mlsanityData to 14 Oct 2026

Statistical Learning Guarantees for Group-Invariant Barron Functions

arXiv 2509.23474 ↗First posted 27 Sep 2025cs.LG math.ST stat.MLcited by 1

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Abstract (arXiv)

We investigate the generalization error of group-invariant neural networks within the Barron framework. Our analysis shows that incorporating group-invariant structures introduces a group-dependent factor δG,Gamma,σ ≤ 1 into the approximation rate. When this factor is small, group invariance yields substantial improvements in approximation accuracy. On the estimation side, we establish that the Rademacher complexity of the group-invariant class is no larger than that of the non-invariant counterpart, implying that the estimation error remains unaffected by the incorporation of symmetry. Consequently, the generalization error can improve significantly when learning functions with inherent group symmetries. We further provide illustrative examples demonstrating both favorable cases, where δG,Gamma,σ≈ |G|-1, and unfavorable ones, where δG,Gamma,σ≈ 1. Overall, our results offer a rigorous theoretical foundation showing that encoding group-invariant structures in neural networks leads to clear statistical advantages for symmetric target functions.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 31 of its 49 references that are in the map. First posted on arXiv 27 Sep 2025.

Builds on

31 of 49 references.

References · 31

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19 more
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Citing papers per year: 2025: 1.

1 paper.

  1. 2025On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functionscited by 0