High-Resolution Dynamic Functional Connectivity Generation with Graph-Variate Flow Matching

2026-09-29

AI Summary

This study addresses the challenge of capturing rapidly evolving brain network interactions, as high-resolution dynamic functional connectivity is inherently noisy and low-rank. We propose GVD-CFM, a generative model that operates on symmetric positive definite matrices within a Riemannian manifold to synthesize high-fidelity brain connectivity trajectories via non-autoregressive flow matching. The method employs a Hadamard construction to elevate low-rank connectivity into the positive definite cone, preserving manifold structure without regularization. By integrating log-Euclidean diffeomorphisms with Transformer-based conditional flow matching, it enables flexible decoding within a single model. Experiments on EEG datasets demonstrate that GVD-CFM achieves superior distributional fidelity and temporal dynamics preservation. Furthermore, the generated synthetic data significantly enhances downstream classification performance while maintaining computational efficiency.

Abstract

High-resolution dynamic functional connectivity (DFC) can reveal rapidly evolving brain-network interactions, but short temporal windows yield noisy, often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this by modulating fast instantaneous interactions with stable trial-level support. This suppresses spurious fluctuations and emphasizes persistent, informative connections. We show that the Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, keeping high-resolution trajectories on the SPD manifold without ridge regularisation or post-hoc projection. We introduce GVD-CFM, a class-conditional generative model for high-resolution dynamic connectivity. Each trial is represented as SPD GVD matrices on a product Riemannian manifold, then mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly and generates the full trajectory non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD sequences. Retaining the full DCT basis also enables decoding on denser temporal grids without retraining. Across multiple EEG motor-imagery datasets, GVD-CFM delivers the strongest overall results for held-out distributional fidelity, temporal-dynamics preservation, and synthetic-to-real classification. It also remains computationally efficient relative to strong raw-signal and direct GVD-space generative baselines. GVD-CFM therefore provides a practical framework for realistic, temporally coherent, high-resolution brain-network generation with preserved manifold structure and resolution-flexible decoding from a single trained model.

Problem

• Dynamic Functional Connectivity
• Symmetric Positive Definite Manifold
• EEG Motor Imagery
• Generative Model

Innovation

• Graph-Variate Dynamic Connectivity
• SPD Manifold
• Conditional Flow Matching
• Non-autoregressive Generation
• Discrete Cosine Transform