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Efficient Learning and Symmetry Discovery under Exact Invariances

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

Learning with group invariances is central to many scientific and geometric learning problems, yet its computational foundations remain poorly understood. Even for classical supervised regression settings, it has been unclear whether one can efficiently compute a regression function that is exactly invariant to a given group action. Recent work showed that exact invariance can be enforced in polynomial time when the underlying group is finite and known, but left open the cases of infinite groups and unknown symmetries. In this paper, we resolve both challenges. First, we present the first poly

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