Author

Sho Sonoda

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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

#machine learning Preprint May 2025

Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning

The message is that the statistical cost of depth is the metric entropy of the set $B(k,F)$ of compositions, and it separates the models whose estimation error is independent of the depth from those whose estimation error grows with it.

Sho Sonoda, Yuka Hashimoto, Isao Ishikawa et al. · 0 citations