Optimal Symmetries in Binary Classification
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Abstract (arXiv)
We develop a theoretical foundation for designing group-equivariant neural networks that align the choice of symmetries with the underlying probability distributions of the data. Utilising the general structure of fibre decompositions on the domain under group equivariant maps and its relation to that of the likelihood ratio, we present a theoretical framework for identifying group actions that maintain optimal classification performance via the Neyman-Pearson lemma. This provides a unified methodology for improving classification accuracy especially in fundamental applications where one has knowledge of the inherent symmetries of the distributions and how they are broken by measurement. As an application to jet classification at the Large Hadron Collider, we find that there can be performance gains when one utilises smaller permutation symmetries within the constituents. This work offers insights and practical guidelines for constructing more effective group equivariant architectures in diverse machine-learning contexts.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 26 of its 41 references that are in the map. First posted on arXiv 16 Aug 2024.
Builds on
26 of 41 references.
References · 26
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14 more
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- 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
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