Author

Yuan-Chao Xu

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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 Oct 2026

Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements

This work introduces an observation-corrected Koopman framework for accelerating frozen diffusion models, and identifies finite-dimensional, time-dependent Koopman approximations that jointly describe the increments of shallow and deep network features.

Han-Ru Bai, Yuan-Chao Xu, Feng-Yi Li · 0 citations

Preprint Sep 2026

Backward Kolmogorov Transport: Sampling Invariant Laws of Reversible Diffusions from Trajectory Data

We consider a reversible diffusion with unknown drift, observed through trajectories, and construct samplers of its invariant law. The trajectories contain samples of this law, but a sampler built from them by density or score estimation inherits the errors of these estimates, in particular on the barriers between meta...

Yuan-Chao Xu, Isao Ishikawa · 0 citations