Geometric Representation Learning

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Overview

The field studies how to represent data whose structure is not well described by ordinary flat vectors, including point clouds, graphs, molecules, shapes, and signals. Approaches include rotation- and group-equivariant networks, learning directly on Riemannian, spherical, or hyperbolic spaces, and using geodesic distances, curvature, or spectral structure to guide training. These methods aim to preserve meaningful geometry so models can generalize across changes in viewpoint, sampling, or domain, with applications from 3D perception and robotics to biology and medical imaging. A central challenge is choosing geometry that fits the task: explicit geometric constraints can improve robustness and data efficiency, but may add computational cost or hinder downstream learning when the chosen structure is mismatched.

Latest papers

CardsList

259 papers32 papers in the last four weeks, up 7% on the four weeks before. 0.2% of all new papers.

  1. GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural Kähler Potentials

    Apr 13, 2026Abdul RahmanGeometric Representation LearningInvariant Representation Learning

  2. Training-free Spatially Grounded Geometric Shape Encoding (Technical Report)

    Apr 8, 2026Yuhang HePositional EncodingGeometric Representation Learning

    Microsoft Research

  3. LiftFormer: Lifting and Frame Theory Based Monocular Depth Estimation Using Depth and Edge Oriented Subspace Representation

    Apr 8, 2026Shuai Li, Huibin Bai, Yanbo Gao +5Depth EstimationMonocular Depth Estimation

    School of Control Science and Engineering, Shandong University, and Key Laboratory of Machine Intelligence and System Control, Ministry of Education, Jinan 250100, China. · School of Software, Shandong University, Jinan 250100, China · Shandong University-WeiHai Research Institute of Industrial Technology, Weihai 264209, China +2

  4. Let Geometry GUIDE: Layer-wise Unrolling of Geometric Priors in Multimodal LLMs

    Apr 7, 2026Chongyu Wang, Ting Huang, Chunyu Sun +3Multimodal Large Language Models3D VLMs

    Xi’an Jiaotong University · Peking University · Institute of Automation, Chinese Academy of Sciences +1

  5. MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation

    Apr 6, 2026Zhe Feng, Shilong Tao, Haonan Sun +3Deformable Object Simulation3D Mesh Deformation

    Academy for Advanced Interdisciplinary Studies, Peking University · School of Computer Science, Peking University · School of Electrical and Computer Science, University of Southampton

  6. The Geometric Alignment Tax: Tokenization vs. Continuous Geometry in Scientific Foundation Models

    Apr 5, 2026Prashant C. RajuNeural Representation GeometryGeometric Representation Learning

  7. Quantum-Inspired Geometric Classification with Correlation Group Structures and VQC Decision Modeling

    Apr 2, 2026Nishikanta Mohanty, Arya Ansuman Priyadarshi, Bikash K. Behera +1Tabular ClassificationHybrid Quantum-Classical ML

    Centre for Quantum Software and Information, University of Technology Sydney, 15 Broadway, Ultimo, Sydney, 2007, NSW, Australia. · Bikash’s Quantum (OPC) Pvt. Ltd., Balindi, Mohanpur, 741246, WB, India. · Universit`a degli Studi di Cagliari, Via Is Mirrions, Cagliari, 09123, Italy.

  8. LA-Sign: Looped Transformers with Geometry-aware Alignment for Skeleton-based Sign Language Recognition

    Mar 30, 2026Muxin Pu, Mei Kuan Lim, Chun Yong Chong +1Sign Language RecognitionRecurrent Transformers

    School of Information Technology, Monash University · S-Lab, Nanyang Technological University

  9. Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flow

    Mar 27, 2026Jicheng Ma, Yunyan Yang, Juan Zhao +1Graph Representation LearningGraph Neural Networks

    School of Mathematics, Renmin University of China, Beijing, China. · School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems of MOE, Beijing Normal University, Beijing, China.

  10. Geo2^\textbf{2}: Geometry-Guided Cross-view Geo-Localization and Image Synthesis

    Mar 26, 2026Yancheng Zhang, Xiaohan Zhang, Guangyu Sun +3Cross-View Geo-LocalizationGeospatial Representation Learning

    Institute of Artificial Intelligence, University of Central Florida · University of Vermont

  11. Patchwork: A compact representation for 3D polygonal shapes

    Mar 24, 2026Ruichen Zheng, Biao Zhang, Michael Birsak +2Geometric Representation Learning3D Representation Learning

    King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia

  12. Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence

    Mar 23, 2026Philip S. Yu, Li SunGraph Foundation ModelsGraph Representation Learning

    University of Illinois Chicago, Chicago, USA · Beijing University of Posts and Telecommunications, Beijing, China

  13. Continual Learning as Shared-Manifold Continuation Under Compatible Shift

    Mar 20, 2026Henry J. KobsContinual LearningGeometric Representation Learning

  14. Cov2Pose: Leveraging Spatial Covariance for Direct Manifold-aware 6-DoF Object Pose Estimation

    Mar 20, 2026Nassim Ali Ousalah, Peyman Rostami, Vincent Gaudillière +4Riemannian Neural NetworksObject Pose Estimation

    CVI2, Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg⋆ · Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France† · Infinite Orbits⋊ +1

  15. Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning

    Mar 20, 2026Haifang Cao, Yu Wang, Timing Li +2Ollivier-Ricci CurvatureGraph Representation Learning

    College of Intelligence and Computing, Tianjin University, Tianjin, China

  16. Manifold-Matching Autoencoders

    Mar 17, 2026Laurent Cheret, Vincent Létourneau, Isar Nejadgholi +3Multidimensional ScalingAutoencoders

    Department of Computer Science, University of Ottawa, Ottawa, Canada · MILA, Montréal, Canada · National Research Council of Canada, Ottawa, Canada

  17. RecBundle: A Next-Generation Geometric Paradigm for Explainable Recommender Systems

    Mar 17, 2026Hui Wang, Tianzhu Hu, Mingming Li +6Recommender SystemsGeometric Representation Learning

    Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · JD.com, Beijing, China · School of Cyberspace Security, University of Chinese Academy of Sciences, Beijing, China

  18. Parallelised Differentiable Straightest Geodesics for 3D Meshes

    Mar 16, 2026Hippolyte Verninas, Caner Korkmaz, Stefanos Zafeiriou +2Riemannian GeometryGeometric Representation Learning

    Imperial College London

  19. Riemannian Motion Generation: A Unified Framework for Human Motion Representation and Generation via Riemannian Flow Matching

    Mar 16, 2026Fangran Miao, Jian Huang, Ting LiHuman Motion GenerationMotion Representation Learning

    Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University · Department of Applied Mathematics, The Hong Kong Polytechnic University · Department of Data Science and Statistics, Southern University of Science and Technology

  20. Geometric and Topological Deep Learning for Predicting Thermo-mechanical Performance in Cold Spray Deposition Process Modeling

    Mar 15, 2026Akshansh MishraSurrogate ModelingManufacturing

    School of Industrial and Information Engineering, Politecnico di Milano, Milan, Italy

  21. SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization

    Mar 13, 2026Tianwei Ye, Xiaoguang Mei, Yifan Xia +3Functional MapsGeometric Representation Learning

    Wuhan University, Wuhan 430072, China

  22. LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning

    Mar 12, 2026Haiying Xu, Zihan Wang, Song Dai +3Multimodal Large Language ModelsMultimodal Reasoning

    The Hong Kong University of Science and Technology (Guangzhou) · Nankai University · Communication University of China

  23. TractoRC: A Unified Probabilistic Learning Framework for Joint Tractography Registration and Clustering

    Mar 11, 2026Yijie Li, Xi Zhu, Junyi Wang +3ClusteringDiffusion MRI

    University of Electronic Science and Technology of China, Chengdu, China · Nanjing University of Science and Technology, Nanjing, China · Harvard Medical School and Brigham and Women’s Hospital, Boston. USA

  24. Geometry-Aware Metric Learning for Cross-Lingual Few-Shot Sign Language Recognition on Static Hand Keypoints

    Mar 10, 2026Chayanin Chamachot, Kanokphan LertniponphanSign Language RecognitionCross-Lingual Transfer

    Department of Computer Engineering Faculty of Engineering, Chulalongkorn University

  25. Neural Precoding in Complex Projective Spaces

    Mar 8, 2026Zaid Abdullah, Merouane Debbah, Symeon Chatzinotas +1Wireless CommunicationsGeometric Representation Learning

    Interdisciplinary Centre for Security, Reliability, and Trust (SnT) at the University of Luxembourg, Luxembourg. · 6G Research Center, Khalifa University of Science and Technology, Abu Dhabi, UAE.

  26. SLNet: A Super-Lightweight Geometry-Adaptive Network for 3D Point Cloud Recognition

    Mar 8, 2026Mohammad Saeid, Amir Salarpour, Pedram MohajerAnsari +1Point Cloud LearningPoint Cloud Classification

    Sirjan University of Technology, Sirjan, Iran · Clemson University, Clemson, SC, USA

  27. LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecture

    Mar 7, 2026Erik Scheurer, Rocco Sedona, Stefan Kesselheim +1Equivariant Representation LearningGeometric Representation Learning

    Jülich Supercomputing Centre (JSC), Forschungszentrum Jülich, 52428 Jülich, Germany · Institute for Visualization and Interactive Systems (VIS), University of Stuttgart, 70569 Stuttgart · School of Engineering and Natural Sciences (SENS), University of Iceland, 102 Reykjavík, Iceland

  28. On Geometry Regularization in Autoencoder Reduced-Order Models with Latent Neural ODE Dynamics

    Mar 3, 2026Mikhail OsipovReduced-Order ModelingAutoencoders

    Independent Researcher, Italy

  29. Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework

    Mar 3, 2026Chenran Lin, Lok Ming LuiGeometric Representation Learning

    Department of Mathematics, The Chinese University of Hong Kong, Hong Kong

  30. E2E-GNet: An End-to-End Skeleton-based Geometric Deep Neural Network for Human Motion Recognition

    Mar 3, 2026Mubarak Olaoluwa, Hassen DriraSkeleton-Based Action RecognitionMotion Representation Learning

    University of Strasbourg, ICube Laboratory, UMR 7357, F-67412 Strasbourg, France