Hyperbolic Representation Learning

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Hyperbolic representation learning studies how negatively curved spaces can encode tree-like hierarchies and scale-free relationships more compactly than flat Euclidean spaces. Common approaches learn embeddings in Poincaré balls or Lorentz hyperboloids, using graph neural networks, entailment cones, contrastive objectives, and curvature-adaptive or manifold-aware layers. Applications span graph prediction, vision-language alignment, time-series forecasting, and biomedical data, with evaluations often testing retrieval, classification, and transfer across levels of a hierarchy. A central open question is when the geometry itself improves results: outcomes depend on objectives, curvature, and optimization stability, and some controlled studies find that hierarchy-aware supervision matters more than the choice of geometry.

Latest papers

92 papers18 papers in the last four weeks, up 6% on the four weeks before. 0.1% of all new papers.

Euclidean Crowding-Driven Adaptive Euclidean-Hyperbolic Graph Learning
Oct 27, 2026Hao Chen, Jian Sun, Chuan Shi +1Graph Representation Learning Hyperbolic Representation Learning
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Beijing Key Lab of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing 100876, China
Organizing Temporal Evidence in Hyperbolic Space for Video Moment Retrieval
Oct 23, 2026Mengnan Liu, Sanping Zhou, Kun Xia +3Video Moment Retrieval Temporal Video Grounding
State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. · School of Computer Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. · Amazon Alexa AI, Bellevue, WA 98004 USA.
Separating Angular Alignment from Radial Ordering in Hyperbolic Vision-Language Models
Oct 23, 2026Mingyang Gao, Yuwei Wu, Shiyu Luo +8Vision-Language Models Hyperbolic Representation Learning
Beijing Institute of Technology · Shenzhen MSU-BIT University
HypTI: Hyperbolic Geometry-Aware Multimodal Feature Fusion Framework for Dementia Detection Based on Tabular-Image Data
Oct 20, 2026Jianfei Xu, Huizhi Liang, Judith Harrison +3Multimodal Fusion Multimodal Classification
Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL
Oct 14, 2026Timo Klein, Thomas Lang, Andrii Shkabrii +3Reinforcement Learning Contrastive RL
Faculty of Computer Science, University of Vienna, Vienna, Austria · UniVie Doctoral School Computer Science, University of Vienna, Vienna, Austria · Department of Machine Learning and Systems Biology, Max Planck Institute of Biochemistry, Martinsried, Germany +1
Revisiting Triplet Contrastive Learning for 3D Shape Understanding
Oct 14, 2026Chaoyang Zhu, Zhe Liao, Jiayi Zhang +33D Representation Learning Cross-Modal Alignment
Xiamen University · Shanghai AI Lab
GeoMER: A Joint Euclidean-Hyperbolic Geometry Framework for Multimodal Emotion Recognition
Oct 13, 2026Ting Zhu, Huizhi Liang, Boguslaw Obara +2Multimodal Emotion Recognition Multimodal Fusion
Newcastle University, Newcastle upon Tyne, United Kingdom · Taiyuan University of Technology, Shanxi, China
HyBRA-EEG: Hyperbolic Global-Local Brain-Region Aggregation for Self-Supervised EEG Representation Learning
Oct 12, 2026Xin Liu, Feng Lu, Wei LiElectroencephalography Self-Supervised Pre-Training
Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics
Oct 11, 2026Sarang Rajendra Patil, Vishal Fenn, Mengjia XuLong-Term Time Series Forecasting Time Series Forecasting
Department of Data Science New Jersey Institute of Technology Newark, NJ 07102, USA
Benchmarking Embedding Geometries and Clustering Algorithms for Unsupervised Patent Claim Classification
Oct 9, 2026Sujith Subramanian, P N Bhargav Teja, Susen Sarkar +1Information Retrieval Hyperbolic Representation Learning
Samsung R&D Institute Bangalore, India
The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective
Oct 5, 2026Xingrun Li, Sho Kuno, Yusuke Mukuta +2Riemannian Optimization Implicit Bias
The University of Tokyo · RIKEN
Hyperbolic Graph Representation Learning: Embed in One Metric, Optimize with Another
Oct 5, 2026Federico Larroca, Paola Bermolen, Marcelo Fiori +1Riemannian Optimization Hierarchical Representation Learning
Facultad de Ingenier´ıa Universidad de la Rep´ublica Uruguay
On the Geometry of Multimodal Saturation: Riemannian VICReg
Oct 5, 2026Nessim Ben Abbes, Duc Han Le, Sabri Mtibaa +1Self-Supervised Learning Geometric Representation Learning
Protectline · Télécom Paris
Temporal Geometry of Deep Networks: Hyperbolic Representations of Training Dynamics for Intrinsic Explainability
Oct 2, 2026Ambarish MoharilNeural Network Interpretability Neural Network Training Dynamics
Data Governance Department Jheronimus Academy of Data Science Eindhoven University of Technology
Hesitation Has a Geometry: Entropy-Trained Hyperbolic Probes for Sparse Activation Steering
Oct 1, 2026Zeyong Zhang, Tung Sum Thomas Kwok, Tengfei Ma +1Language Model Steering Activation Steering
Department of Data Science New Jersey Institute of Technology Newark, NJ, USA · Department of Statistics and Data Science University of California, Los Angeles Los Angeles, CA, USA · Department of Biomedical Informatics Stony Brook University Stony Brook, NY, USA
Curvature Under Attack in hZACH-ViT: Gauge Symmetry, Boundary Saturation, and Adversarial Failure
Sep 30, 2026Athanasios Angelakis, Marta Gomez-BarreroVision Transformer Adversarial Robustness
BioML, Research Institute CODE, University of the Bundeswehr Munich, Munich, Germany · Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands
Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations
Sep 29, 2026Zhongping JiVisual Representation Learning Hierarchical Representation Learning
CurvSpec: Adaptive Multi-Curvature Learning for Partial Relevant Video Retrieval
Sep 29, 2026Zhen Liu, Letian Li, Jinpeng Wang +4Cross-Modal Retrieval Video Representation Learning
SIGS, Tsinghua University Shenzhen, China · Harbin Institute of Technology, Shenzhen Shenzhen, China
Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation
Sep 28, 2026Ping Xiong, Shanglin Li, Yi Ding +2Neural Network Interpretability Layer-Wise Relevance Propagation
BIFOLD, Germany · Technische Universität Berlin, Germany · Nanyang Technological University, Singapore +3
Rethinking the Fully Hyperbolic Vision Transformer in Polar Coordinates
Sep 26, 2026Ahmad Bdeir, Niels LandwehrVision Transformer Hyperbolic Representation Learning
Data Science Group University of Hildesheim Hildesheim, Germany
Topology-Adaptive Hyperbolic Graph Attention Networks Guided by the Hyperbolic Sombor Index
Sep 26, 2026Haifang Cao, Boan Tao, Xiyuan Gao +3Graph Neural Networks Graph Attention Networks
Tianjin University Tainjin, China
HCOE: Hyperbolic Clinical Ontology Embeddings from Biomedical Language Models
Sep 25, 2026Yixuan Li, Weihao Li, Ziyang SongMedication Recommendation Hierarchical Representation Learning
McGill University · Northwestern University · Ohio University
Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution
Sep 24, 2026Jiahong Liu, Ming Shen, Xiaohao Liu +4Cross-Modal Alignment Hyperbolic Representation Learning
The Chinese University of Hong Kong · National University of Singapore · Yale University +1
hyperbolix: Hyperbolic Deep Learning in JAX
Sep 23, 2026Timo Klein, Thomas Lang, Yllka Velaj +1Hyperbolic Representation Learning Riemannian Neural Networks
Faculty of Computer Science, University of Vienna, Vienna, Austria · UniVie Doctoral School Computer Science, University of Vienna, Vienna, Austria · ds:UniVie, University of Vienna, Vienna, Austria
A Hierarchy-Aware Video-Language Model Evaluation and Hyperbolic Baseline for Surgery
Sep 22, 2026Ana Manzano Rodríguez, Pascal Mettes, Marlies P. Schijven +1Video-Language Model Evaluation Hierarchical Representation Learning
Data Science Center HAVA-Lab, University of Amsterdam · Video & Image Sense Lab, Informatics Institute, University of Amsterdam · Amsterdam UMC Location University of Amsterdam, Surgery +2
Geometry-Aware Hyperbolic Residual-Quantized Variational Autoencoders
Sep 22, 2026Alessio Colombo, Melika AyoughiResidual VQ Hierarchical Representation Learning
Universiteit van Amsterdam, Amsterdam, Netherlands
Hyperbolic Restricted Boltzmann Machine Neural Quantum State
Sep 22, 2026H. L. DaoNeural Quantum States Quantum Many-Body Physics
What Drives Hierarchy-Aware Image Retrieval? Taxonomy Alignment, Objective Choice, and Geometry
Sep 22, 2026Ling ShiImage Retrieval Hierarchical Representation Learning
Southeast University
HyperCLIP++: Fine-tuning CLIP forOpen-vocabulary Semantic Segmentation in Hyperbolic Space
Sep 21, 2026Zelin Peng, Zhengqin Xu, Changsong Wen +4VLM Adaptation Open-Vocabulary Semantic Segmentation
MoE Key Lab of Artificial Intelligence, AI Institute, School of Computer Science, Shanghai Jiao Tong University, Shanghai 200240, China · State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, Shanghai, 200083, China · Meituan, Shanghai, 200051, China
Hyperbolic Graph Representation Learning for Differential Diagnosis on Biomedical Knowledge Graphs
Sep 16, 2026Pietro Miotto, Lucia Mellini, Tommaso Marzi +5KG Embedding Knowledge Graphs
Department of Computer Science, Università degli Studi di Milano, Milan, Italy · Università della Svizzera italiana (USI), Lugano, Switzerland · Politecnico di Milano, Milan, Italy +2

Oct 27, 2026J/K move · Enter open · S save

Euclidean Crowding-Driven Adaptive Euclidean-Hyperbolic Graph Learning

Hao Chen, Jian Sun, Chuan Shi, Hongying Zhang

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Beijing Key Lab of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing 100876, China

Graph Representation Learning Hyperbolic Representation Learning Geometric Representation Learning Hierarchical Representation Learning

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Hyperbolic graph representation learning has emerged as a powerful paradigm for modeling hierarchical data. Unlike Euclidean space, which exhibits polynomial volume growth, hyperbolic space grows exponentially with radius, naturally accommodating tree-like structures without the geometric distortion known as Euclidean crowding. Despite strong empirical performance, the theoretical mechanisms underlying hyperbolic embeddings remain poorly understood. In this work, we provide a geometric quantifcation research for Euclidean crowding, a generalization-theoretic explanation for the superiority of hyperbolic space on hierarchical data, and further develop an adaptive Euclidean-hyperbolic fusion learning framework toward bridging this gap. Specifically, we first establish a geometric quantification of Euclidean crowding by analyzing layer-wise minimum separation in node embeddings, proving that fixed-dimensional Euclidean embeddings of tree-like graphs inevitably exhibit layer-wise crowding that leads to weaker margin-based generalization bounds. Second, we provide a generalization-bound for the superiority of hyperbolic geometry on hierarchical data. Third, we propose EH-Fusion, a geometry-adaptive framework that lifts Euclidean GNN representations into hyperbolic space via exponential mapping and adaptively fuses both geometries based on node-level neighborhood expansion patterns. Extensive experiments validate our theoretical insights and demonstrate the effectiveness of EH-Fusion on benchmark datasets.