Quantitative Approximation Rates for Group Equivariant Learning

ArXi:2602.20370v2 Announce Type: replace The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitative approximation rates for ReLU networks on the class of $\alpha$-H\"older functions $f: [0,1]^N \to \mathbb{R}$. The goal of this paper is to provide similar quantitative approximation results in the context of group equivariant learning, where the learned $\alpha$-H\"older function is known to obey certain group symmetries.