Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or by Stone--Weierstrass-type density; these prove that approximants exist but say little about how the parameters depend on the target. We take a constructive route. We extend the ridgelet transform, an integral transform related to the Fourier, Radon, and wavelet transforms, to continuous maps on a separable infinite-dimensional Hilbert space, replacing the Lebesgue measure that is unavailable in infinite dimensions by Gaussian weights with a homogeneous mixture on the direction space. The resulting transform ha...
| Authors | Sho Sonoda, Luca Galimberti, Yuanchao Xu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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