NeuroBRIDGE: Behavior-Conditioned Koopman Dynamics with Riemannian Alignment for Early Substance Use Initiation Prediction from Longitudinal Functional Connectome

Badhan Mazumder; Sir-Lord Wiafe; Vince D. Calhoun; Dong Hye Ye

cs.CVMar 31, 2026

NeuroBRIDGE: Behavior-Conditioned Koopman Dynamics with Riemannian Alignment for Early Substance Use Initiation Prediction from Longitudinal Functional Connectome

Authors: Badhan Mazumder, Sir-Lord Wiafe, Vince D. Calhoun, Dong Hye Ye

Organizations: Department of Computer Science, Georgia State University · Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, and Emory University

Abstract

Early identification of adolescents at risk for substance use initiation (SUI) is vital yet difficult, as most predictors treat connectivity as static or cross-sectional and miss how brain networks change over time and with behavior. We proposed NeuroBRIDGE (Behavior conditioned RIemannian Koopman Dynamics on lonGitudinal connEctomes), a novel graph neural network-based framework that aligns longitudinal functional connectome in a Riemannian tangent space and couples dual-time attention with behavioral-conditioned Koopman dynamics to capture temporal change. Evaluated on ABCD, NeuroBRIDGE improved future SUI prediction over relevant baselines while offering interpretable insights into neural pathways, refining our understanding of neurodevelopmental risk and informing targeted prevention.

Figures & tables

Figure 1: NeuroBRIDGE overview: Longitudinal rs-fMRIs (Baseline and 2-Year) were processed to generate FNCs $(53\times 53)$ via $NeuroMark$ , then SPD-regularized and aligned in a shared Riemannian tangent space to form geometry-aware $k$ NN graphs with multi-scale heat-kernel tokens as node features followed by an edge-gated GNN encoding visit-specific embeddings, which are fused by dual-time self/cross attention into a subject-wise vector. A spectrally bounded, CBCL-conditioned Koopman module then models longitudinal change, and employed the predicted–observed year-2 latent to estimate 4-year SUI status, jointly optimized by three different loss terms in an end-to-end manner.

Method	Accuracy	Sensitivity	Specificity
SPDNet [ 6 ]	77.57 $\pm$ 0.0854	68.18 $\pm$ 0.1122	77.86 $\pm$ 0.0811
BrainNetCNN [ 8 ]	76.53 $\pm$ 0.0932	68.64 $\pm$ 0.1213	76.78 $\pm$ 0.0866
BNT [ 7 ]	79.02 $\pm$ 0.0794	74.42 $\pm$ 0.0976	79.16 $\pm$ 0.0754
EvolveGCN [ 18 ]	74.68 $\pm$ 0.0989	67.27 $\pm$ 0.1281	74.91 $\pm$ 0.0891
RBGM [ 21 ]	75.73 $\pm$ 0.0912	72.82 $\pm$ 0.1056	75.85 $\pm$ 0.0844
NeuroBRIDGE	84.71 $\pm$ 0.0692	86.36 $\pm$ 0.0514	84.66 $\pm$ 0.0658

Table 1: Performance comparison against sate-of-the-art (SOTA) baselines [Unit: %] (Mean

\pm

Standard Deviation).

Method Variant	Accuracy	Sensitivity	Specificity
w/o CBCL scores	82.13 $\pm$ 0.0882	77.73 $\pm$ 0.1281	82.27 $\pm$ 0.0798
w/o Midpoint anchor	82.58 $\pm$ 0.0745	84.55 $\pm$ 0.0608	82.51 $\pm$ 0.0816
w/o Trace-free deflation	83.84 $\pm$ 0.0712	85.91 $\pm$ 0.0549	83.78 $\pm$ 0.0794
w/o Riemannian (in Euclidean)	75.27 $\pm$ 0.1183	75.91 $\pm$ 0.1025	75.24 $\pm$ 0.1241
w/o Gaussian RBF kernel $\Pi^{(\tau)}_{ij}$	83.79 $\pm$ 0.0697	85.45 $\pm$ 0.0562	83.74 $\pm$ 0.0739
w/o Edge gate $g^{(\tau)}_{ij}$	82.71 $\pm$ 0.0873	84.55 $\pm$ 0.0726	82.66 $\pm$ 0.0921

Table 2: Performance outcomes from ablation experiment [Unit: %] (Mean

\pm

Standard Deviation).

Figure 2: Axial view of group-mean, time-mixed edge weights (top $3\%$ ) for SUI and non-SUI cohorts across the seven networks: cerebellar (CBN), default mode (DMN), cognitive control (CON), visual (VSN), sensorimotor (SMN), auditory (ADN), and subcortical (SCN). Intra-network connections are color-coded by network; cross-network connections are shown in gray. Line width scales with edge weight, emphasizing relatively stronger connections.

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Functional connectome analysis examines brain-region interactions to understand and identify disorders such as autism spectrum disorder and Alzheimer's disease. Existing methods typically use GNNs and Transformers to model the full functional connectivity matrix. However, processing tens of thousands of connections introduces redundancy and noise, increases computational cost, and limits connection-level interpretability. This raises a central question: do we really need complex interaction modeling, or is identifying a small set of disease-relevant connectivity patterns sufficient? To answer this question, we propose BrainLinear, a lightweight geometry-aware framework for mining disease-discriminative connectome patterns. BrainLinear first maps each functional connectivity matrix to a shared tangent space centered at the Fréchet mean of the training set, capturing subject-specific deviations while respecting matrix geometry. It then scores each ROI-pair tangent direction by its classification contribution and disease--control difference, retaining Top-

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relative to the closest baseline in AUC. The selected directions are directionally consistent with between-group displacements and organized across major functional systems, supporting connection-level interpretation.

Abstract

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