Deep KANs with edge functions from a finite affine family plus one fixed non-affine continuous function σ are dense in C(K) for compact K precisely when σ is non-affine.
de Boor, A practical guide to splines, Revised Edition
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Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks
Deep KANs with edge functions from a finite affine family plus one fixed non-affine continuous function σ are dense in C(K) for compact K precisely when σ is non-affine.