Code for running simulations for the paper

"Capacity of Group-invariant Linear Readouts from Equivariant Representations:
How Many Objects can be Linearly Classified Under All Possible Views?",

by Matthew Farrell, Blake Bordelon, Shubhendu Trivedi, and Cengiz Pehlevan.


Note that the file models/vgg.py contains copyright statements for
the original authors and modifiers of the script.

The python packages used for the simulations are contained in
environment.yml (this may include extra packages that are not necessary).


To generate Figure 1, run

python manifold_plots.py

This script is fairly simple and self-explanatory.


To generate Figures 2 and 3, run

python plot_cnn_capacity.py

At the bottom of the plot_cnn_capacity.py script, the plotting function
is called for different panels. Comment out lines to generate specific
figures. This script searches for a match with sets of parameters defined
in cnn_capacity_params.py. To modify parameters used for simulations,
modify the dictionaries in cnn_capacity_params.py or define your own
parameter sets. For a description of different parameter options,
see the docstring for the function cnn_capacity.get_capacity.

The simulations take quite a lot of time to run, even
with parallelization. Also a word of warning that
the simulations take a lot of memory (~100GB for n_cores=5).
To speed things up and reduce memory usage, one can set
perceptron_style=efficient or pool_over_group=True, or reduce n_dichotomies.
One can also choose to set seeds to seeds = [3] in plot_cnn_capacity.py.


cnn_capacity_utils.py contains utility functions. The VGG model can be found
in models/vgg.py. The direct sum (aka "grid cell") convolutional network model
can be found in models/gridcellconv.py The code for generating datasets can be
found in datasets.py.


The code was modified and superficially refactored in preparation for
releasing to the public. The simulations haven't been thoroughly tested after
this refactoring so it's not 100% guaranteed that the code is correct (though
it doesn't appear to throw errors). Fingers crossed that everything works
the way it should.

The development of this code was supported by the Harvard Data Science Initiative.