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About this paper
Jiajun He, Zijing Ou, Francisco Vargas, Yingzhen Li, José Miguel Hernández-Lobato, Carles Domingo-Enrich, Yuanqi Du
The authors extend escorted free-energy estimation to general Markov transports, learning forward and backward paths between endpoint distributions and estimating normalization-constant ratios from path likelihoods without specifying an energy path. In a 25×25 Ising bridge at β=0.2↔0.6, discrete flow matching estimates −476.21±0.81 versus reference −476.71, while masked Generator Matching estimates −539.61±35.3, showing results depend on the tested variant.
Key insights
- The Jarzynski Equality and Crooks Fluctuation Theorem can be formally extended to arbitrary time-inhomogeneous Markov processes while maintaining their thermodynamic interpretation.
- Marginalization of conditionally time-reversible dynamics preserves time-reversal properties, simplifying the design of neural network-based transport for general state spaces.
- Infinitesimal time reversal and generalized Doob's h-transforms form a group isomorphic to a generalized dihedral group, uncovering a fundamental algebraic structure for generator transformations.
Summary by alphaXiv.
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