{"ID":2854215,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15814","arxiv_id":"2510.15814","title":"On Universality of Deep Equivariant Networks","abstract":"Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional hidden spaces, or they target specialized architectures, often confined to the invariant setting. This work develops a more general account. For invariant networks, we establish a universality theorem under separation constraints, showing that the addition of a fully connected readout layer secures approximation within the class of separation-constrained continuous functions. For equivariant networks, where results are even scarcer, we demonstrate that standard separability notions are inadequate and introduce the sharper criterion of $\\textit{entry-wise separability}$. We show that with sufficient depth or with the addition of appropriate readout layers, equivariant networks attain universality within the entry-wise separable regime. Together with prior results showing the failure of universality for shallow models, our findings identify depth and readout layers as a decisive mechanism for universality, additionally offering a unified perspective that subsumes and extends earlier specialized results.","short_abstract":"Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional hidden spaces, or they target specialized architectures, often confined to the...","url_abs":"https://arxiv.org/abs/2510.15814","url_pdf":"https://arxiv.org/pdf/2510.15814v1","authors":"[\"Marco Pacini\",\"Mircea Petrache\",\"Bruno Lepri\",\"Shubhendu Trivedi\",\"Robin Walters\"]","published":"2025-10-17T16:51:31Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}