Computer Science > Machine Learning
arXiv:2603.08758 (cs)
[Submitted on 8 Mar 2026]
Title:Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields
View a PDF of the paper titled Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields, by Alejandro Garc\'ia-Castellanos and 4 other authors
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Abstract:Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts transitively on a space $M$, any $G$-invariant function on a product space $X \times M$ can be reduced to an invariant of the isotropy subgroup $H$ of $M$ acting on $X$ alone. Our approach establishes an explicit orbit equivalence $(X \times M)/G \cong X/H$, yielding a principled reduction that preserves expressivity. We apply this characterization to Equivariant Neural Fields, extending them to arbitrary group actions and homogeneous conditioning spaces, and thereby removing the major structural constraints imposed by existing methods.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2603.08758 [cs.LG] |
| (or arXiv:2603.08758v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.08758
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arXiv-issued DOI via DataCite
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Submission history
From: Alejandro García-Castellanos [view email][v1] Sun, 8 Mar 2026 10:41:23 UTC (2,337 KB)
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View a PDF of the paper titled Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields, by Alejandro Garc\'ia-Castellanos and 4 other authors
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