Zero-Flow Encoders

2026/01/31 by Yakun Wang, Leyang Wang, Song Liu +1 · 1 voice
Computer Science · Mathematics · #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.2602.00797

arxiv published 2026/01/31 · arxiv updated 2026/06/07

Abstract

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at t=0.5 if and only if the source and target distributions are identical. We term this property the zero-flow criterion. Second, we show that this criterion can certify conditional independence, thereby extracting sufficient information from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

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