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Published in Proceedings of Machine Learning Research, 4th Annual Conference on Learning for Dynamics and Control, Vol 168:1–11, 2022
Published in Proceedings of the 2nd Annual Workshop on Topology, Algebra, Geometry and Machine Learning, International Conference of Machine Learning, Honolulu, Hawaii, USA, 2023
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.