GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling

2026-09-29

AI Summary

This study addresses the challenge of disentangling graph-structural noise from deterministic contributions in predicting time-varying EEG functional connectivity by proposing a graph-structured residual flow framework. The method decouples conditional mean prediction from stochastic residual transport, pioneering the integration of graph Gaussian sources into rectified flows while explicitly distinguishing transport time from physical time. By encoding dependencies via Laplacian-basis covariance and combining conditional flow matching with graph neural networks, it enables effective dynamic modeling. Furthermore, this work establishes control conditions that differentiate valid residual transport from deterministic improvements, precisely quantifying the value of residual transport and significantly enhancing the interpretability of distributional predictions.

Abstract

Forecasting time-varying functional connectivity from electroencephalography (EEG) requires modeling both history-dependent trends and structured variability across channels. Conditional flow matching provides a framework for distributional forecasting, yet it remains unclear whether graph-informed source distributions offer practical advantages over isotropic noise and strong deterministic predictors. We introduce a graph-structured residual flow framework that separates conditional mean prediction from stochastic residual transport. A history-only predictor estimates the future connectivity graph, while a graph Gaussian source encodes dependencies derived from past connectivity through a Laplacian-based covariance. A conditional velocity field transports source samples to future graph residuals, with transport time explicitly distinguished from physical EEG time. Our study identifies the conditions and controls needed to distinguish useful residual transport from improvements attributable to deterministic prediction, learned representations, and sampling effects.

Problem

• EEG functional connectivity forecasting
• conditional flow matching
• graph-structured source distributions
• residual transport
• distributional forecasting

Innovation

• Graph-Structured Rectified Flows
• EEG Dynamic Modeling
• Conditional Flow Matching
• Residual Transport
• Laplacian-based Covariance