Equivariant GNNs

GNN: Graph Neural Network

Equivariant graph neural networks study how to make predictions that transform consistently when inputs are rotated, translated, permuted, or changed by other symmetries. Common approaches use scalar, vector, and higher-order tensor features with message passing, spherical harmonics and tensor products, or learned geometric transport between nodes. These methods are used for molecular and materials properties, physical dynamics, protein structures, and graph tasks where respecting geometry can improve data efficiency and generalization. A central challenge is balancing expressive symmetry-aware models with their computational cost, while matching the encoded symmetries to real settings where symmetry may be broken.

Latest papers

43 papers11 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

Attention as Lattice Gauge Theory: Relations Interact Only Through Wilson Loops
Oct 27, 2026Aakash Sarkar, Ananya Mukherjee, Motoshige SatoGraph Attention Networks Equivariant GNNs
University of California, San Francisco · Brigham and Women’s Hospital
Accelerating SO(2)-Equivariant Materials Models through Low-Precision Emulation
Oct 26, 2026Denghui Lu, Alexander Maeder, Alexandros Nikolaos Ziogas +2Equivariant Neural Networks Equivariant GNNs
D-ITET, ETH Zurich, Zurich, Switzerland
SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism
Oct 21, 2026Erh-Wei Sheng, Beom Seok Kang, Yuchao Lin +2Equivariant GNNs Molecular Property Prediction
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA · Department of Chemical Engineering, National Tsing Hua University, Hsinchu 300044, Taiwan · Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
Refined Topology-Pass Scheduling: Damped Trust-Region Compensation for Dynamic k-NN Graphs in SE(3)-Equivariant Structure Prediction
Oct 13, 2026Jiankai Huang, Hanwen ShenProtein Structure Prediction k-Nearest Neighbors
Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networks
Oct 13, 2026Ali Rayat, Gia-Wei ChernEquivariant GNNs GNN Expressivity
Department of Physics, University of Virginia, Charlottesville, VA 22904, USA
LunaTP: Enabling Efficient and Scalable Tensor Product for Equivariant MLIPs
Oct 13, 2026Yuanchang Zhou, Mingzhen Li, Chen Wang +3Machine Learning Interatomic Potentials GPU Kernel Optimization
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences
NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning
Oct 7, 2026Jay L. Kaplan, Samuel Varner, Rebecca Willett +1Machine Learning Interatomic Potentials Equivariant GNNs
Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, NY 10012, USA · Department of Chemical and Biomolecular Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA · Department of Statistics, The University of Chicago, Chicago, IL 60637, USA +3
Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics
Oct 7, 2026Ridham PatelPDE Surrogate Modeling PDE Operator Learning
Indian Institute of Technology Gandhinagar, Gandhinagar, India
FlashCart: Fast Cartesian Tensor Products for Equivariant Interatomic Potentials
Oct 5, 2026Viktor Zaverkin, Payman Goodarzi, Sergey V. Sukhomlinov +4Machine Learning Interatomic Potentials GPU Kernel Optimization
INM – Leibniz Institute for New Materials · Saarland University · German Research Center for Artificial Intelligence (DFKI) +2
CrossGMN: Graph Metanetworks for Cross-Architecture Weight-Space Transformations
Oct 1, 2026Adir Dayan, Yam Eitan, Haggai MaronModel Compression Hypernetworks
Technion – Israel Institute of Technology · NVIDIA Research
Clifford Sheaf Neural Networks
Oct 1, 2026Kotaro Kamiya, Joel NichollsSheaf Neural Networks Equivariant GNNs
SyntheticGestalt KK
Multi-Attractor GNNs: Set-Valued Expressivity Beyond Unique Equilibria
Sep 28, 2026Jialin LiuGNN Expressivity Combinatorial Optimization
Edge-Level Automorphism in GNNs: A Quantitative Framework and Effective Designs For Link Prediction
Sep 28, 2026Chen Shao, Donald Loveland, Tobias Käfer +1Link Prediction GNN Expressivity
Karlsruhe Institute of Technology Karlsruhe, Germany · Department of Computer Science University of Michigan Ann Arbor, MI, USA · Computer Science & Engineering University of Michigan Ann Arbor, MI, USA
Equivariant Neural Primal-Dual Assignment for Maximum Common Edge Subgraphs
Sep 26, 2026Jiaqing Xie, Yanchao Li, Zhuo Yang +3Graph Matching Equivariant GNNs
Fudan University · Shanghai AI Lab · Shanghai Innovation Institute +2
Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs
Aug 28, 2026Alessio Borgi, Mario Severino, Fabrizio Silvestri +1Equivariant Neural Networks Sheaf Neural Networks
Department of Computer Science and Technology, University of Cambridge · Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Information Engineering, University of Padua
Alignment Matters Inside and Out in Equivariant Graph Flow Matching
Aug 27, 2026Moritz Piening, Christian WaldFlow Matching Optimal Transport
Institute of Computer Science University of Göttingen Göttingen, Germany · Institut Camille Jordan INSA Lyon Villeurbanne, France
EnsembleEGNN: Set-Based Graph Learning for Thermodynamic Ensembles of Cyclic Peptides
Jul 23, 2026Aaron L. Feller, Kris Deibler, Maxim SecorEquivariant GNNs Molecular Property Prediction
Interdisciplinary Life Sciences, University of Texas at Austin, Austin, TX. · Molecular AI, Novo Nordisk, Lexington, MA.
GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks
Jul 21, 2026Daniele Angioletti, Marco Nobile, Vittorio LimongelliFlow Matching Generative Modeling
Faculty of Biomedical Sciences, Euler Institute, Universit´a della Svizzera italiana, 6900 Lugano, Switzerland
Sobek: Streaming Equivariant Tensor Product Convolutions
Jul 20, 2026Vladimir Chorošajev, Cédric BényGPU Kernel Optimization GPU Acceleration
Cortex Discovery
Stability of Flow Models for Graph Signals
Jul 8, 2026Martin Schmidt, Gonzalo MateosGraph Signal Processing Flow Matching
Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$ -Equivariant Networks
Jul 1, 2026Chenxing Liang, Yuchao Lin, Andrii Kryvenko +5Machine Learning Interatomic Potentials Equivariant Neural Networks
Department of Computer Science and Engineering, Texas A&M University · Lambda, Inc. · Department of Materials Science and Engineering, Texas A&M University +3
Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials
Jun 28, 2026Can Polat, Erchin Serpedin, Mustafa Kurban +1Machine Learning Interatomic Potentials Equivariant GNNs
Dept. of Electrical & Computer Eng. Texas A&M Univ. College Station, TX, USA · Dept. of Prosthetics & Orthotics College of Science & Eng. Ankara Univ., Ankara, Turkey · Hamad Bin Khalifa Univ. and Texas A&M Univ. at Qatar Doha, Qatar
Equivariant Graph Neural Networks Improve Optical Spectra Prediction for Materials Screening
Jun 17, 2026Kasper Helverskov Petersen, François R J Cornet, Martin Ovesen +3Materials Property Prediction Equivariant GNNs
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark · Department of Physics, Technical University of Denmark, Kongens Lyngby, Denmark
Scalar-pathway fidelity improves physical accuracy in short-range equivariant interatomic potentials
Jun 14, 2026Jia Bi, Alin Marin Elena, Samuel PinillaMachine Learning Interatomic Potentials Equivariant GNNs
Science and Technology Facilities Council, Harwell Campus, Didcot, OX11 0QX, Oxfordshire, United Kingdom. · Science and Technology Facilities Council, Keckwick Lane, Daresbury, WA4 4AD, Cheshire, United Kingdom. · Diamond Light Source, Harwell Science and Innovation Campus,2026 Didcot, OX11 0QX, Oxfordshire, United Kingdom.
EvoStruct: Bridging Evolutionary and Structural Priors for Antibody CDR Design via Protein Language Model Adaptation
May 20, 2026Mansoor Ahmed, Sujin Lee, Umar Khayaz +1Protein Language Models Equivariant GNNs
Georgia State University, Atlanta, USA · Georgia Institute of Technology, Atlanta, USA
Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction
May 20, 2026Tilman Tröster, David Mirkovic, Veronika Oehl +1Equivariant Neural Networks Equivariant GNNs
Department of Physics ETH Zürich
Tensor Channel Equivariant Graph Neural Networks for Molecular Polarizability Prediction
May 16, 2026Jean Philip Filling, Daniel Franzen, Michael WandEquivariant GNNs Molecular Property Prediction
Institute for Computer Science, Johannes Gutenberg University Mainz, Germany
Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivariance
May 14, 2026Dongzhe Zheng, Christine Allen-BlanchetteRiemannian Metric Learning Physics-Informed GNNs
1Princeton University
QT-Net: Rethinking Evaluation of AI Models in Atomic Chemical Space
May 11, 2026Pablo Martínez Crespo, Stefano Ribes, Martin Rahm +6Graph Neural Networks Quantum Chemistry
Department of Computer Science and Engineering Chalmers University of Technology and University of Gothenburg · Department of Chemistry and Chemical Engineering Chalmers University of Technology · Technology Research Intel Corporation +3
Compact SO(3) Equivariant Atomistic Foundation Models via Structural Pruning
May 9, 2026Chen Wang, Siyu Hu, Guangming Tan +1Equivariant GNNs Structured Pruning
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences

Oct 27, 2026J/K move · Enter open · S save

Attention as Lattice Gauge Theory: Relations Interact Only Through Wilson Loops

Aakash Sarkar, Ananya Mukherjee, Motoshige Sato

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

Graph Attention Networks Equivariant GNNs

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Relations compose through the entity they share - Alice is Bob's mother and Bob is Carol's father, so Alice is Carol's grandmother - and the order matters, since a father's mother is not a mother's father; verifying a composed relation means closing the loop. We show that if each entity's coordinate frame may be rotated independently (per-entity frame freedom), three things follow. In the pure-gauge sector, relations that share no cycle cannot interact at all. The only gauge-invariant score of a triangle is a class function of its holonomy

H = T_{ij} T_{jk} T_{ki}

- a Wilson loop. And the only equivariant update of an edge is

U = Ψ(H)\, T_{ij}

with

Ψ

conjugation-equivariant. Edge attention by Wilson loops is therefore not one design among many but the unique form the symmetry permits. Three communities hold pieces of this form: the commuting-operator embeddings of knowledge graphs are its abelian (commuting) sector; AlphaFold's triangle update and the Edge Transformer have its shape - an edge updated through the third vertex - without its constraints; and lattice QCD builds it equivariantly on lattices. We instantiate the equivariant sub-family on general relational graphs as holonomy attention. With no training and composition alone, it infers unobserved

S_4

relations on sparse graphs at 0.88 with a fifth of the edges corrupted, at or slightly below specialist synchronization algorithms, where every commutative architecture is capped at 0.083; its holonomy score flags corrupted triangles at AUC 0.99 where commuting scores are capped at 0.76 by a second selection rule, and it separates clusters without labels.