[2603.19486] Any-Subgroup Equivariant Networks via Symmetry Breaking

Computer Science > Machine Learning arXiv:2603.19486 (cs) [Submitted on 19 Mar 2026] Title:Any-Subgroup Equivariant Networks via Symmetry Breaking Authors:Abhinav Goel, Derek Lim, Hannah Lawrence, Stefanie Jegelka, Ningyuan Huang View a PDF of the paper titled Any-Subgroup Equivariant Networks via Symmetry Breaking, by Abhinav Goel and 4 other authors View PDF HTML (experimental) Abstract:The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for symmetries chosen a priori, and not applicable to datasets with other symmetries. This precludes the development of flexible, multi-modal foundation models capable of processing diverse data equivariantly. In this work, we build a single model -- the Any-Subgroup Equivariant Network (ASEN) -- that can be simultaneously equivariant to several groups, simply by modulating a certain auxiliary input feature. In particular, we start with a fully permutation-equivariant base model, and then obtain subgroup equivariance by using a symmetry-breaking input whose automorphism group is that subgroup. However, finding an input with the desired automorphism group is computationally hard. We overcome this by relaxing from exact to approximate symmetry breaking, leveraging the notion of 2-closure to derive fast algorithms. Theoretically, we show that our subgroup-equivariant...