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Learning reversible symplectic dynamics

Published in Proceedings of Machine Learning Research, 4th Annual Conference on Learning for Dynamics and Control, Vol 168:1–11, 2022

Learning Lie Group Symmetry Transformations with Neural Networks

Published in Proceedings of the 2nd Annual Workshop on Topology, Algebra, Geometry and Machine Learning, International Conference of Machine Learning, Honolulu, Hawaii, USA, 2023

Efficient equivariant learning using algebraic invariant theory

Published in (pre-print coming soon to Arxiv, under review), 2024

Abstract: We exploit algebraic invariant theory to provide a natural structure to equivariant learning algorithms. In particular, this avoids repeated averaging over group orbits, which is a common inefficiency in existing equivariant learning implementations. Invariant theory provides a flexible and universal theoretical framework for equivariant learning without the need for architectures tailored to specific groups. We provide a Python package to calculate algebraic generators for equivariant functions, which underpin practical implementations of this framework, and demonstrate the efficiency of our approach in the context of equivariant neural fields.