Optimal Stability of KL Divergence under Gaussian Perturbations
We study the problem of characterizing the stability of Kullback-Leibler (KL) divergence under Gaussian perturbations beyond Gaussian families. Existing relaxed triangle inequalities for KL divergence critically rely on the assumption that all involved distributions are Gaussian, which limits their applicability in modern applications such as out-of-distribution (OOD) detection with flow-based generative models. In this paper, we remove this restriction by establishing a sharp stability bound between an arbitrary distribution and Gaussian families under mild moment conditions. Specifically, let $P$ be a distribution with finite second moment, and let $\mathcal{N}_1$ and $\mathcal{N}_2$ be...
| Authors | Jialu Pan, Yufeng Zhang, Nan Hu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 16 April 2026 |
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