Equivariant Representation Learning

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Overview

Equivariant representation learning studies how to encode data so that transformations such as rotation or translation produce corresponding, predictable changes in a model’s features. Group-equivariant convolutions, irrep-based graph networks, and equivariant transformers encode these rules directly; data augmentation and self-supervised consistency objectives can encourage them from examples, and some methods learn the transformations themselves. These representations are useful in vision, molecular and physical prediction, robotics, and audio, where they can support data efficiency and generalization across viewpoints or configurations. A central tension is balancing exact symmetry guarantees with flexibility, computational cost, and task accuracy: exact equivariance ensures consistent behavior across transformations but does not guarantee strong predictions, while softer or learned symmetry may be easier to scale but can miss important constraints.

Latest papers

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54 papers11 papers in the last four weeks, up 22% on the four weeks before. 0.1% of all new papers.

  1. GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks

    Jul 21, 2026Daniele Angioletti, Marco Nobile, Vittorio LimongelliFlow MatchingGenerative Modeling

    Faculty of Biomedical Sciences, Euler Institute, Universit´a della Svizzera italiana, 6900 Lugano, Switzerland

  2. MIDI-RAE-JEPA: Hierarchical Representation Learning and Generation for Symbolic Music

    Jul 16, 2026Scott H. HawleyRepresentation LearningSelf-Supervised Pre-Training

    Department of Chemistry & Physics, Belmont University, Nashville, TN, USA

  3. When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws

    Jul 7, 2026Fabien PollyEquivariant Neural NetworksEquivariant Representation Learning

  4. Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks

    Jul 4, 2026Yoshihiro MaruyamaGraph Neural NetworksEquivariant Neural Networks

    Department of Mathematical and Information Sciences, Kyoto University, Kyoto, Japan.

  5. A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of O(2)\mathrm{O}(2)

    Jun 26, 2026Tīkun Ông, Georg BökmanVision TransformerEquivariant Neural Networks

    Independent Researcher · University of Amsterdam

  6. Equivariant Neural Belief Propagation

    Jun 4, 2026Zehua Cheng, Wei Dai, Jiahao SunEquivariant Representation LearningFactor Graph Optimization

    Department of Computer Science, University of Oxford, Oxford, United Kingdom · FLock.io, London, United Kingdom

  7. Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group

    Jun 2, 2026Hongbo WangWorld Models for RoboticsWorld Models

    Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA

  8. SSR: Scaling Surefooted and Symmetric Humanoid Traversal to the Open World

    May 29, 2026Ruiqi Yu, Yiwen Wang, Yuan Hao +2Humanoid Robot LocomotionTerrain-Aware Robot Locomotion

    Zhejiang University

  9. On the Equivariant Learning of the QQ-tensor Order Parameter

    May 26, 2026Julia Navarro, Mark WilkinsonEquivariant Neural NetworksMaterials Science

    Nottingham Trent University, UK · Berea College, USA

  10. How the Optimizer Shapes Learned Solutions in Equivariant Neural Networks

    May 26, 2026Teodor-Mihai Stupariu, Andrei ManolacheNeural Representation GeometryNeural Network Optimization

    1Bitdefender, Romania · 2Tudor Vianu High School of Com · University of Stuttgart, Germany +1

  11. Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules

    May 19, 2026Paulina Hoyos, Shashanka Ubaru, Dongsung Huh +5Scientific DiscoverySymmetry Discovery

    UT Austin · IBM Research · Independent +2

  12. PHALAR: Phasors for Learned Musical Audio Representations

    May 5, 2026Davide Marincione, Michele Mancusi, Giorgio Strano +4Audio Representation LearningRepresentation Learning

    Department of Computer Science, Sapienza University of Rome, Italy · Moises Systems, Inc. · Paradigma, Inc.

  13. Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors

    Apr 14, 2026Feiyu Tan, Heran Yang, Qihong Duan +3Image-to-Image TranslationUnpaired Image-to-Image Translation

    School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi, P.R.China · MOE Key Lab for Intelligent Networks and Networks Security, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University, Shaanxi, P.R.China

  14. Rotation Equivariant Convolutions in Deformable Registration of Brain MRI

    Apr 9, 2026Arghavan Rezvani, Kun Han, Anthony T. Wu +2Medical Image RegistrationDeformable Image Registration

    University of California, Irvine

  15. How unconstrained machine-learning models learn physical symmetries

    Mar 25, 2026Michelangelo Domina, Joseph William Abbott, Paolo Pegolo +2Equivariant Representation LearningPhysics-Based Simulation

    Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

  16. Generalized multi-object classification and tracking with sparse feature resonator networks

    Mar 23, 2026Lazar Supic, Alec Mullen, E. Paxon FradyObject-Centric Representation LearningMulti-Object Tracking

    Redwood Center for Theoretical Neuroscience, UC Berkeley · Neuromorphic Computing Lab, Intel

  17. Disentangled Representation Learning through Unsupervised Symmetry Group Discovery

    Mar 12, 2026Barthélémy Dang-Nhu, Louis Annabi, Sylvain ArgentieriDisentangled Representation LearningUnsupervised Representation Learning

    Sorbonne Universit´e, CNRS, Institut des Syst`emes Intelligents et de Robotique, ISIR, F-75005 Paris, France

  18. 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

  19. Soft Equivariance Regularization for Invariant Self-Supervised Learning

    Mar 4, 2026Joohyung Lee, Changhun Kim, Hyunsu Kim +2Self-Supervised Visual Representation LearningEquivariant Representation Learning

    AITRICS · Voronoi Inc. · Korea Advanced Institute of Science and Technology (KAIST)

  20. Coalgebras for categorical deep learning: Representability and universal approximation

    Mar 3, 2026Dragan MašulovićEquivariant Representation LearningInvariant Representation Learning

    University of Novi Sad, Faculty of Sciences Department of Mathematics and Informatics Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia

  21. Balancing Symmetry and Efficiency in Graph Flow Matching

    Feb 20, 2026Benjamin Honoré, Alba Carballo-Castro, Yiming Qin +1Generative ModelingEquivariant GNNs

    LTS4, EPFL, Lausanne, Switzerland

  22. L-GTA: Latent Generative Modeling for Time Series Augmentation

    Jul 31, 2025Luis Roque, Vitor Cerqueira, Carlos Soares +1Variational AutoencodersSynthetic Data Augmentation

    Faculdade de Engenharia da Universidade do Porto, Porto, Portugal · University of Coimbra, Coimbra, Portugal · Fraunhofer Portugal AICOS, Portugal +1

  23. Representation Learning for Equivariant Inference with Guarantees

    May 26, 2025Daniel Ordoñez-Apraez, Vladimir Kostić, Alek Fröhlich +3Disentangled Representation LearningRepresentation Learning

    CSML, Italian Institute of Technology, Genova, Italy · Universit`a di Genova, Genova, Italy · University of Novi Sad, Novi Sad, Serbia +2

  24. NeuSE: Neural SE(3)-Equivariant Embedding for Long-Term Object-Based Simultaneous Localization and Mapping

    Mar 13, 2023Jiahui Fu, Yilun Du, Kurran Singh +2Simultaneous Localization and MappingVisual SLAM

    MIT CSAIL