AI 中文总结
本文针对支撑在嵌入黎曼流形上的未归一化玻尔兹曼分布采样问题，提出基于伴随薛定谔桥的硬约束采样方法，通过随机最优控制视角实现状态空间层面的可行性约束，并在物理应用中得到验证。
AI 中文摘要
诸多任务需要从支撑在流形上的未归一化玻尔兹曼分布中进行采样。本文在伴随匹配与伴随薛定谔桥采样的基础上，从随机最优控制视角出发，提出一种理论上可证的方法，以解决光滑、紧致、路径连通的嵌入黎曼流形上的该采样问题。与现有文献相比，本文的创新点在于在状态空间层面实施可行性约束，即受控扩散过程是内在地定义在弯曲空间上的。本文针对若干物理应用提供了实验验证。
英文摘要
A variety of tasks require sampling from unnormalized Boltzmann distributions supported on manifolds. Building upon the foundations of adjoint matching and adjoint Schrödinger bridge sampling, this paper provides a theoretically justified method, through the lens of stochastic optimal control, to address this problem on smooth, compact, path-connected embedded Riemannian manifolds. As an element of novelty compared to existing literature, feasibility is enforced at the level of the state space, meaning the controlled diffusion is defined intrinsically on the curved space. Empirical validations are provided for several physics applications.
