Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs

arXiv:2610.05071v1 Announce Type: new Abstract: Learning population dynamics from unpaired temporal marginals is an ill-posed inverse problem that requires structural assumptions on the underlying dynamics. We introduce extit{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.

Related

• A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
• One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State
• Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions
• KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots

Source: arXiv cs.LG | 2026-10-06