Author

Luca Galimberti

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Preprint Oct 2026

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 ta...

Sho Sonoda, Luca Galimberti, Yuan-Chao Xu et al. · 0 citations

Preprint Aug 2026

$L^p$ approximation results for infinite dimensional Neural Networks

A global universal approximation theorem in the topology of L^p(\mu) is shown, where any function $f:\mathfrak X\to \mathbb R$ in $L^p(\mu)$ can be approximated to any degree of accuracy by suitable infinite dimensional architectures.

Luca Galimberti · 0 citations