arXiv:2604.23765v3 Announce Type: replace Abstract: We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-affine functions are needed, in addition to affine ones, to ensure universality? We show that a single one suffices. More precisely, we prove that deep KANs in which all edge functions are either affine or equal to a fixed continuous function $\sigma$ are dense in $C(K)$ for every compact set $K\subset\mathbb{R}^n$ if and only if $\sigma$ is non-
Source: arXiv cs.LG — read the full report at the original publisher.