Conditional flow matching improves transport between markov processes
Conditional Flow Matching for Transport Between Markov Processes
Machine Learning
Summary
Moving from one style of changing information over time to another can be tricky, especially when data follows patterns that depend on the past. The authors created a method to learn how to best convert one set of changes into another while keeping the order and rules intact. They tested this method on made-up data and on brain signals to match images people saw. Using their approach increased the accuracy of identifying images from brain recordings. This shows promise for handling complex time-based data.
What this means in practice
- •For neuroscience engineers: Improve decoding accuracy of brain signals to identify viewed images by modeling subject-specific variability in EEG data.
- •For time series analysts: Develop transport maps to adapt time-series data between different domains while preserving temporal dependencies.
Authors
Syamantak Kumar, Dheeraj Nagaraj, Saptarshi Roy, Purnamrita Sarkar
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.