arXiv：cs.LG· Syamantak Kumar, Dheeraj Nagaraj, Saptarshi Roy, Purnamrita Sarkar·· 4 小时前AI 评分33
面向马尔可夫过程间传输的条件流匹配
Conditional Flow Matching for Transport Between Markov Processes
AI 导读
研究提出一种基于流匹配的算法，学习从源分布到目标轨迹分布的传输映射，同时保持马尔可夫结构，并证明其在总体极限下的一致性，在混合时间假设下推导出有限样本误差界。作者还构造下界，表明即使条件转移为规则高斯分布，依赖混合时间的样本复杂度也不可避免。
正文
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.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.07229 [cs.LG] |
| (or arXiv:2610.07229v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.07229 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Syamantak Kumar [view email]
[v1]
Mon, 5 Oct 2026 18:35:47 UTC (235 KB)
来源：arXiv：cs.LG · arxiv.org