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

arXiv: https://arxiv.org/abs/2606.29200 · HTML: https://mlsanity.com/paper/2606.29200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 51 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Adaptive Prototype Learning and Allocation for Few-Shot Segmentation](https://mlsanity.com/paper/2104.01893/) (2021)
- [Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation](https://mlsanity.com/paper/2110.04202/) (2021)
- [Generalized Source-free Domain Adaptation](https://mlsanity.com/paper/2108.01614/) (2021)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Prototype Rectification for Few-Shot Learning](https://mlsanity.com/paper/1911.10713/) (2019)
- [Source-Free Domain Adaptation via Distribution Estimation](https://mlsanity.com/paper/2204.11257/) (2022)
- [Generalize then Adapt: Source-Free Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2108.11249/) (2021)
- [Discriminative Adversarial Domain Adaptation](https://mlsanity.com/paper/1911.12036/) (2019)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [Building Deep Networks on Grassmann Manifolds](https://mlsanity.com/paper/1611.05742/) (2016)
- [Structural Re-weighting Improves Graph Domain Adaptation](https://mlsanity.com/paper/2306.03221/) (2023)
- [Spectral Graph Convolutions for Population-based Disease Prediction](https://mlsanity.com/paper/1703.03020/) (2017)
- [Covariance Pooling For Facial Expression Recognition](https://mlsanity.com/paper/1805.04855/) (2018)
- [BrainMass: Advancing Brain Network Analysis for Diagnosis with Large-scale Self-Supervised Learning](https://mlsanity.com/paper/2403.01433/) (2024)
- [Rethinking Class Relations: Absolute-relative Supervised and Unsupervised Few-shot Learning](https://mlsanity.com/paper/2001.03919/) (2020)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [SGAC: A Graph Neural Network Framework for Imbalanced and Structure-Aware AMP Classification](https://mlsanity.com/paper/2412.16276/) (2024)
- [Nested Graph Pseudo-Label Refinement for Noisy Label Domain Adaptation Learning](https://mlsanity.com/paper/2508.00716/) (2025)
- [USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation](https://mlsanity.com/paper/2602.08431/) (2026)
- [Contrastive Brain Network Learning via Hierarchical Signed Graph Pooling Model](https://mlsanity.com/paper/2207.07650/) (2022)

## Built on by (most cited first, 2 of 2)

- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)
- [Beyond Site Agreement: Re-estimation for Brain Network Generalization](https://mlsanity.com/paper/2609.34611/) (2026)

## Abstract (arXiv)

Multi-site functional MRI (fMRI) studies are essential for robust neuropsychiatric diagnosis yet suffer severe domain shifts from scanner heterogeneity, demographics, and site-specific acquisition protocols. Traditional domain adaptation requires concurrent source and target data access, violating clinical privacy regulations. Moreover, functional connectivity matrices lie on the Symmetric Positive Definite (SPD) manifold, where Euclidean operations cause geometric distortions corrupting diagnostic patterns. We propose BrainRiem, a source-free domain adaptation framework learning compact Riemannian brain prototypes via manifold-aware bi-level optimization. It employs the Log-Euclidean Metric to ensure prototypes remain valid SPD matrices, while Dirichlet Energy spectral calibration aligns their frequency characteristics with real brain networks. Only anonymized prototypes are transmitted to target sites, serving as stable anchors for training local models without source data access and reducing leakage under the evaluated 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 diverse scanners and demographics. Notably, learned prototypes exhibit biologically interpretable connectivity patterns aligning with established neuroscience findings, validating the necessity of Riemannian geometry for brain network analysis.