BrainRiem: Riemannian Prototype Learning for Source-Free Cross-Site Brain Network Diagnosis

Multi-site functional MRI (fMRI) studies are essential forrobust neuropsychiatric diagnosis yet suffer severe domain shifts fromscanner heterogeneity, demographics, and site-specific acquisition pro-tocols. Traditional domain adaptation requires concurrent source andtarget data access, violating clinical privacy regulations. Moreover, func-tional connectivity matrices lie on the Symmetric Positive Definite (SPD)manifold, where Euclidean operations cause geometric distortions cor-rupting diagnostic patterns. We propose BrainRiem, a source-free do-main adaptation framework learning compact Riemannian brain pro-totypes via manifold-aware bi-level optimization. It employs the Log-Euclidean Metric to ensure prototypes remain valid SPD matrices, whileDirichlet Energy spectral calibration aligns their frequency characteris-tics with real brain networks. Only anonymized prototypes are trans-mitted to target sites, serving as stable anchors for training local mod-els without source data access and reducing leakage under the evalu-ated attacks. Comprehensive experiments on ABIDE and REST-meta-MDD show BrainRiem consistently outperforms state-of-the-art source-free, traditional, and graph domain adaptation methods across diversescanners and demographics. Notably, learned prototypes exhibit biolog-ically interpretable connectivity patterns aligning with established neu-roscience findings, validating the necessity of Riemannian geometry forbrain network analysis.