Year: 2026
Type: preprint
Abstract: We establish fractional-posterior contraction for shallow ReLU networks in Gaussian random-design regression with a $β$-Hölder target, using priors independent of the sample size and smoothness parameters. For any fixed design law $P_X$ on $[0,1]^d$, we obtain contraction in Rényi divergence and, after clipping posterior draws at a bound on the target range, in squared $\mathcal{L}^2(P_X)$ loss at rate $(\log n/n)^{2β/(2β+d)}$. This matches the classical Hölder minimax rate up to a logarithmic factor. These priors have random finite width and use width-dependent uniform or Gaussian weight distributions, or width-independent Student $t$ distributions, including Cauchy distributions.
Source: arXiv (Cornell University)
Institutions: Kyushu University, La Trobe University, Institute of Mathematics for Industry, Kyushu University, The University of Queensland, Institut polytechnique de Grenoble, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Jean Kuntzmann, Université Grenoble Alpes
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222980525