[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83186-en":3,"doc-seo-83186-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83186,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis","Functional brain networks follow a hierarchical organization across ROI, community, and whole-brain levels, enabling local processing, inter-community coordination, and global integration. Community-aware graph modeling has shown promise for diagnosis and biomarker discovery, yet many brain graph methods do not adequately capture ROI–community interactions across these hierarchy levels. HLBG projects multi-level representations into Lorentzian hyperbolic space and enforces two geometric entailment constraints. A Graph-aware Mamba (GaMamba) adds topology-derived structural prompts to preserve graph information. Experiments on ABIDE-I and REST-MDD demonstrate superior performance and disorder-relevant biomarkers.","Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis⋆  \narXiv :2607 .07077v 1 [ cs .CV] 8 Jul 2026  \nYapeng Lia , Bo Jianga,∗ , Ziyan Zhanga , Dongdong Chena and Zhengzheng Tua,∗  \na School of Computer Science and Technology, Anhui University, 111 Jiulong Road, Hefei, 230601, China  \nARTICLE INFO  \nKeywords:  \nBrain Disorder Hyperbolic Space Graph Neural Networks Mamba  \nAB STRACT  \nFunctional brain networks exhibit a hierarchical organization across ROI, community, and whole-brain levels, supporting local processing, inter-community coordination, and global integration. Recent studies have demonstrated that brain community-aware modeling is beneficial for both diagnosis and biomarker identification of brain networks. However, existing brain graph modeling methods often struggle to model ROI–community interactions, thereby failing to fully exploit the hierarchy across ROI, community, and whole-brain network levels. To address this issue, inspired by deep hyperbolic learning in modeling hierarchical structures, we propose a novel framework, termed Hyperbolic Learning on Brain Graphs (HLBG) for brain network analysis. The core idea of HLBG is to exploit the inherent hierarchical geometry of hyperbolic space to model the hierarchical relationships among ROIs, functional communities, and the whole-brain network, thereby learning hierarchy-aware and highly discriminative representations for brain network data. Specifically, HLBG first projects representations from ROIs, communities, and whole-brain network into the Lorentzian hyperbolic space. Then, the multi-level hierarchy is imposed via two geometric entailment constraints. In addition, we further introduce a new Graph-aware Mamba (GaMamba) model, which incorporates topology-derived structural prompts into Mamba to capture long-range dependencies while preserving graph topological information. Experiments on ABIDE-I and REST-MDD demonstrate that HLBG outperforms state-of-the-art methods and identifies disorder-relevant functional biomarkers.  \n1. Introduction  \nBrain disorders such as autism spectrum disorder (ASD) and major depressive disorder (MDD) severely impair patients’ cognitive, emotional, motor, and social functions, imposing a substantial burden on families and society (Wing and Gould, 1979; Insel and Cuthbert, 2015; Qiu, Sun, Shi, Duan, Wang and Ma, 2025) . Accurate and timely diagnosis is crucial for effective treatment and improved long-term outcomes. However, disease-related alterations in the brain’s intrinsic functional architecture are often subtle, posing significant challenges for precise diagnosis (Li, Liu, Jiang, Liu and Lei, 2021b; Ma, Cui, Liu, Guo, Chen and Li, 2023) . Functional magnetic resonance imaging (fMRI) constitutesan effective framework for investigating such abnormalities, tracking neural activity patterns through blood oxygen leveldependent (BOLD) signals (Li, Zhou, Dvornek, Zhang, Gao, Zhuang, Scheinost, Staib, Ventola and Duncan, 2021a) . In particular, functional connectivity (FC), computed as the correlation between BOLD signal series extracted from different regions of interest (ROIs), has been widely used to model aberrant brain connectivity patterns for disorder diagnosis (Luo, Wu, Yang, Xue, Beheshti, Sheng, McAlpine, Sowman, Giral and Yu, 2024) . Accordingly, the brain can be represented as a graph constructed from the FC matrix, where ROIs are modeled as nodes and their functional  \n⋆  \n∗Corresponding author  \n [liyapeng_w@163.com](liyapeng_w@163.com) (Y. Li); [jiangbo@ahu.edu.cn](jiangbo@ahu.edu.cn) (B. Jiang); [zhangziyanahu@163.com](zhangziyanahu@163.com) (Z. Zhang); [chendongdong@ahu.edu.cn](chendongdong@ahu.edu.cn) (D. Chen); [zhengzhengahu@163.com](zhengzhengahu@163.com) (Z. Tu)  \nORCID(s):  \nassociations as edges (Peng, Huang, Dong, Yu, Xia, Zhang and Jin, 2025) .  \nGraph neural networks (GNNs) have been widely used for brain network analysis tasks, supporting disease prediction and biomarker identi","cbCaih1E9BN6SQdK","https://ap.wps.com/l/cbCaih1E9BN6SQdK","pdf",1540439,4,1,12,"English","en",105,"# Introduction\n## Background on brain disorders and fMRI connectivity\n## Graph modeling and existing GNN/Transformer approaches\n## Mamba and graph extensions\n## Motivation for hierarchy-aware hyperbolic learning\n# Method: HLBG Framework","[{\"question\":\"What problem does HLBG address in brain graph modeling?\",\"answer\":\"HLBG targets the difficulty many methods have in modeling interactions between ROI and functional communities while fully exploiting hierarchy across ROI, community, and whole-brain levels.\"},{\"question\":\"How does HLBG represent hierarchical brain information?\",\"answer\":\"HLBG maps representations from ROIs, communities, and whole-brain networks into Lorentzian hyperbolic space, then applies two geometric entailment constraints to impose multi-level hierarchy.\"},{\"question\":\"What role does GaMamba play in the framework?\",\"answer\":\"GaMamba incorporates topology-derived structural prompts into Mamba, aiming to capture long-range dependencies while preserving graph topological 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