Discrete Action Matching learns stochastic dynamics from population snapshots on graphs
FrancescoLocat8 · x · 2026-10-07
A new arXiv paper (2610.05071) by Persiianov and Korotin introduces Discrete Action Matching (DAM) for the ill-posed problem of learning population dynamics from unpaired temporal marginals. Key points:
- DAM is a finite-state counterpart of Action Matching built on discrete Wasserstein geometry, deriving an action-minimization objective for the canonical minimum-kinetic-energy current
- The key observation: density dependence of the discrete action reduces to neighboring density ratios, which are estimated first along an empirical interpolation of snapshots, then an action potential is learned
- The learned fields also define a graph-supported Markov sampler
- Experiments on synthetic dynamics and real mouse gastrulation data evaluate marginal reconstruction and interpolation
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