Zero-Flow Encoders

Researchers introduced Zero-Flow Encoders, a flow-inspired framework for representation learning that uses a zero-flow criterion to certify conditional independence and extract sufficient information from data. The method enables learning amortized Markov blankets and latent representations, showing effectiveness on simulated and real-world datasets.

Statistics Machine Learning Submitted on 31 Jan 2026 v1 https://arxiv.org/abs/2602.00797v1 , last revised 7 Jun 2026 this version, v3 Title:Zero-Flow Encoders View PDF /pdf/2602.00797 HTML experimental https://arxiv.org/html/2602.00797v3 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: this https URL . Submission history From: Yakun Wang view email /show-email/039a3d78/2602.00797 Sat, 31 Jan 2026 16:11:01 UTC 6,198 KB v1 /abs/2602.00797v1 Thu, 4 Jun 2026 16:53:55 UTC 3,466 KB v2 /abs/2602.00797v2 v3 Sun, 7 Jun 2026 16:59:20 UTC 3,466 KB Current browse context: stat.ML References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .