GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling

Haohui Jia; Zheng Chen; Jathurshan Pradeepkumar; Xu Cao; Yasuko Matsubara; Yasushi Sakurai; Takashi Matsubara

cs.AISep 29, 2026

GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling

Authors: Haohui Jia, Zheng Chen, Jathurshan Pradeepkumar, Xu Cao, Yasuko Matsubara, Yasushi Sakurai, Takashi Matsubara

Organizations: Faculty of Information Science and Technology, Hokkaido University, Japan · SANKEN, The University of Osaka, Japan · Department of Computer Science, University of Illinois Urbana-Champaign, USA · PediaMed AI, USA

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.

Figures & tables

Model	Formulation	Continuous	Graphical	Stochastic
CNN-LSTM	Spatial-temporal encoding	✗	✗	✗
BIOT ( Yang et al., 2023 )	Biosignal Transformer	✗	✗	✗
EvolveGCN ( Pareja et al., 2020 )	Evolving graph convolution	✗	✓	✗
DCRNN	Diffusion-graph convolutional RNN	✗	✓	✗
neural ODE	latent dynamics	✓	✗	✗
neural SDE	Stochastic latent dynamics	✓	✗	✓

Table 1: Comparison of representative methods for modeling EEG dynamics.

Figure 1: (Left) Continuous EEG real-time neuronal activity recordings. (Mid) An isotropic gaussian source-based method learns dynamic representations. (Right) Ours provides a graph conditioned source-based approach for learning the neuronal population dynamics.

Figure 2: Overview of the proposed GRFBrain . (a) Temporal EEG features and functional association graphs define state-dependent states and a graph Gaussian residual source, whose covariance is adapted to the observed graph states. (b) A joint node-edge velocity network transports node and edge residuals along a shared flow coordinate, coupling channel-wise state variations.

Model	Method	T(s)	AUROC	F1
Flow-based	BIOT	12	0.772 $\pm$ 0.006	0.294 $\pm$ 0.006
		60	0.642 $\pm$ 0.009	0.256 $\pm$ 0.003
	DCRNN	12	0.825 $\pm$ 0.002	0.416 $\pm$ 0.009
		60	0.802 $\pm$ 0.003	0.413 $\pm$ 0.005
	Flow matching	12	0.813 $\pm$ 0.002	0.372 $\pm$ 0.013
		60	0.725 $\pm$ 0.006	0.311 $\pm$ 0.028

Table 2: Results (AUROC

\uparrow

, F1

\uparrow

) on TUSZ (12s and 60s seizure detection). The upper block compares GRFBrain with discrete and continuous baselines (bold = best); the lower block ablates the node-edge interaction routes within GRFBrain .

Method	TUSZ			TUAB
Method	Acc	F1	AUROC	Acc	F1	AUROC
CNN-LSTM	$0.735\pm 0.003$	$0.347\pm 0.012$	$0.757\pm 0.003$	$0.741\pm 0.002$	$0.736\pm 0.007$	$0.813\pm 0.003$
BIOT	$0.702\pm 0.003$	$0.294\pm 0.006$	$0.772\pm 0.006$	$0.717\pm 0.002$	$0.713\pm 0.004$	$0.788\pm 0.002$
EvolveGCN	$0.769\pm 0.002$	$0.385\pm 0.005$	$0.791\pm 0.004$	$0.708\pm 0.003$	$0.707\pm 0.002$	$0.777\pm 0.003$
DCRNN	$0.816\pm 0.002$	$0.416\pm 0.009$	$0.825\pm 0.002$	$0.768\pm 0.004$	$0.769\pm 0.002$	$0.848\pm 0.002$
latent-ODE	$0.827\pm 0.004$	$0.470\pm 0.005$	$0.849\pm 0.004$	$0.749\pm 0.003$	$0.745\pm 0.002$	$0.829\pm 0.004$

Table 3: Main results on TUSZ (12s seizure detection) and TUAB abnormal EEG classification, reported as mean

\pm

standard deviation over three seeds. Bold and underline indicate the best and second-best results for each metric, respectively.

\dagger

denotes models trained with a multi-step predictive objective, and

\ddagger

denotes models trained with a single-step predictive objective.

Figure 3: Visualization of the proposed joint node-edge velocity field $v_{\theta}$ (middle) obtained by GRFBrain . The learned velocity exists the distinct patterns of graph reconfiguration, which seizure represents higher and dense magnitude and non-seizure represents lower and sparse magnitude.

Figure 4: Results on (a) graph similarity and (b) functional connections.

Figure 5: Effect of source geometry in GRFBrain . IID Gaussian, global GGRF, and our conditioned GGRF sources are compared across downstream classification metrics. Our conditional GGRF consistently improves the learned representation quality.

Figure 6: Summary of ablation study. (a) Velocity-network parameterization, (b) node and edge transport targets, and (c) forecasting horizon. The proposed joint node–edge velocity network, joint transport supervision, and short-horizon prediction provide the strongest overall performance.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Method	TUSZ			TUAB
Method	Acc	F1	AUROC	Acc	F1	AUROC
Max pooling	$\mathbf{0.878\pm 0.001}$	$\mathbf{0.523\pm 0.014}$	$\mathbf{0.877\pm 0.003}$	$\mathbf{0.787\pm 0.004}$	$\mathbf{0.786\pm 0.004}$	$\mathbf{0.877\pm 0.006}$
Mean pooling	$0.851\pm 3$	$0.461\pm 2$	$0.857\pm 2$	$0.788\pm 5$	$0.784\pm 4$	$0.872\pm 6$
Sum pooling	$0.867\pm 2$	$0.506\pm 5$	$0.863\pm 4$	$0.788\pm 7$	$0.785\pm 6$	$0.877\pm 3$

Appendix

Table 4: Ablation of pooling options on TUSZ (12s seizure detection) and TUAB . Bold indicates best result.

Figure 7: Visualization results of latent joint node-edge dynamic field.

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TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching

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Conditional Flow Matching Matrix

Open paper AskPDF arXiv

Many complex systems such as brain networks, financial markets, and gene-regulatory circuits are described not by a fixed graph but by one that changes over time. A standard way to summarise such structure at each instant is the sparse precision (inverse-covariance) matrix, and the time-varying graphical lasso (TVGL) turns a multivariate signal into a smooth chain of these matrices. We introduce TVGL-CFM, a single model that learns the distribution of such chains and can both generate new, realistic time-varying network trajectories for a given class and forecast how an observed trajectory will continue. Each precision matrix lives on a curved space of positive-definite matrices, but a log-Euclidean chart flattens an entire trajectory into an ordinary vector space, so a simple conditional flow-matching model can be trained and sampled there while every decoded matrix is guaranteed to be a valid precision matrix. For forecasting we start the flow not from noise but from a rough extrapolation of the recent history, so the model only has to learn a small correction. Across EEG motor-imagery, chaotic systems, and gene-expression data, TVGL-CFM generates trajectories that keep the class-discriminative structure of real data, and it forecasts future connectivity more accurately than raw-signal baselines. Generating the structured precision trajectory directly is therefore more faithful than generating raw signals and estimating connectivity afterwards.

Abstract

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