arXiv：cs.LG· Xavier Aramayo-Carrasco, Petr Mokrov, Alexander Korotin·· 3 小时前AI 评分36
ManifoldLightOT：在黎曼流形上学习轻量熵最优传输耦合
Light Entropic Optimal Transport on Riemannian Manifolds
AI 导读
研究者提出 ManifoldLightOT，一种直接在常见流形上学习核诱导熵最优传输（EOT）耦合的轻量方法。该方法为球面、环面、SO(3) 和 SE(3) 构建几何专属 Gibbs 核与兼容的势函数参数化，实现闭式归一化和可直接采样的条件分布，并可自然扩展到流形乘积。实验表明其在合成与真实任务上常优于现有流形 OT 方法，同时保留直接采样能力。
正文
Abstract:Entropic Optimal Transport (EOT) has become a practical framework for learning stochastic couplings between complex distributions, with applications in generative modeling and domain adaptation. However, most EOT solvers are designed for Euclidean spaces, while manifold extensions remain limited and often rely on costly iterative methods, simulated dynamics, or generic neural models that do not fully exploit the underlying geometry. We introduce ManifoldLightOT, a light approach for learning kernel-induced EOT couplings directly on common manifolds. Using the kernel form of the EOT solution, we construct geometry-specific Gibbs kernels together with compatible potential parameterizations for spheres, tori, $\mathrm{SO}(3)$, and $\mathrm{SE}(3)$. These choices yield closed-form normalization and directly sampleable conditional distributions. Our formulation naturally extends to products of manifolds, making it applicable to more complex geometries. The parameters of the potentials are optimized directly from samples using Monte Carlo estimates of the learning objective. Through synthetic and real-world experiments, we show that ManifoldLightOT often outperforms existing manifold OT methods while retaining direct sampling.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.03085 [cs.LG] |
| (or arXiv:2610.03085v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03085 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xavier Aramayo Carrasco [view email]
[v1]
Fri, 2 Oct 2026 10:04:43 UTC (2,433 KB)
来源：arXiv：cs.LG · arxiv.org