It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification

Cross-site out-of-distribution (OOD) generalization in resting-state functional magnetic resonance imaging (rs-fMRI) often relies on learning task-discriminative representations from full-scan functional connectivity (FC) graphs and promoting invariance across source sites. However, FC graphs are estimated from finite, temporally correlated blood-oxygen-level-dependent (BOLD) sequences. Cross-site agreement therefore does not necessarily imply that predictive evidence remains supported under FC re-estimation within the same scan. In this paper, we propose Brain Network Re-estimation-Informed OOD Learning (BRIO), a framework that uses within-scan FC re-estimation to guide cross-site alignment. BRIO maps fullscan graphs and their re-estimates into consistently indexed connectome factors, enabling comparisons of their predictive contributions. It assesses re-estimation support from changes in these contributions relative to within-class subject variability and class separation. For each source-site pair and class, this task-calibrated support from both sites is combined with predictive relevance to form pairwise qualifications, which determine relative factor weights and overall alignment strength. Leave-one-site-out experiments on four real-world datasets (ABIDE, REST-metaMDD, SRPBS, and ABCD) show that BRIO consistently outperforms competitive baselines, with relative improvements of up to 3.8% in accuracy. These gains also persist under an alternative brain parcellation on ABIDE.

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form operations or depend on arbitrary region ordering, limiting scalability. We introduce a scalable geometric framework with two components: (i) the Off-log metric, a smooth transformation mapping correlation matrices to symmetric zero-diagonal matrices. This enables closed-form expressions for distances, Frechet means, and linear models, allowing standard statistical modeling without complex manifold optimization. (ii) Grassmannian subspace discrimination, which compares subjects via principal-angle distances between eigenvector subspaces, resolving inherent sign and basis ambiguities. Both components integrate into standard machine-learning workflows for inference, regression, and classification. Validated across two clinical cohorts (Parkinson's and psychosis) and three ageing fMRI datasets, the Off-log metric increased sensitivity in permutation tests and matched or exceeded Riemannian and Euclidean baselines in classification. Brain-age prediction performance was comparable, with Riemannian metrics excelling in two of three cohorts. The Grassmannian method consistently outperformed Euclidean baselines, highlighting disease-relevant networks. Overall, geometry-aware representations improve sensitivity and predictive performance while remaining straightforward to deploy at scale.

Self-supervised pretraining reshaped prediction in language and vision, and brain foundation models (BFMs) inherited its promise. Representations learned from large unlabelled corpora should capture individual functional dynamics and generalise across cohorts. However, kernel ridge regression (KRR) fitted on functional connectivity (FC) matrices still predicts individual phenotypes more accurately than any BFM we tested. In this paper, we show that KRR is weighted by the eigenvalues of the FC which are miscalibrated for phenotype prediction. We apply an efficient spectral filter to recalibrate the eigenvalues of each subject's FC matrix, enabling the model to exploit more inter-individual variance. Across the 5 datasets, 11 parcellations and 6 prediction targets we tested, we match or exceed the KRR baseline. Based on this finding, we then pretrain a small encoder model on about 4,000 hours of fMRI from 162 open datasets, whereby we align the pairwise similarities between the embeddings of recording snippets with those between the recalibrated connectomes. Our model performs on par with the best of the 6 published BFMs we tested while having an order of magnitude fewer parameters. Our encoder performs better than FC on short scans and in smaller cohorts, especially in fingerprinting. We release the pretrained model weights, the code and the pretraining data, preprocessed and parcellated.