离散伴随薛定谔桥采样器
Discrete Adjoint Schrödinger Bridge Sampler
AI总结：
本文提出discrete ASBS，通过将伴随匹配方法扩展到离散空间，解决离散神经采样器的梯度缺失问题，提升训练效率和可扩展性。
摘要：
学习离散神经采样器具有挑战性，因为缺乏梯度和组合复杂性。虽然随机最优控制（SOC）和薛定谔桥（SB）提供了系统性的解决方案，但高效的SOC求解器如伴随匹配（AM），在连续领域表现出色，尚未在离散空间中得到探索。我们通过揭示AM的核心机制是状态空间无关的，引入了discrete ASBS，一个统一的框架，将AM和伴随薛定谔桥采样器（ASBS）扩展到离散空间。理论上，我们分析了离散SB问题的最优条件及其与SOC的联系，确定了在状态空间上必须存在一个必要的循环群结构才能实现这种扩展。实验上，discrete ASBS在样本质量上具有竞争力，同时在训练效率和可扩展性方面有显著优势。
英文摘要：
Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
