Hyperbolic Learning

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8 papers in the last four weeks, up 167% on the four weeks before. 0.1% of all new papers.

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The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective
Oct 5, 2026Xingrun Li, Sho Kuno, Yusuke Mukuta +2Hyperbolic Learning Multiclass Classification
The University of Tokyo · RIKEN
Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations
Sep 29, 2026Zhongping JiHyperbolic Learning Hyperbolic Space
CurvSpec: Adaptive Multi-Curvature Learning for Partial Relevant Video Retrieval
Sep 29, 2026Zhen Liu, Letian Li, Jinpeng Wang +4Hyperbolic 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 +2Hyperbolic Learning Propagation
BIFOLD, Germany · Technische Universität Berlin, Germany · Nanyang Technological University, Singapore +3
hyperbolix: Hyperbolic Deep Learning in JAX
Sep 23, 2026Timo Klein, Thomas Lang, Yllka Velaj +1Hyperbolic Learning Hyperbolic Space
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
HyCoSeq: Contextual Hyperbolic Representation Learning for Genomic Sequences
Sep 15, 2026Chenhao Zeng, Zhibin Pu, Shufei GeHyperbolic Learning Genome-Wide Association Study
Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China
Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics
Sep 14, 2026Daniela Vega, Paula Cárdenas, Hannah Ceballos +2Spatial Transcriptomics Spatio-Temporal Transformers
Center for Research and Formation in Artificial Intelligence Universidad de los Andes, Colombia
$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition
Sep 14, 2026Xingrun Li, Yusuke Mukuta, Xin Yang +2Representation Space Hyperbolic Learning
The University of Tokyo · Stanford University
Hyperbolic Geometry for Open-World Object Detection in Remote Sensing Imagery
Sep 10, 2026Wuzhou Li, Jiawei Zhou, Shenghang Wang +1Remote Sensing Object Detection
School of Computer Science and Artificial Intelligence, Wuhan Textile University, Wuhan 430072, China · Electronic Information School, Wuhan University, Wuhan 430072, China · Electrical and Computer Engineering, Ohio State University, Columbus, OH, USA +1
HYDRA: Hyperbolic Dynamic Representation Architecture for Kolmogorov-Arnold Networks
Aug 12, 2026Zhao Su, Yuxin Xia, Haoran Li +4Kolmogorov-Arnold Networks Hyperbolic Learning
School of Information Science and Engineering, Lanzhou University · Department of Data Science and AI, Monash University · School of Computing and Information Technology, University of Wollongong +1
HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry
Aug 12, 2026Haoran Pei, Zhao Su, Zetao Lin +6Fuzzy Hyperbolic Learning
school of Information Science and Engineering, Lanzhou University · Department of Data Science and AI, Monash University · School of Computing and Information Technology, University of Wollongong +1
Hyperbolic Multimodal Continual Learning
Aug 10, 2026Jiahong Liu, Ming Shen, Xiaohao Liu +4Hyperbolic Learning Replay-Based Continual Learning
Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China · School of Computing, National University of Singapore, Singapore · Department of Computer Science, Yale University, New Haven, CT, United States +1
H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation
Aug 7, 2026Jia Wang, Jiaming Cai, Zunying Hu +4Semi-Supervised Medical Image Segmentation Hyperbolic Learning
HyTBE: Hyperbolic Target-Background Expert Model for Cross-Domain Infrared Small Target Detection
Aug 6, 2026Aohua Li, Jin Kuang, Yubing Lu +1Infrared Small Target Detection Infrared
College of Software, Jilin University, Changchun, Jilin 130000, China · Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou, 423300, China · College of Computer Science and Technology, Jilin University, Changchun, Jilin 130012, China +1
Riemannian Deep Learning: Modules, Networks, and Geometries
Jul 21, 2026Ziheng ChenData Manifold Geometric Deep Learning
Doctoral School in Information and Communication Technology, Università di Trento
After the Euclidean Highway: Hyperbolic Expert AI as the Next Innovation
Jul 20, 2026Kwan Soo Shin, In Seok Kang, Munho LeeHyperbolic Learning
1*PolymathMinds Lab, Asan, Republic of Korea. · 2aSSIST University, Seoul, Republic of Korea. · 3Samsung Engineering, Seoul, Republic of Korea.
A Hyperbolic Neural Closure for M1 Radiation Transfer
Jul 11, 2026Bongseok Kim, Jiahao Zhang, Johannes Krotz +3Jacobian Solar Irradiance
School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA · Department of Mathematics, Purdue University, West Lafayette, IN, USA · Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA +2
HiHR: Hierarchical Hyperbolic Representation for Aerial-Ground Person Re-Identification
Jul 10, 2026Qiwei Yang, Pingping ZhangRe-Identification Cross-View Fusion
Dalian University of Technology, Dalian, China
Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis
Jul 8, 2026Yapeng Li, Bo Jiang, Ziyan Zhang +2Human Brain Networks Hyperbolic Learning
School of Computer Science and Technology, Anhui University, 111 Jiulong Road, Hefei, 230601, China
Hyperbolic Neural Population Geometry Benefits Computation
Jun 8, 2026Dennis Wu, Yi-Chun Hung, Braden Yuille +2Hopfield Networks Neural Circuits
Department of Computer Science, Northwestern University · Center for Foundation Models and Generative AI, Northwestern University · Integrated Science Program, Northwestern University +3
Navigating the Emotion Tree: Hierarchical Hyperbolic RAG for Multimodal Emotion Recognition
May 16, 2026Zeheng Wang, Bo Zhao, Yijie Zhu +6Emotion Recognition Multimodal Reasoning
Great Bay University Guangdong, Dongguan, China · Tencent Youtu Lab Shanghai, China · CUHK, shenzhen Guangdong, Shenzhen, China
ECHO: Continuous Hierarchical Memory for Vision-Language-Action Models
May 9, 2026Yanbin Hu, Jin Cui, Jiayi Lu +6Generalist Vision--Language--Action Long-Horizon Manipulation
School of Software, Xi’an Jiaotong University · State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · School of Artificial Intelligence, Xi’an Jiaotong University
Hyperbolic Concept Bottleneck Models
May 7, 2026Daniel Uyterlinde, Swasti Shreya Mishra, Pascal MettesDermoscopic Concept Bottleneck Models Concept Bottleneck Models
Informatics Institute, University of Amsterdam, The Netherlands
Hyp2Former: Hierarchy-Aware Hyperbolic Embeddings for Open-Set Panoptic Segmentation
May 4, 2026Yao Lu, Rohit Mohan, Florian Drews +2Panoptic Segmentation Open-Vocabulary Object Detection
Department of Computer Science, University of Freiburg, Germany · Bosch Research, Robert Bosch GmbH, Germany
A Unified Framework of Hyperbolic Graph Representation Learning Methods
Apr 30, 2026Sofía Pérez Casulo, Marcelo Fiori, Bernardo Marenco +1Hyperbolic Learning Spherical Latent Space
Facultad de Ingenier´ıa, Universidad de la Rep´ublica, Uruguay · Centro Interdisciplinario en Ciencia de Datos y Aprendizaje Autom´atico (CICADA), Universidad de la Rep´ublica, Uruguay
Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
Apr 29, 2026Shayan Hundrieser, Insung Kong, Johannes Schmidt-HieberConvolutional Neural Networks Hyperbolic Learning
*Department of Applied Mathematics, University of Twente, Enschede, The Netherlands
HSG: Hyperbolic Scene Graph
Apr 19, 2026Liyang Wang, Zeyu Zhang, Hao Tang3D Scene Graphs Hyperbolic Learning
School of Computer Science, Peking University
Hyperbolic Enhanced Representation Learning for Incomplete Multi-view Clustering
Apr 18, 2026Tianyi Chen, Haobo Wang, Kai Tang +5Hyperbolic Learning Multi-View
School of Software Technology, Zhejiang University, Zhejiang 310027, China · College of Computer Science and Technology, Zhejiang University, Zhejiang 310027, China · Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing 100044, China +2

Oct 5, 2026, cs.LGJ/K move · Enter open · S save

The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective

Xingrun Li, Sho Kuno, Yusuke Mukuta, Xin Yang+1

The University of Tokyo · RIKEN

Hyperbolic Learning Multiclass Classification Decision Boundaries

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We study the implicit bias of Riemannian gradient flow for hyperbolic multiclass classification with fixed class prototypes in hyperbolic space

\mathbb{H}^n

. Our framework accommodates general permutation invariant relative margin (PERM) losses, a class that includes cross entropy and other standard multiclass losses. Our analysis is based on a decomposition: at large radius, the distance to each prototype splits into a radial term and a direction-dependent term described by the Busemann function. This yields two main results. First, we prove a radial dichotomy: the sign of a drift coefficient

μ

determines whether the radius is pushed toward the ideal boundary or back toward the interior; if the positive drift persists, then

r(t)=\frac{1}{2}\log t+O(1)

, while persistent negative drift returns the trajectory to the large-radius threshold in finite time. Second, we show that the boundary direction converges to a critical point of the Busemann risk on

\partial\mathbb{H}^n

. These results provide a rigorous asymptotic perspective on two phenomena we refer to as boundary saturation and near-boundary clustering in hyperbolic representation learning.

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