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 the reproducing kernel Hilbert spaces. 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 seven baseline methods on the 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.

翻译：本文提出平坦希尔伯特贝叶斯推断（FHBI），一种旨在增强贝叶斯推断泛化能力的算法。该方法采用迭代式两步流程，包含再生核希尔伯特空间内的对抗性函数扰动步骤与函数下降步骤。此方法得到了理论分析的支持，该分析将先前关于泛化能力的研究成果从有限维欧几里得空间推广至无限维函数空间。为评估FHBI的有效性，我们在VTAB-1K基准测试上对七种基线方法进行了全面比较，该基准涵盖不同领域、具有多样语义的19个数据集。实证结果表明，FHBI始终以显著优势超越所有基线方法，突显了其实际效能。