Geometric Representation Learning

Follow this topic Ask about this topic

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

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

Rigidity-Aware Geometric Pretraining for Protein Design and Conformational Ensembles
Mar 2, 2026Zhanghan Ni, Yanjing Li, Zeju Qiu +4Protein Structure Generation Generative Modeling
University of Illinois Urbana-Champaign · University of Washington · MPI for Intelligent Systems, Tübingen +3
Social-JEPA: Emergent Geometric Isomorphism
Feb 28, 2026Youjin WangRepresentation Learning Visual Representation Learning
Renmin University of China
Hereditary Geometric Meta-RL: Nonlocal Generalization via Task Symmetries
Feb 28, 2026Paul Nitschke, Shahriar TalebiSymmetry Discovery Meta-Reinforcement Learning
P. Nitschke is with the Paulson School Of Engineering And Applied Sciences, Harvard University, Cambridge, US. · S. Talebi is with the UCLA Samueli School of Engineering and Applied Science, University of California, Los Angeles, US.
Compositional Generalization Requires Linear, Orthogonal Representations in Vision Embedding Models
Feb 27, 2026Arnas Uselis, Andrea Dittadi, Seong Joon OhNeural Representation Geometry Visual Representation Learning
Tübingen AI Center, University of Tübingen · Helmholtz · Technical University of Munich
RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs
Feb 26, 2026Haohui Jia, Zheng Chen, Lingwei Zhu +4EEG Decoding Geometric Representation Learning
Information Science and Techinology, Hokkaido University, Japan · SANKEN, The University of Osaka, Japan · Great Bay University, China +1
SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization
Feb 26, 2026Bruno Aristimunha, Ce Ju, Antoine Collas +5Geometric Representation Learning Neural Decoding
A&O, LISN, Université Paris-Saclay, CNRS, Inria TAU/NERV, France · Yneuro, France · University of San Diego, EUA +6
What Topological and Geometric Structure Do Biological Foundation Models Learn? Evidence from 141 Hypotheses
Feb 25, 2026Ihor KendiukhovNeural Representation Geometry Genomic Foundation Models
Department of Computer Science, University of Tübingen, Tübingen, Germany
IRIS-SLAM: Unified Geo-Instance Representations for Robust Semantic Localization and Mapping
Feb 21, 2026Tingyang Xiao, Liu Liu, Wei Feng +6Open-Vocabulary Semantic Mapping Simultaneous Localization and Mapping
Horizon Robotics · D-Robotics · S-Lab, Nanyang Technological University +1
Spectral Convolution on Orbifolds for Geometric Deep Learning
Feb 16, 2026Tim Mangliers, Bernhard Mössner, Benjamin HimpelGeometric Representation Learning Spectral Graph Convolution
Department of Computer Science Reutlingen University, Germany
Geometry-Preserving Neural Architectures on Manifolds with Boundary
Feb 3, 2026Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum +4Geometric Representation Learning Neural Network Approximation Theory
Los Alamos National Laboratory · Boston College
Discovering Data Manifold Geometry through Geometric Properties
Feb 2, 2026David Vigouroux, Lucas Drumetz, Ronan Fablet +1Unsupervised Representation Learning Geometric Representation Learning
ANITI, IMT Atlantique - DSD, LaTIM · IRT Saint Exupery, ANITI, Toulouse, France · IMT Atlantique, LaTIM UMR 1101 INSERM, Brest, France +5
Geometric Stability: The Missing Axis of Representations
Jan 14, 2026Prashant C. RajuRepresentational Similarity Analysis Neural Representation Geometry
GeoMotionGPT: Geometry-Aligned Motion Understanding with Large Language Models
Jan 12, 2026Zhankai Ye, Bofan Li, Yukai Jin +5Motion Representation Learning Cross-Modal Alignment
Florida State University · Texas Tech University · William & Mary University
PGOT: A Physics-Geometry Operator Transformer for Complex PDEs
Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE Solvers PDE Surrogate Modeling
National University of Defense Technology · Peking University · National University of Singapore +2
Freeze, Diffuse, Decode: Task-Aware Adaptation of Transformer Embeddings for Antimicrobial Peptide Design
Nov 28, 2025Pankhil Gawade, Adam Izdebski, Myriam Lizotte +4Representation Learning Geometric Representation Learning
Institute of AI for Health, Helmholtz Munich · School of Computation, Information and Technology, Technical University of Munich · Mila - Quebec AI institute; Univ. de Montreal +3
Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery
Nov 24, 2025Sanjeev Manivannan, Chandra Shekar LakshminarayanCross-Subject EEG Decoding MI Classification
Department of Biotechnology · Department of Data Science and Artificial Intelligence
Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
Nov 4, 2025Ronald KatendeIntrinsic Dimensionality Information Bottleneck
Department of Mathematics, Kabale University, Katuna Road, Kikungiri Hill, Kabale, 317, Uganda
eVGGT: An Efficient Geometry-Aware Vision Encoder for Visuomotor Policies
Sep 19, 2025An Dinh Vuong, Minh Nhat Vu, Ian ReidVisual Representation Learning Visuomotor Policy Learning
Department of Computer Vision, Mohammed bin Zayed University of Artificial Intelligence, UAE · AIT Austrian Institute of Technology GmbH, Austria
Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches
Dec 13, 2023Gregor Kobsik, Isaak Lim, Leif KobbeltPoint Cloud Learning Geometric Representation Learning
Visual Computing Institute, RWTH Aachen University, Germany

Mar 2, 2026J/K move · Enter open · S save

Rigidity-Aware Geometric Pretraining for Protein Design and Conformational Ensembles

Zhanghan Ni, Yanjing Li, Zeju Qiu, Bernhard Schölkopf+3

University of Illinois Urbana-Champaign · University of Washington · MPI for Intelligent Systems, Tübingen+3

Protein Structure Generation Generative Modeling Protein Design Self-Supervised Pre-Training Protein Representation Learning Geometric Representation Learning

Open paper AskPDF arXiv

Generative models have recently advanced

\textit{de novo}

protein design by learning the statistical regularities of natural structures. However, current approaches face three key limitations: (1) Existing methods cannot jointly learn protein geometry and design tasks, where pretraining can be a solution; (2) Current pretraining methods mostly rely on local, non-rigid atomic representations for property prediction downstream tasks, limiting global geometric understanding for protein generation tasks; and (3) Existing approaches have yet to effectively model the rich dynamic and conformational information of protein structures. To overcome these issues, we introduce

\textbf{RigidSSL}

(

\textit{Rigidity-Aware Self-Supervised Learning}

), a geometric pretraining framework that front-loads geometry learning prior to generative finetuning. Phase I (RigidSSL-Perturb) learns geometric priors from 432K structures from the AlphaFold Protein Structure Database with simulated perturbations. Phase II (RigidSSL-MD) refines these representations on 1.3K molecular dynamics trajectories to capture physically realistic transitions. Underpinning both phases is a bi-directional, rigidity-aware flow matching objective that jointly optimizes translational and rotational dynamics to maximize mutual information between conformations. Empirically, RigidSSL variants improve designability by up to 43% while enhancing novelty and diversity in unconditional generation. Furthermore, RigidSSL-Perturb improves the success rate by 5.8% in zero-shot motif scaffolding and RigidSSL-MD captures more biophysically realistic conformational ensembles in G protein-coupled receptor modeling.