MatrixNet: Learning over symmetry groups using learned group representations
This work addresses the need for more flexible and efficient symmetry handling in ML applications like robotics and protein modeling, though it appears incremental as it builds on existing equivariant network concepts.
The authors tackled the problem of incorporating symmetry transformations in machine learning tasks by proposing MatrixNet, a neural network that learns matrix representations of group elements instead of using predefined ones, achieving higher sample efficiency and generalization over baselines in prediction tasks for finite groups and the Artin braid group, including generalization to longer word lengths.
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.