For an interactive version of the below see https://www.dtubbenhauer.com/pl-reps/site/index.html.
I collected Mathematica code relevant for the paper Equivariant neural networks and piecewise linear representation theory https://arxiv.org/abs/2408.00949 on this page.
The code is in .n files that can be downloaded from this site and you can run it with Mathematica.
An Erratum for the paper Equivariant neural networks and piecewise linear representation theory can be found at the bottom of the page.
If you find any errors in the paper Equivariant neural networks and piecewise linear representation theory please email me:
You can also email Joel Gibson and Geordie Williamson. Same goes for any errors related to this page.
Also, let me know if there are any questions!
The code is hopefully pretty straightforward, so let me only comment on the various pieces briefly.
SizeTable := {0.07, 0.2, 0.2, 0.3, 0.3, 0.3, 0.4, 0.4, 0.4, 0.4, 0.5,
0.5, 0.6, 0.7, 0.8, 0.8, 0.9, 0.9, 1.1, 1};
is for scaling the output, and can be changed if needed.
The graphs for ReLU and Abs are the created using
AdMatrix[n_] :=
Table[If[i == j, 1,
If[Divisible[OrderActionP[n, i - 1], OrderAction[n, j - 1]], 1,
0]], {i, 1, Length[Division[n]]}, {j, 1, Length[Division[n]]}];
AdMatrixAbs[n_] :=
Table[If[Divisible[OrderActionP[n, i - 1], OrderAction[n, j - 1]],
1, 0], {i, 1, Length[Division[n]]}, {j, 1, Length[Division[n]]}];
The rest of the code is for visualiztion purpuses only.
For example, here is the cyclic group of order eight:
)
The file cyclic-maps.nb contains the plots of maps from 2d representations to the trivial representation of the cyclic group. The maps have been precomputed with coordinates stored in
XX
The maps are then animated (the style can be easily changed) using, for example
Animate[{Plot3D[PlotFunction[n, a, b], {a, -3, 3}, {b, -3, 3},
PlotPoints -> 45, ImageSize -> 400, MaxRecursion -> 0],
ContourPlot[PlotFunction[n, a, b], {a, -3, 3}, {b, -3, 3},
PlotPoints -> 40, ImageSize -> 400, MaxRecursion -> 0]}, {n, 1, 8,
1}, LabelStyle -> {20}, DefaultDuration -> 70]
One gets the following pictures:
The actual calculations are contained in the file cyclic.nb.
The file is badly documented, sorry for that. Feel free to shot me an email fi you need details.
Empty so far.