Worst-Case Optimal $\sqrt{\epsilon}$-Rate Stability of KL Divergence under Perturbations of Gaussian Distributions

arXiv:2604.11026v4 Announce Type: replace-cross Abstract: We establish a stability bound for the Kullback-Leibler (KL) divergence when its Gaussian reference distribution is perturbed. Existing relaxed triangle inequalities of KL divergence between Gaussian distributions require all three distributions to be Gaussian, which limits their use in applications such as out-of-distribution detection with flow-based generative models. Let $\mathcal{N}_1$ and $\mathcal{N}_2$ be $d$-dimensional Gaussian distributions, and let $P$ be any $d$-dimensional distribution satisfying $\mathbb{E}_P[\|X\|^2]<\in

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