Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency
This work addresses the challenge of costly or approximate equivariance methods in machine learning, offering a more efficient and exact solution for encoding symmetries, though it is incremental in improving existing frame averaging techniques.
The paper tackles the problem of achieving equivariance in machine learning systems by proposing Minimal Frame Averaging (MFA), a framework for constructing provably minimal frames that are exactly equivariant, which extends to more groups like the Lorentz and unitary groups and demonstrates efficiency across tasks such as n-body simulation and top tagging.
We consider achieving equivariance in machine learning systems via frame averaging. Current frame averaging methods involve a costly sum over large frames or rely on sampling-based approaches that only yield approximate equivariance. Here, we propose Minimal Frame Averaging (MFA), a mathematical framework for constructing provably minimal frames that are exactly equivariant. The general foundations of MFA also allow us to extend frame averaging to more groups than previously considered, including the Lorentz group for describing symmetries in space-time, and the unitary group for complex-valued domains. Results demonstrate the efficiency and effectiveness of encoding symmetries via MFA across a diverse range of tasks, including $n$-body simulation, top tagging in collider physics, and relaxed energy prediction. Our code is available at https://github.com/divelab/MFA.