Zero-Flow Encoders

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 \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.

Artificial intelligence systems known as "flow models" are excellent at generating highly detailed, realistic data, such as images or audio. However, they are rarely used to uncover the hidden, essential structures buried inside complex data. To tackle this, we developed a new way for these models to learn. We discovered a unique mathematical property, which we call the "zero-flow criterion." It acts like a highly precise scale that balances perfectly at zero only when two sets of data are exactly identical. We translated this rule into a new, efficient learning tool that helps the AI filter out noise and pinpoint exactly key information. When tested on both simulations and real-world datasets, our method identifies key patterns from a variety of datasets. This gives researchers a powerful, computationally efficient new tool to extract the most meaningful insights from messy, real-world data.