arXiv：cs.LG· Chenguang Duan, Johannes Hertrich, Gabriele Steidl·· 4 小时前AI 评分27
基于 Wasserstein–Fisher–Rao JKO 方案的加权归一化流神经采样
Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme
AI 导读
研究者提出一种从非归一化 Boltzmann 密度中采样的神经算法，基于 Wasserstein–Fisher–Rao 几何下 KL 散度的 JKO 方案。理论证明显示，任意固定步长下精确 WFR JKO 迭代随迭代次数增加以指数速度收敛到目标分布，且无需 log-concavity 或对数 Sobolev 不等式等结构假设。
正文
Abstract:We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kinderlehrer--Otto scheme for the Kullback--Leibler divergence in the Wasserstein--Fisher--Rao geometry (WFR JKO scheme). Our contributions are twofold. First, we prove that, for any fixed step size, the exact WFR JKO iterates converge exponentially fast to the target as the number of iterations tends to infinity. Notably, this result requires no structural assumptions on the target, such as log-concavity or a logarithmic Sobolev inequality. Second, we develop a neural implementation of the WFR JKO scheme that parametrizes its transport and reaction components using reweighted normalizing flows. Numerical experiments on challenging multimodal targets demonstrate the promising performance of the proposed method.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.10278 [math.NA] |
| (or arXiv:2610.10278v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10278 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Chenguang Duan [view email]
[v1]
Wed, 7 Oct 2026 15:44:29 UTC (5,025 KB)
来源：arXiv：cs.LG · arxiv.org