \draw [rectangle, draw, fill=\colEnc] (\xenc,\xMaxEnc/2-\i) rectangle (\xenc+1,\xMaxEnc/2-\i+1) node {}; + } + \end{scope} + + \path [draw,->] (\xenc+1.5,0) -- (\xencsym-0.5,0) node [pos=0.5,above,align=left] {$\psi_2$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMaxEnc} { + \draw [rectangle, draw, fill=\colSym] (\xencsym,\xMaxEnc/2-\i) rectangle (\xencsym+1,\xMaxEnc/2-\i+1) node {}; + } + \end{scope} + + \path [draw,->] (\xencsym+1.5,0) -- (\xintr-0.5,0) node [pos=0.5,above,align=left] {$A_2$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMaxIntr} { + \draw [rectangle, draw, fill=\colIntr] (\xintr,\xMaxIntr/2-\i) rectangle (\xintr+1,\xMaxIntr/2-\i+1) node {}; + } + \end{scope} + + \path [draw,->] (\xintr+1.5,0) -- (\xdecsym-0.5,0) node [pos=0.5,above,align=left] {$A_3^+$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMaxEnc} { + \draw [rectangle, draw, fill=\colSym] (\xdecsym,\xMaxEnc/2-\i) rectangle (\xdecsym+1,\xMaxEnc/2-\i+1) node {}; + } + \end{scope} + + \path [draw,->] (\xdecsym+1.5,0) -- (\xdec-0.5,0) node [pos=0.5,above,align=left] {$\psi_3$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMaxDec} { + \draw [rectangle, draw, fill=\colDec] (\xdec,\xMaxDec/2-\i) rectangle (\xdec+1,\xMaxDec/2-\i+1) node {}; + } + \end{scope} + + \path [draw,->] (\xdec+1.5,0) -- (\xoutsym-0.5,0) node [pos=0.5,above,align=left] {$A_4^+$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMax} { + \draw [rectangle, draw, fill=\colSym] (\xoutsym,\xMax/2-\i) rectangle (\xoutsym+1,\xMax/2-\i+1) node [pos=.5] {}; + } + \end{scope} + + \path [draw,->] (\xoutsym+1.5,0) -- (\xout-0.5,0) node [pos=0.5,above,align=left] {$\psi_4$}; + + \begin{scope} + \foreach \i in {\xMin,...,\xMax} { + \draw [rectangle, draw, fill=\colOut] (\xout,\xMax/2-\i) rectangle (\xout+1,\xMax/2-\i+1) node [pos=.5] {$\tilde{x}_\i$}; + } + \end{scope} + + +% \node[rectangle,draw,fill=teal!,text width=.3cm] (11) at (0,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ \\ $x_5$ \\ $x_6$ \\ $x_7$ \\ $x_8$}; +% \node[rectangle,draw,fill=teal!,text width=.3cm] (12) at (1,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ \\ $x_5$ \\ $x_6$ \\ $x_7$ \\ $x_8$}; +% \node[rectangle,draw,fill=olive!,text width=.3cm] (21) at (2,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ }; +% \node[rectangle,draw,fill=olive!,text width=.3cm] (22) at (3,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ }; +% \node[rectangle,draw,fill=lightgray!,text width=.3cm] (3) at (4,0) {$x_1$ \\ $x_2$ }; +% \node[rectangle,draw,fill=olive!,text width=.3cm] (41) at (5,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ }; +% \node[rectangle,draw,fill=olive!,text width=.3cm] (42) at (6,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ }; +% \node[rectangle,draw,fill=teal!,text width=.3cm] (51) at (7,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ \\ $x_5$ \\ $x_6$ \\ $x_7$ \\ $x_8$}; +% \node[rectangle,draw,fill=teal!,text width=.3cm] (52) at (8,0) {$x_1$ \\ $x_2$ \\ $x_3$ \\ $x_4$ \\ $x_5$ \\ $x_6$ \\ $x_7$ \\ $x_8$}; +% \path[draw,->] (11.east) -- (12.west) node[pos=0.5,above,align=left] {$\psi_1$}; +% \path[draw,->] (21.east) -- (22.west) node[pos=0.5,above,align=left] {$\psi_2$}; +% \path[draw,->] (41.east) -- (42.west) node[pos=0.5,above,align=left] {$\psi_3$}; +% \path[draw,->] (51.east) -- (52.west) node[pos=0.5,above,align=left] {$\psi_4$}; +% \path[draw,->] (12.east) -- (21.west) node[pos=0.5,above,align=left] {$A_1$}; +% \path[draw,->] (22.east) -- (3.west) node[pos=0.5,above,align=left] 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z*ec5H4791DD5G?*iHbDt5jbtFU_m`&0ZhIa6E|IH^Eij$7VxA;AeF6dD-mI7?YK0> zk{lYow`ktAZSwT=Zqt*M6n+VTQO9u_`x`2LPyut><(plNc|S^M4u#(BC_ zjAQin!k_FOf#LRpPqw3Mo1p7_HNNEpT@=t%tADX$`6N)d<)~giqc9_S-I-!*Z-47658}3b4~4~>Qmyx!yWL9nD+hG&GZLxSx)E@c})r8%VQKY zwdZ@SVU|%{JlE9C0MPMrG2E)i&73byyKT(Ye9gSVhM7F9N+>rjP6MiYBddJH43Fs7 z4J%UrJ*@=@EX~}5+;v~6q)k&$fj2WWt#eog9MsE6zg=Q+-|FhJ)ET+$EyKgoWP8U! z7>)Wf@8FQ5+{?~)xq>|tg-e;R z?4_EuHmWmp|ysAJswC4%H6d z_u-fH8-#k1zmLc$svSUW(csb3yMRu9`>*8mFY#CJl>A!O;XVQp;fp0JHAI>JDm MpFBcHJb(Lt0SL1L`Tzg` From 60b97956df058eae5cdeefad604769c257c38cb6 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:03:39 +0100 Subject: [PATCH 05/13] Added mha tikz. --- docs/src/tikz/Makefile | 4 ++++ docs/src/tikz/mha.tex | 46 ++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 50 insertions(+) create mode 100644 docs/src/tikz/mha.tex diff --git a/docs/src/tikz/Makefile b/docs/src/tikz/Makefile index 814cf0cef..9da9a4fbd 100644 --- a/docs/src/tikz/Makefile +++ b/docs/src/tikz/Makefile @@ -8,6 +8,8 @@ pdf: xelatex -shell-escape structs_visualization xelatex -shell-escape logo xelatex -shell-escape symplectic_autoencoders + xelatex -shell-escape solution_manifold_2 + xelatex -shell-escape mha png: pdftocairo -png -r 150 -transp -singlefile adam_optimizer.pdf adam_optimizer @@ -19,6 +21,8 @@ png: pdftocairo -png -r 150 -transp -singlefile structs_visualization.pdf structs_visualization pdftocairo -png -r 150 -transp -singlefile logo.pdf logo pdftocairo -png -r 150 -transp -singlefile symplectic_autoencoders.pdf symplectic_autoencoders + pdftocairo -png -r 150 -transp -singlefile solution_manifold_2.pdf solution_manifold_2 + pdftocairo -png -r 150 -transp -singlefile mha.pdf mha logo: xelatex -shell-escape logo_with_name diff --git a/docs/src/tikz/mha.tex b/docs/src/tikz/mha.tex new file mode 100644 index 000000000..e32fb7b1a --- /dev/null +++ b/docs/src/tikz/mha.tex @@ -0,0 +1,46 @@ +% code taken from https://tex.stackexchange.com/questions/688104/how-could-i-create-these-figures-in-tikz (with modifications) +\documentclass[tikz]{standalone} + +\usepackage{xcolor} +\definecolor{morange}{RGB}{255,127,14} +\definecolor{mblue}{RGB}{31,119,180} +\definecolor{mred}{RGB}{214,39,40} +\definecolor{mpurple}{RGB}{148,103,189} +\definecolor{mgreen}{RGB}{44,160,44} + +\usepackage{tikz} +\usetikzlibrary{positioning} +\usetikzlibrary{calc} +\usetikzlibrary{fit} +\usetikzlibrary{shadows} +\usetikzlibrary{decorations} + +\begin{document} +\begin{tikzpicture}[module/.style={draw, very thick, rounded corners, minimum width=15ex}, + attmodule/.style={module, fill=morange!30}, + linear/.style={module, fill=mblue!30}, + concat/.style={module, fill=mpurple!30}, + arrow/.style={-stealth, thick, rounded corners}, +] +\node (input) {Input}; +\node[above of=input, linear, align=center, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_center) {Linear}; +\node[left of=linear_center, linear, align=center, xshift=-1.5cm, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_left) {Linear}; +\node[right of=linear_center, linear, align=center, xshift=1.5cm, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_right) {Linear}; +\node[above of=linear_center, attmodule, align=center, yshift=.5cm, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (sha) {Attention Mechanism}; +\node[above of=sha, concat, yshift=.4cm] (concat) {Concatenate}; +\node[above of=concat] (output) {Output}; + +% to have the shadows displayed in the final pdf +\node[right of=linear_right, xshift=.4cm] (right_of_linear_right) {}; + +\draw[arrow, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (input) -- (linear_left); +\draw[arrow, double copy shadow={opacity=.2, shadow yshift=1.7ex, shadow xshift=1.2ex}] (input) -- (linear_center); +\draw[arrow, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (input) -- (linear_right); +\draw[arrow, double copy shadow={opacity=.2, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_left) -- (sha.south west); +\draw[arrow, double copy shadow={opacity=.2, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_center) -- (sha.south); +\draw[arrow, double copy shadow={opacity=.5, shadow yshift=1.7ex, shadow xshift=1.2ex}] (linear_right) -- (sha.south east); +\draw[arrow, double copy shadow={opacity=.2, shadow yshift=1.7ex, shadow xshift=1.2ex}] (sha) -- (concat.south); +\draw[arrow] (concat) -- (output); + +\end{tikzpicture} +\end{document} \ No newline at end of file From 0e78a67fdb58ecb3d988d3a103c53925e5e3096a Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:03:51 +0100 Subject: [PATCH 06/13] Changed colours to Julia colours. --- docs/src/tikz/transformer_encoder.tex | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/docs/src/tikz/transformer_encoder.tex b/docs/src/tikz/transformer_encoder.tex index 9484e8d9b..22e8a386d 100644 --- a/docs/src/tikz/transformer_encoder.tex +++ b/docs/src/tikz/transformer_encoder.tex @@ -15,14 +15,18 @@ \tikzset{set/.style={draw,circle,inner sep=0pt,align=center}} +\definecolor{morange}{RGB}{255,127,14} +\definecolor{mblue}{RGB}{31,119,180} \definecolor{mred}{RGB}{214,39,40} +\definecolor{mpurple}{RGB}{148,103,189} \definecolor{mgreen}{RGB}{44,160,44} + \begin{document} \begin{tikzpicture}[module/.style={draw, very thick, rounded corners, minimum width=15ex}, - attmodule/.style={module, fill=orange!20}, - ffnnmodule/.style={module, fill=cyan!20}, - addmodule/.style={module, fill=yellow!20}, + attmodule/.style={module, fill=morange!30}, + ffnnmodule/.style={module, fill=mblue!30}, + addmodule/.style={module, fill=mpurple!30}, arrow/.style={-stealth, thick, rounded corners}, ] \node (input) {Input}; From a7913d8b2b596db8fbd153dec3dc7d27eb4cfad7 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:04:16 +0100 Subject: [PATCH 07/13] Added solution manifold tikz. --- docs/src/tikz/solution_manifold_2.tex | 50 +++++++++++++++++++++++++++ 1 file changed, 50 insertions(+) create mode 100644 docs/src/tikz/solution_manifold_2.tex diff --git a/docs/src/tikz/solution_manifold_2.tex b/docs/src/tikz/solution_manifold_2.tex new file mode 100644 index 000000000..98ebd9f85 --- /dev/null +++ b/docs/src/tikz/solution_manifold_2.tex @@ -0,0 +1,50 @@ +\documentclass[border = .2cm]{standalone} + +\usepackage{pgfplots} + +\pgfplotsset{compat = newest} + +\definecolor{mblue}{RGB}{66,164,233} + +\pgfplotsset{ + colormap={cmblue}{ + rgb255(0cm)=(132,233,233); + rgb255(1cm)=(66,164,233); + rgb255(2cm)=(132,233,233); + }, + colormap={whiteblack}{color=(black) color=(white)}, + tick label style={color=white}, +} + +\begin{document} + \begin{tikzpicture} + + \begin{axis}[ + view = {-25}{25}, + mesh/interior colormap name=cmblue, colormap name=whiteblack, + xmax = +3, + xmin = -3, + ymax = +3, + ymin = -3, + zmax = +10, + zmin = -10, + xtick = {-3,-2,-1,0,1,2,3}, + ytick = {-3,-2,-1,0,1,2,3}, + ztick = {-10,-5,0,5,10}, + grid, + 3d box = complete* + ] + + \addplot3 [ + domain = -3:3, + domain y = -3:3, + samples = 50, + samples y = 50, + surf, + shader = flat + ] {x^2 - y^2}; + +\end{axis} + +\end{tikzpicture} +\end{document} From a9d18a2cd695993731a2b609638dd9a280a6f32d Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:05:25 +0100 Subject: [PATCH 08/13] Deleted remaining image files. --- docs/src/images/mha.png | Bin 73496 -> 0 bytes docs/src/images/solution_manifold_2.png | Bin 259675 -> 0 bytes 2 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 docs/src/images/mha.png delete mode 100644 docs/src/images/solution_manifold_2.png diff --git a/docs/src/images/mha.png b/docs/src/images/mha.png deleted file mode 100644 index 40628aa5f41d686a4d3d17b027a47a4399220421..0000000000000000000000000000000000000000 GIT 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From 4bc6e3b103833893db8d6bcd45e880b21a7559c9 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:13:19 +0100 Subject: [PATCH 09/13] Renamed file. (it's only one autoencoder). --- .../{symplectic_autoencoders.tex => symplectic_autoencoder.tex} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/src/tikz/{symplectic_autoencoders.tex => symplectic_autoencoder.tex} (100%) diff --git a/docs/src/tikz/symplectic_autoencoders.tex b/docs/src/tikz/symplectic_autoencoder.tex similarity index 100% rename from docs/src/tikz/symplectic_autoencoders.tex rename to docs/src/tikz/symplectic_autoencoder.tex From 81db86732ef0145478a7b9b30c261952e3f030dc Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:15:58 +0100 Subject: [PATCH 10/13] Changed the file paths to the tikz folder (there is no image folder anymore). --- docs/src/layers/multihead_attention_layer.md | 2 +- docs/src/reduced_order_modeling/autoencoder.md | 2 +- docs/src/reduced_order_modeling/symplectic_autoencoder.md | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/src/layers/multihead_attention_layer.md b/docs/src/layers/multihead_attention_layer.md index c97193316..c11aede3b 100644 --- a/docs/src/layers/multihead_attention_layer.md +++ b/docs/src/layers/multihead_attention_layer.md @@ -19,7 +19,7 @@ where $n$ is the dimension of the vectors in $V$, $Q$ and $K$. The softmax activ The transformer contains a **self-attention mechanism**, i.e. takes an input $X$ and then transforms it linearly to $V$, $Q$ and $K$, i.e. $V = P^VX$, $Q = P^QX$ and $K = P^KX$. What distinguishes the multihead attention layer from the singlehead attention layer, is that there is not just one $P^V$, $P^Q$ and $P^K$, but there are several: one for each **head** of the multihead attention layer. After computing the individual values, queries and vectors, and after applying the softmax, the outputs are then concatenated together in order to obtain again an array that is of the same size as the input array: -![](../images/mha.png) +![](../tikz/mha.png) Here the various $P$ matrices can be interpreted as being projections onto lower-dimensional subspaces, hence the designation by the letter $P$. Because of this interpretation as projection matrices onto smaller spaces that should **capture features in the input data** it makes sense to constrain these elements to be part of the Stiefel manifold. diff --git a/docs/src/reduced_order_modeling/autoencoder.md b/docs/src/reduced_order_modeling/autoencoder.md index 50da204dc..13dedc3eb 100644 --- a/docs/src/reduced_order_modeling/autoencoder.md +++ b/docs/src/reduced_order_modeling/autoencoder.md @@ -14,7 +14,7 @@ To any parametric PDE we associate a **solution manifold**: \mathcal{M} = \{z(\mu):F(z(\mu);\mu)=0, \mu\in\mathbb{P}\}. ``` -![](../images/solution_manifold_2.png) +![](../tikz/solution_manifold_2.png) In the image above a 2-dimensional solution manifold is visualized as a sub-manifold in 3-dimensional space. In general the embedding space is an infinite-dimensional function space. diff --git a/docs/src/reduced_order_modeling/symplectic_autoencoder.md b/docs/src/reduced_order_modeling/symplectic_autoencoder.md index 2f35fb92d..5ee114044 100644 --- a/docs/src/reduced_order_modeling/symplectic_autoencoder.md +++ b/docs/src/reduced_order_modeling/symplectic_autoencoder.md @@ -77,7 +77,7 @@ PSD suffers from the similar shortcomings as regular POD: it is a linear map and In order to overcome this difficulty we use neural networks, more specifically [SympNets](../architectures/sympnet.md), together with cotangent lift-like matrices. The resulting architecture, symplectic autoencoders, are demonstrated in the following image: -![](../images/symplectic_autoencoder.png) +![](../tikz/symplectic_autoencoder.png) So we alternate between SympNet and PSD layers. Because all the PSD layers are based on matrices $\Phi\in{}St(n,N)$ we have to [optimize on the Stiefel manifold](../Optimizer.md). From 8fd4ad7897291b4558985fcfd8c161c3fa265e17 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:17:25 +0100 Subject: [PATCH 11/13] Added new tikz pictures and the option -p for the mkdir command (assets directory). --- docs/src/tikz/Makefile | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/src/tikz/Makefile b/docs/src/tikz/Makefile index 9da9a4fbd..3a889ec42 100644 --- a/docs/src/tikz/Makefile +++ b/docs/src/tikz/Makefile @@ -7,7 +7,7 @@ pdf: xelatex -shell-escape sympnet_architecture xelatex -shell-escape structs_visualization xelatex -shell-escape logo - xelatex -shell-escape symplectic_autoencoders + xelatex -shell-escape symplectic_autoencoder xelatex -shell-escape solution_manifold_2 xelatex -shell-escape mha @@ -20,7 +20,7 @@ png: pdftocairo -png -r 150 -transp -singlefile sympnet_architecture.pdf sympnet_architecture pdftocairo -png -r 150 -transp -singlefile structs_visualization.pdf structs_visualization pdftocairo -png -r 150 -transp -singlefile logo.pdf logo - pdftocairo -png -r 150 -transp -singlefile symplectic_autoencoders.pdf symplectic_autoencoders + pdftocairo -png -r 150 -transp -singlefile symplectic_autoencoder.pdf symplectic_autoencoder pdftocairo -png -r 150 -transp -singlefile solution_manifold_2.pdf solution_manifold_2 pdftocairo -png -r 150 -transp -singlefile mha.pdf mha @@ -31,6 +31,7 @@ logo: pdftocairo -png -r 500 -transp -singlefile logo_with_name.pdf logo_with_name pdftocairo -png -r 500 -transp -singlefile logo_with_name_dark.pdf logo_with_name_dark + mkdir -p ../assets cp logo_with_name.png ../assets/logo.png cp logo_with_name_dark.png ../assets/logo-dark.png @@ -46,5 +47,6 @@ empty: clean rm -f *.png rm -f *.svg rm -f ../assets/*.png + rm -f ../assets all: pdf png logo clean \ No newline at end of file From ec3d0c1bf483449cd9febe223bafe0154df44090 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:31:01 +0100 Subject: [PATCH 12/13] Added additional comments and files to the index. --- docs/src/index.md | 37 +++++++++++++++++++++++++++++++++++++ 1 file changed, 37 insertions(+) diff --git a/docs/src/index.md b/docs/src/index.md index 8eefe9299..afc9dd294 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -15,6 +15,8 @@ GeometricMachineLearning.jl implements various scientific machine learning model ## Architectures +There are several architectures tailored towards problems in scientific machine learning implemented in `GeometricMachineLearning`. + ```@contents Pages = [ "architectures/sympnet.md", @@ -23,9 +25,44 @@ Pages = [ ## Manifolds +`GeometricMachineLearning` supports putting neural network weights on manifolds. These include: + ```@contents Pages = [ "manifolds/grassmann_manifold.md", "manifolds/stiefel_manifold.md", ] ``` + +## Special Neural Network Layer + +Many layers have been adapted in order to be used for problems in scientific machine learning. Including: + +```@contents +Pages = [ + "layers/attention_layer.md", +] +``` + +## Tutorials + +Tutorials for using `GeometricMachineLearning` are: + +```@contents +Pages = [ + "tutorials/sympnet_tutorial.md", + "tutorials/mnist_tutorial.md", +] +``` + +## Reduced Order Modeling + +A short description of the key concepts in **reduced order modeling** (where `GeometricMachineLearning` can be used) are in: + +```@contents +Pages = [ + "reduced_order_modeling/autoencoder.md", + "reduced_order_modeling/symplectic_autoencoder.md", + "reduced_order_modeling/kolmogorov_n_width.md", +] +``` \ No newline at end of file From 550749826acd30ce811507c40a4b822f09fde3a6 Mon Sep 17 00:00:00 2001 From: benedict-96 Date: Tue, 12 Dec 2023 16:34:33 +0100 Subject: [PATCH 13/13] Removed comment. (This is not true anymore) --- docs/src/tikz/mha.tex | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/src/tikz/mha.tex b/docs/src/tikz/mha.tex index e32fb7b1a..18f19c049 100644 --- a/docs/src/tikz/mha.tex +++ b/docs/src/tikz/mha.tex @@ -1,4 +1,3 @@ -% code taken from https://tex.stackexchange.com/questions/688104/how-could-i-create-these-figures-in-tikz (with modifications) \documentclass[tikz]{standalone} \usepackage{xcolor}