English

Improving Generalization with Flat Hilbert Bayesian Inference

Machine Learning 2025-06-10 v2 Machine Learning

Abstract

We introduce Flat Hilbert Bayesian Inference (FHBI), an algorithm designed to enhance generalization in Bayesian inference. Our approach involves an iterative two-step procedure with an adversarial functional perturbation step and a functional descent step within a reproducing kernel Hilbert space. This methodology is supported by a theoretical analysis that extends previous findings on generalization ability from finite-dimensional Euclidean spaces to infinite-dimensional functional spaces. To evaluate the effectiveness of FHBI, we conduct comprehensive comparisons against nine baseline methods on the \texttt{VTAB-1K} benchmark, which encompasses 19 diverse datasets across various domains with diverse semantics. Empirical results demonstrate that FHBI consistently outperforms the baselines by notable margins, highlighting its practical efficacy.

Keywords

Cite

@article{arxiv.2410.04196,
  title  = {Improving Generalization with Flat Hilbert Bayesian Inference},
  author = {Tuan Truong and Quyen Tran and Quan Pham-Ngoc and Nhat Ho and Dinh Phung and Trung Le},
  journal= {arXiv preprint arXiv:2410.04196},
  year   = {2025}
}

Comments

Accepted (ICML 2025)

R2 v1 2026-06-28T19:09:48.735Z