@inproceedings{
laird2024matrixnet,
title={MatrixNet: Learning over symmetry groups using learned group representations},
author={Lucas Laird and Circe Hsu and Asilata Bapat and Robin Walters},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=b8jwgZrAXG}
}
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use known
symmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set. Our code is available at https://github.com/lucas-laird/MatrixNet.
MatrixNet: Learning over symmetry groups using learned group representations
Lucas Laird Circe Hsu Asilata Bapat Robin Walters