Equivariant Neural Networks

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Overview

Equivariant neural networks build in known symmetries, so rotating or relabeling an input transforms the prediction in a predictable way rather than requiring the model to relearn the same pattern. Common approaches include group convolutions and steerable kernels, irreducible-representation tensor products, geometric-algebra layers, and equivariant transformers, diffusion models, and neural operators. They are used in settings where geometry or physical laws matter, including molecular modeling, fluid simulation, medical imaging, point clouds, and robotics, and are often evaluated for accuracy, data efficiency, robustness to transformations, and generalization across resolutions or domains. A central tension is choosing symmetries that match the data: exact constraints can improve reliability and efficiency, but may be too restrictive when symmetries are broken, while efficient implementations and reliable training remain important challenges.

Latest papers

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162 papers17 papers in the last four weeks, down 15% on the four weeks before. 0.1% of all new papers.

  1. Low-Rank Clebsch--Gordan Coupling for Equivariant Spherical Forecasting

    Nov 2, 2026Yaojun Li, Zhixuan Zhao, Dongzhe Zheng +1Equivariant Neural NetworksNeural Operators

    Princeton University

  2. Pair-Relative Partial Equivariance for Rotation-Robust Keypoint Descriptor Matching

    Nov 2, 2026Jongmin LeeImage MatchingEquivariant Representation Learning

    Chung-Ang University

  3. HamFormer: A Hamiltonian Flow-based SE(3)-Transformer for Conformation Optimization

    Oct 31, 2026Minjie Cheng, Zhenghao Liu, Yitian Wang +3TransformerMolecular Optimization

    Gaoling School of Artificial Intelligence, Renmin University of China · Laboratory for Human-Oriented Mobility Eco-system, École Polytechnique Fédérale de Lausanne · Beijing Key Laboratory of Research on Large Models and Intelligent Governance +1

  4. GC-LIF: Spiking Group-Equivariant Neural Network With Group-Coupled Membrane Dynamics

    Oct 29, 2026Nhan Trong Luu, Duong Trung Luu, Thang Cong TruongEquivariant Neural NetworksSpiking Neural Networks

    College of ICT, Can Tho University, Can Tho, Vietnam. · Center for Digital Transformation and Communication, Can Tho University, Can Tho, Vietnam. · Department of Computer Science and Engineering, The University of Aizu, Japan.

  5. Accelerating SO(2)-Equivariant Materials Models through Low-Precision Emulation

    Oct 26, 2026Denghui Lu, Alexander Maeder, Alexandros Nikolaos Ziogas +2Equivariant Neural NetworksEquivariant GNNs

    D-ITET, ETH Zurich, Zurich, Switzerland

  6. Relational Composition as Parallel Transport: What Per-Entity Frames Force in Attention

    Oct 26, 2026Aakash Sarkar, Ananya Mukherjee, Motoshige SatoRelational ReasoningCompositional Representation Learning

    University of California, San Francisco · Brigham and Women’s Hospital

  7. Interpretable Brain Age Prediction Using White Matter Fiber Orientation Distributions with Rotation-Equivariant Deep Learning

    Oct 26, 2026Chenyang Fan, Robert D. Sanders, Elie Matar +5Brain Age PredictionExplainable Medical Image Analysis

    School of Biomedical Engineering and Brain and Mind Centre at the University of Sydney, Sydney, NSW 2050 Australia · Brain and Mind Centre and Central Clinical School at the University of Sydney, Sydney, NSW, 2050 Australia · Department of Electronic Engineering, Chinese University of Hong Kong, Hong Kong SAR 999077, China +5

  8. Asymmetry Tunneling Beyond Adaptive Equivariance Relaxation

    Oct 21, 2026Eunho Jeong, Joon Jang, Hyeonjin KimEquivariant Neural NetworksEquivariant Representation Learning

    Seoul National University.

  9. Motion Equivariant Convolutional LSTM: When Motion Becomes a Gauge Symmetry

    Oct 20, 2026Vahid Hosseinzadeh, T. Anderson Keller, Michael PuthawalaEquivariant Neural NetworksConvolutional LSTM

    Department of Mathematics & Statistics, South Dakota State University · The Kempner Institute at Harvard University · Cusp AI

  10. Degree Bounds for Separating Polynomial and Neural Invariants for Point Clouds

    Oct 19, 2026Snir Hordan, Harm Derksen, Mircea Petrache +1Point Cloud LearningEquivariant Neural Networks

    Technion – Israel Institute of Technology · Northeastern University · Pontificia Universidad Católica de Chile

  11. Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere

    Oct 16, 2026Joshua Williamson, Niall Jeffrey, Lorne WhitewayEquivariant Neural NetworksConvolutional Neural Networks

    Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK · Department of Physics & King’s Institute for Artificial Intelligence, King’s College London, Strand, London WC2R 2LS, United Kingdom

  12. LEMON: Equivariant Learning over Attention Maps for Zero-Shot Misbehavior Monitoring on New LLMs

    Oct 15, 2026Guy Bar-Shalom, Mor Geva, Fabrizio Frasca +1LLM Safety MonitoringLLM Auditing

    Technion · Tel Aviv University · Technion, NVIDIA

  13. Interfaces and Modules: A Scalable Representation for Weight-Space Learning across Architectures

    Oct 15, 2026Michał Kozyra, Michael BronsteinWeight-Space LearningWeight-Space Analysis

    University of Oxford · AITHYRA

  14. Looped Reasoning Finishes Earlier Than You Think

    Oct 13, 2026Sumin Park, T. Konstantin RuschNeural Algorithmic ReasoningContinuous Latent Reasoning

    ELLIS Institute Tübingen · Max Planck Institute for Intelligent Systems · Tübingen AI Center +1

  15. On Making SE(2)\mathrm{SE}(2)-Invariant Networks Optimal

    Oct 12, 2026Tomas Karella, Emily Shinkle, Alice Elisabeth Anastasia Allen +3Invariant Representation LearningEquivariant Neural Networks

    CAI-3: Information Sciences Los Alamos National Laboratory · Machine Learning in Molecular Dynamics Max Planck Institute for Polymer Research · T-5: Applied Mathematics and Plasma Physics Los Alamos National Laboratory

  16. Phase-Conditioned Affordance Fields for SE(3)-Equivariant Visuomotor Policies

    Oct 12, 2026Xinzhe Chen, Liqi Huang, Sihua Ren +5Visuomotor Policy LearningRobot Learning

    National Key Laboratory of Human-Machine Hybrid Augmented Intelligence Institute of Artificial Intelligence and Robotics Xi’an Jiaotong University, Xi’an, China

  17. ASPIRE: Saddle-Point Discovery through Set Prediction and Physical Refinement

    Oct 7, 2026Yucheng Zhao, Quanyou Zhang, Shaoxiang Qin +2Set PredictionEquivariant Neural Networks

    University of Tennessee, Knoxville · McGill University

  18. REViT-v2: Hierarchical Windowed Roto-reflection Equivariant ViT for Equivariant Feature Extraction

    Oct 6, 2026Sheir A. Zaheer, Jihwan Moon, Chan Y. ParkVision TransformerEquivariant Neural Networks

    KC Machine Learning Lab, Rep. of Korea · NFOCZ Inc and Seoul National University, Rep. of Korea

  19. SO(3)-RoPE for Spherical Transformers

    Oct 5, 2026Christian Libner, Chase van de Geijn, Alexander S. Ecker +1Rotary Positional EmbeddingsTransformer

    Institute of Computer Science & CIDAS, University of Göttingen · Max Planck Institute for Dynamics and Self-Organization, Göttingen · MIT CSAIL

  20. EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization

    Oct 4, 2026Ruogu Chen, Jie HanCombinatorial OptimizationNeural Combinatorial Optimization

    Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 1H9

  21. BranchIP: Learning Adaptive Equivariant Computation for Interatomic Potentials

    Oct 1, 2026Laura Zichi, Gil Harari, Chuin Wei Tan +6Machine Learning Interatomic PotentialsEquivariant Neural Networks

    Harvard University · Robert Bosch LLC Research and Technology Center

  22. Screw Attention: Rigid-Body Algebra Inside a Transformer

    Oct 1, 2026Aly MagassoubaMultibody DynamicsEquivariant Neural Networks

    School of Computer Science, University of Nottingham, Nottingham, United Kingdom

  23. EquivDP3: A SIM(3)-Invariant Point-Cloud Encoder for Data-Efficient Humanoid Loco-Manipulation

    Sep 29, 2026Abu Hanif Muhammad Syarubany, Chang D. YooHumanoid Loco-ManipulationPoint Cloud Learning

    School of Electrical Engineering Korea Advanced Institute of Science & Technology (KAIST) Daejeon, Republic of Korea

  24. Transversal Pooling Neural Networks

    Sep 28, 2026Emily J. King, Dustin G. Mixon, Michael Perlmutter +1Tropical Cyclone Intensity ForecastingEquivariant Neural Networks

    Department of Mathematics, Colorado State University, Fort Collins, CO, USA · Department of Mathematics and Translational Data Analytics Institute, The Ohio State University, Columbus, OH, USA · Department of Mathematics, Boise State University, Boise, ID, USA +1

  25. E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPU

    Sep 28, 2026Olivier Peltre, Armand Picard, Adrien Pichard +6AI Accelerator InferenceGPU Kernel Optimization

    InstaDeep · Prima Mente

  26. Permutation-Equivariant Flow Matching for Alignment-Free Neural Weight Generation

    Sep 26, 2026Arkadi Piven, Yam Eitan, Guy Bar-Shalom +5Permutation-Equivariant Neural NetworksFlow Matching

    Technion – Israel Institute of Technology · Technical University of Munich · Munich Center for Machine Learning +1

  27. Response-state Learning for Transferable Vibrational Spectroscopic Characterization with Electron Prior

    Sep 24, 2026Zetong Li, Zhuosong Xie, Hengyu Fan +6Infrared SpectroscopyEquivariant Neural Networks

    Innovation Center for AI and Drug Discovery, School of Pharmacy, East China Normal University, Shanghai 200062, China.

  28. EMERGE: Resolution-Agnostic Point Cloud Generation with Equivariant Graph-Based Diffusion

    Sep 22, 2026Ilias Mitsouras, Nikolaos Chaidos, Giorgos Stamou +1Graph Neural NetworksEquivariant Neural Networks

    National Technical University of Athens Athens, Greece

  29. Theory for groupoid equivariant neural networks: an approach for steerable CNNs on bounded domains

    Sep 22, 2026Alberto Ibort, Maria Jimenez-Vazquez, Juan M. Perez-PardoEquivariant Neural NetworksPartial Differential Equations

    Universidad Carlos III de Madrid, ROR: 03ths8210, Departamento de Matem´aticas, Avenida de la Universidad 30 (edificio Sabatini), 28911 Legan´es (Madrid), Espa˜na. · Instituto de Ciencias Matem´aticas ICMAT (CSIC-UAM-UC3M-UCM), ROR: 05e9bn444, Campus de Cantoblanco UAM, Calle Nicol´as Cabrera 13-15, 28049 Madrid, Espa˜na.

  30. Graded Representation Theory of Equivariant Neural Networks

    Sep 22, 2026Mani ShayestehfarEquivariant Neural NetworksEquivariant Representation Learning