Zero-Flow Encoders

2026-01-31

AI Summary

This work proposes a novel flow-based framework for representation learning, designed to efficiently extract sufficient information from data and rigorously test conditional independence. The key innovation lies in the introduction of the “zero-flow criterion,” which leverages the property that the adjusted flow velocity vanishes at time t = 0.5 to construct a computable loss function that obviates the need for sampling or simulation. This enables amortized learning of Markov blankets and self-supervised representation extraction. By extending flow models beyond generative modeling into the domain of representation learning, the method demonstrates strong empirical performance in both conditional independence testing and latent representation learning, as validated on synthetic and real-world datasets.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{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.

Problem

• representation learning
• conditional independence
• Markov blanket
• sufficient information
• flow-based models

Innovation

• zero-flow criterion
• rectified flow
• conditional independence
• amortized Markov blanket
• self-supervised representation learning