Conditional Flow Matching for Transport Between Markov Processes

2026-10-05

AI Summary

This study addresses the challenge of cross-subject variability in time-series domain adaptation by tackling distribution transport between Markov process trajectories. To this end, it proposes a conditional flow matching-based algorithm that learns a source-to-target trajectory transport map while preserving the underlying Markov structure. Theoretically, the authors derive finite-sample error bounds, establish consistency under mixing-time assumptions, and determine an irreducible lower bound on sample complexity. Empirically, the method demonstrates its effectiveness on the THINGS-EEG2 image retrieval task, improving Top-5 accuracy from 43.87% to 49.05%, representing an 11.82% relative gain. These results validate the efficacy of structure-preserving trajectory transport for mitigating inter-subject distribution shifts in temporal domain adaptation.

Abstract

Motivated by sequence-to-sequence transport in the context time-series domain adaptation, we study the problem of transportation between trajectories of Markov processes. Given a limited number of trajectories from source distribution and the target distribution, we formulate a flow matching based algorithm which learns a transport map from the source to target trajectory distribution, while preserving the Markov structure. We show that this is consistent in the population limit and derive finite-sample error bounds under mixing time assumptions, following the analysis of classical statistical problems including regression (Nagaraj et al., 2020), principal component analysis (Kumar and Sarkar, 2023), and matrix concentration (Neeman et al., 2024) in the Markov setting. We complement that with a lower-bound construction showing that a mixing-time dependent sample complexity is unavoidable even with regular Gaussian conditional transitions. We evaluate on synthetic and real-world data. For image retrieval from electroencephalography (EEG) on THINGS-EEG2 (Gifford et al., 2022), the task is to identify the viewed image from EEG signals captured from human subjects, which suffers from high inter subject variability. We augment the ENIGMA decoder (Kneeland et al., 2026) with a conditional flow before its subject-specific temporal map. This improves mean top-5 retrieval accuracy from 43.87% to 49.05%, an 11.82% relative improvement.

Problem

• Markov process transport
• time-series domain adaptation
• trajectory distribution matching
• flow matching

Innovation

• Conditional Flow Matching
• Markov Processes
• Domain Adaptation
• Sample Complexity
• EEG Decoding