Simple 2d example illustrating the role of the Jacobian determinant in the change of variables formula. Inspired by Ari Seff in https://youtu.be/i7LjDvsLWCg?t=250.
Edit and compile if you like:
% Simple 2d example illustrating the role of the Jacobian determinant in the change of variables formula. Inspired by Ari Seff in https://youtu.be/i7LjDvsLWCg?t=250.\documentclass[tikz]{standalone}\usepackage{mathtools}\usetikzlibrary{calc,positioning,shapes.geometric}\renewcommand\vec[1]{\boldsymbol{#1}}\begin{document}\begin{tikzpicture}[thick, node distance=15mm,set/.style={draw, diamond, text width=8mm, align=center},op/.style={draw, circle, text width=5mm, align=center, fill=orange!40},]\node[set, fill=blue!20] (z1) {$\vec z_{1:d}$};\node[op, right=of z1] (eq) {\raisebox{-1ex}=};\node[set, right=of eq, fill=blue!20] (x1) {$\vec x_{1:d}$};\draw[->] (z1) edge (eq) (eq) edge (x1);\node[set, below=1 of z1, fill=green!30] (z2) {$\mathclap{\vec z_{d+1:D}}$};\node[op, right=of z2] (g) {$g$};\node[below=1em of g] (forward) {forward pass};\node[set, right=of g, fill=yellow!40] (x2) {$\mathclap{\vec x_{d+1:D}}$};\draw[->] (z2) edge (g) (g) edge (x2);\node[op] (m) at ($(z1)!0.5!(g)$) {$m$};\draw[->] (z1) edge (m) (m) edge (g);\begin{scope}[xshift=9cm]\node[set, fill=blue!20] (z1) {$\vec z_{1:d}$};\node[op, right=of z1] (eq) {\raisebox{-1ex}=};\node[set, right=of eq, fill=blue!20] (x1) {$\vec x_{1:d}$};\draw[<-] (z1) edge (eq) (eq) edge (x1);\node[set, below=1 of z1, fill=green!30] (z2) {$\mathclap{\vec z_{d+1:D}}$};\node[op, right=of z2] (g) {$\mathclap{g^{-1}}$};\node[below=1em of g] (inverse) {inverse pass};
Click to download: nf-coupling-layer.tex
Open in Overleaf: nf-coupling-layer.tex
This file is available on tikz.netlify.app and on GitHub and is MIT licensed.
See more on the author page of Janosh Riebesell..