发表机构
Google DeepMind; The University of Texas at Austin; Mohamed bin Zayed University of Artificial Intelligence（谷歌DeepMind; 德克萨斯大学奥斯汀分校; 穆罕默德·本·扎耶德人工智能大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对马尔可夫过程轨迹间的传输问题，提出一种保持马尔可夫结构的条件流匹配算法，在总体极限下一致且具有有限样本误差界，并在EEG图像检索任务中显著提升准确率。
AI 中文摘要
受时间序列领域自适应背景下序列到序列传输的启发，我们研究了马尔可夫过程轨迹之间的传输问题。给定来自源分布和目标分布的有限数量的轨迹，我们提出了一种基于流匹配的算法，该算法学习从源轨迹分布到目标轨迹分布的传输映射，同时保持马尔可夫结构。我们证明了这在总体极限下是一致的，并在混合时间假设下推导了有限样本误差界，遵循了马尔可夫设置中经典统计问题的分析，包括回归（Nagaraj等人，2020）、主成分分析（Kumar和Sarkar，2023）和矩阵集中（Neeman等人，2024）。我们补充了一个下界构造，表明即使使用正则高斯条件转移，依赖于混合时间的样本复杂度也是不可避免的。我们在合成和真实数据上进行了评估。对于THINGS-EEG2（Gifford等人，2022）上从脑电图（EEG）进行图像检索的任务，该任务是从人类受试者捕获的EEG信号中识别所观看的图像，这受到高受试者间变异性的影响。我们在ENIGMA解码器（Kneeland等人，2026）的受试者特定时间映射之前增加了一个条件流。这将平均前5名检索准确率从43.87%提高到49.05%，相对提高了11.82%。
英文摘要
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.
