离散动作匹配：通过状态图从样本中学习随机动力学
Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs
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中文总结 AI 辅助
提出离散动作匹配（DAM），利用状态图和离散Wasserstein几何从样本学习随机动力学，通过估计密度比率与学习动作势实现边际重建与插值。
中文摘要 AI 辅助
从未配对的时间边际学习群体动力学是一个不适定的逆问题，需要对底层动力学施加结构假设。我们提出了离散动作匹配（DAM），这是基于离散Wasserstein几何的动作匹配的有限状态对应物。对于给定的边际路径和传输几何，我们推导了其规范最小动能电流的动作最小化目标。我们的关键观察是，离散动作的密度依赖性简化为相邻密度比率。沿着快照的经验插值，DAM首先估计这些比率，然后学习动作势。学习到的场还定义了一个图支持的马尔可夫采样器。在受控合成动力学和真实小鼠原肠胚形成数据上的实验评估了边际重建和插值。额外的实验从配对样本中近似数值表面传输路径。
英文摘要
Learning population dynamics from unpaired temporal marginals is an ill-posed inverse problem that requires structural assumptions on the underlying dynamics. We introduce $\textit{Discrete Action Matching}$ (DAM), a finite-state counterpart of Action Matching based on discrete Wasserstein geometry. For a prescribed marginal path and transport geometry, we derive an action-minimization objective for its canonical minimum-kinetic-energy current. Our key observation is that the density dependence of the discrete action reduces to neighboring density ratios. Along an empirical interpolation of the snapshots, DAM first estimates these ratios and then learns an action potential. The learned fields also define a graph-supported Markov sampler. Experiments on controlled synthetic dynamics and real mouse gastrulation data evaluate marginal reconstruction and interpolation. Additional experiments approximate numerical surface-transport paths from paired samples.
发表机构
- Applied AI Institute（应用人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。
