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equivariant-convolutions

This repo contains the code to replicate the experiments of our CVPR2022 paper Enabling Equivariance for Arbitrary Lie Groups. In particular:

lie.py contains the code to establish a LieGroup class, which corresponds to either the affine or homography groups. A LieGroup class instantiates the Lie algebra basis described in the Preliminaries section of the paper, with corresponding basis of the adjoint representation, as well as functions to compute the exponential and action of a Lie algebra vector on two-dimensional Euclidean space.
sampling.py contains the code used to generate samples in parallel from right Haar measure given a LieGroup, as described in Section 4.2 of the paper.
layers.py contains the code used for the Lie group convolutional layers described in Sections 4.1 and 4.2 of the paper.
data.py contains the code we used to create PyTorch datasets from the homNIST and affNIST .mat files.
experiment.py is the code to train a G-equivariant convolutional model on (padded) MNIST, to then test on GNIST (where G denotes either the affine or homography group).
experiment_e2.py is the code we used to benchmark the E2SFCNN E(2)-equivariant convolutional model of General $E(2)$-Equivariant Steerable CNNs on affNIST and homNIST after training on (padded) MNIST. Running this file requires the e2sfcnn.py file, as well as the e2cnn library. The model is trained with the recommended hyperparameters.
create_homNIST.py is the code we used to generate the homNIST test set.

To replicate our experiments using the experiment.py file:

From this link, download and extract into local folder /data the files: training.mat.zip as training.mat, and test.mat.zip as test.mat. The files training.mat and test.mat contain the black-padded MNIST training and test sets respectively.
From this link, download and extract into local folder /data the file test.mat.zip as affNIST_test.mat. The file affNIST_test.mat contains the affNIST test set.
From this link, download the homNIST.mat file. It contains the homNIST test set.

The experiment consists of training a model on (padded) MNIST, and then testing on either affNIST or homNIST. To run the former, in experiment.py simply set group = 'affine'; for the latter set group = 'homography'.