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Existing methods learn an equivariant action on the latent space, or design architectures that are equivariant by construction. These approaches often deliver strong empirical results but can involve architecture-specific constraints, large parameter counts, and high computational cost. We challenge the paradigm of complex equivariant architectures with a parameter-free approach grounded in group representation theory. We prove that for an equivariant encoder over a finite group, the latent space must almost surely contain one copy of its regular representation for each linearly independent data orbit, which we explore with a number of empirical studies. Leveraging this foundational algebraic insight, we impose the group's regular representation as an inductive bias via an auxiliary loss, adding ","title":"Algebraic Priors for Approximately Equivariant Networks","url":"https://arxiv.org/abs/2506.08244","vendor":"arxiv_cs_ai"},"summary":"arXiv:2506.08244v2 Announce Type: replace-cross \nAbstract: Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are equivariant by construction. These approaches often deliver strong empirical results but can involve architecture-specific constraints, large parameter counts, and high computational cost. We challenge the paradigm of complex equivariant architectures with a parameter-free approach grounded in group representation theory. 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