Equivariant Representation Learning

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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.

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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.

Physical structure as an organizing principle for universal Hamiltonian learning
Oct 26, 2026Mingkang Liu, Zhanghao Zhouyin, Guanghui Wang +3Computational Materials Science Physics-Informed ML
Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore · Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada +4
Asymmetry Tunneling Beyond Adaptive Equivariance Relaxation
Oct 21, 2026Eunho Jeong, Joon Jang, Hyeonjin KimEquivariant Neural Networks Equivariant Representation Learning
Seoul National University.
Inducing Fourier Geometry: A Smoothness Prior Imposes Approximate Translation Equivariance in Multimodal Stellar Embeddings
Oct 16, 2026Ilay Kamai, Alex M. Bronstein, Hagai B. PeretsGeometric Representation Learning Equivariant Representation Learning
Technion - Israel Institute of Technology · ISTA - Institute of Science and Technology Austria
SIEVE: Overcoming Topological Obstruction in Equivariant Self-Supervised Learning
Oct 15, 2026Jongann Lee, Sun Woo Park, Yun Young ChoiSelf-Supervised Point Cloud Learning Point Cloud Learning
Max Planck Institute of Mathematics Bonn, Germany · SolverX Seoul, Republic of Korea
Measuring Learned Equivariance: An Information Theoretic Approach
Oct 12, 2026Claire Schlesinger, Wolfgang Gatterbauer, Robin WaltersEquivariant Representation Learning
Khoury College of Computer Sciences Northeastern University Boston, MA 02115, USA
Intrinsic Geometry Matching: learning observation-equivariant process geometry
Oct 12, 2026Manuel Lecha, Michael Bronstein, Iolo JonesGeometric Representation Learning Equivariant Representation Learning
AITHYRA · University of Oxford
How Do Transformers Learn to Represent Symmetries?
Oct 7, 2026Eduardo Santos-Escriche, Valerie Engelmayer, Ya-Wei Eileen Lin +1Invariant Representation Learning Transformer
Technical University of Munich Munich Center for Machine Learning · Massachusetts Institute of Technology
PEACE: Covariant learning of nonadiabatic manifolds with parity-resolved Hamiltonians
Oct 7, 2026Rongzhi Gao, Shuguang Chen, Yang Zhou +3Molecular Dynamics Simulation Quantum Chemistry
Department of Chemistry, The University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China · Hong Kong Quantum AI Lab, Pak Shek Kok, Hong Kong SAR, China · MattVerse Limited, Pak Shek Kok, Hong Kong SAR, China +1
Symmetry-Aware Feature Learning: A Polynomial Separation for Multi-Index Models
Oct 6, 2026Jivan Waber, Vanessa Piccolo, Yatin Dandi +1Representation Learning Data Augmentation
Information, Learning and Physics Laboratory École Polytechnique Fédérale de Lausanne (EPFL) · Statistical Physics of Computation Laboratory École Polytechnique Fédérale de Lausanne (EPFL)
REViT-v2: Hierarchical Windowed Roto-reflection Equivariant ViT for Equivariant Feature Extraction
Oct 6, 2026Sheir A. Zaheer, Jihwan Moon, Chan Y. ParkVision Transformer Equivariant Neural Networks
KC Machine Learning Lab, Rep. of Korea · NFOCZ Inc and Seoul National University, Rep. of Korea
From Isolated Feature to Orbits: Discovering Music Concepts via Multi-SAE Alignment
Oct 1, 2026Liwei Lin, Gus XiaRepresentation Learning Sparse Autoencoders
Computer Science Department, NYU Shanghai · Machine Learning Department, MBZUAI
Reformulation-Contrastive Learning for Mixed Integer Programs
Sep 30, 2026Ousema Bouaneni, Mathis Le Bail, Clément Elliker +2Contrastive Learning Representation Learning
LIX (École Polytechnique, IP Paris, CNRS) · AMIAD (Agence Ministérielle pour l’IA de Défense)
Gauge-Equivariant Attention for Rotation-Stable $360^\circ$ Scene Understanding
Sep 23, 2026Tianjian Zhou, Yishan Li, Jie Jiang +13D Scene Understanding Equivariant Representation Learning
National University of Defense Technology (NUDT), Changsha, China · Northwestern Polytechnical University, Xi’an, China
Graded Representation Theory of Equivariant Neural Networks
Sep 22, 2026Mani ShayestehfarEquivariant Neural Networks Equivariant Representation Learning
BiRoAD: Learning Shared and Role-Adaptive Representations for Bimanual Manipulation
Sep 20, 2026Yan Shen, Yuchen Liu, Feng Jiang +5Representation Learning Bimanual Robotic Manipulation
CFCS, School of Computer Science, Peking University
Physically Typed and Geometry-Aware Representations for Earth Foundation Models
Sep 12, 2026Rajiv RanjanGeospatial Foundation Models Geospatial Representation Learning
Plaksha University
Equivariance Breaks the Learning Rate
Sep 8, 2026Andrei Manolache, Mathias NiepertEquivariant Neural Networks Equivariant Representation Learning
University of Stuttgart, Germany · Bitdefender, Romania
ModularPhaseNet: Finite-Cyclic Phase Geometry for Computable Semantic Hierarchy, Direction, and Context Consistency in Standard Transformers
Sep 5, 2026Kiyotaka Kasubuchi, Kazuo FukiyaTransformer Transformer Attention
Pix2Rep-v2: Data-Efficient Representation Learning for Dense Medical Imaging Applications
Sep 1, 2026S. Sifaoui, E. Angelini, S. Toupin +2Representation Learning Visual Representation Learning
LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France · MIRACL.ai Laboratory, Hôpital Universitaire Lariboisière (AP-HP), Paris, France · Université Paris Cité, Inserm MASCOT, Paris, France
Rotational Equivariance in Machine Learning: A Comprehensive Tutorial
Aug 31, 2026Peter Lippmann, Fred A. HamprechtEquivariant Neural Networks Geometric Representation Learning
Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, 69120 Heidelberg, Germany
Inherent Trade-offs when Enforcing Correct Data Symmetries in Multi-head Self-attention
Aug 31, 2026Tīkun Ông, Georg BökmanAttention Head Analysis Equivariant Neural Networks
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
Real-Valued Hyperdimensional Sequence Representations with Hadamard Product Binding and Shift Equivariance
Aug 28, 2026Kenny Schlegel, Dmitri A. Rachkovskij, Denis Kleyko +3Positional Encoding Hyperdimensional Computing
Chemnitz University of Technology, Germany · Luleå University of Technology, Sweden · Örebro University, Sweden +2
Exploring the Design Space of Representation Learning for Audio Transformations
Aug 28, 2026Sungho Lee, Marco Martínez-Ramírez, Junghyun Koo +3Audio Representation Learning Equivariant Representation Learning
Department of Intelligence and Information, Seoul National University, Seoul, South Korea · Sony AI, Tokyo, Japan · Sony Group Corporation, Tokyo, Japan
From Symmetry to Invariance: Learning Galois Equivalent Representations in Finite Fields
Aug 23, 2026Zheng Zhang, Na ZhangInvariant Representation Learning Equivariant Representation Learning
Department of Mathematics, Towson University, 7800 York Rd, Towson, MD 21204, USA
Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning
Aug 21, 2026Blaise Delaney, Dominic Dootson, Juan Jose Juan Castella +5Electrocardiogram Representation Learning Self-Supervised Time Series Representation Learning
TimeTrace Labs · University of Cambridge · University of Oxford +1
Boosting Data Augmentation with Stochastic Weight Averaging
Aug 14, 2026Longde Huang, Axel Flinth, Jan E. GerkenData Augmentation Equivariant Representation Learning
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden. · Department of Mathematics and Mathematical Statistics, Umeå University, Linnéus väg 49, 901 87 Umeå, Sweden.
Reducing Symmetry Increase in Equivariant Neural Networks
Aug 12, 2026Ning Lin, Jiacheng Cen, Anyi Li +2Equivariant Neural Networks Equivariant Representation Learning
Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China
Equivariant Music Transformer
Aug 4, 2026Zixun Guo, Simon DixonRepresentation Learning Transformer
Centre for Digital Music, Queen Mary University of London, United Kingdom
Generator-Aligned Representation Interfaces for Diagnostic Soft Equivariance
Jul 28, 2026Weitao Li, Gong ChengEquivariant Neural Networks Equivariant Representation Learning
School of Mathematical Sciences Tongji University Shanghai 200092, China · School of Mathematical Sciences Key Laboratory of Intelligent Computing and Applications (Ministry of Education) Tongji University Shanghai 200092, China

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Physical structure as an organizing principle for universal Hamiltonian learning

Mingkang Liu, Zhanghao Zhouyin, Guanghui Wang, Daye Zheng+2

Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore · Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada+4

Computational Materials Science Physics-Informed ML Quantum Chemistry Materials Property Prediction Equivariant Representation Learning

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Density functional theory (DFT) gives the electronic structure of materials, but its cost limits large-supercell calculations and materials screening. Machine-learned Hamiltonians bypass the self-consistent cycle but are usually system-specific; universal ones could cover new compositions and disordered solids. Such models must generalize across chemistry and keep downstream properties physical, while staying inexpensive for large cells. Here we introduce UniTB, a universal E(3) equivariant Hamiltonian representation framework that integrates physical priors rooted in density-functional tight-binding theory with deep learning. UniTB's network, which corrects a prior Hamiltonian, generalizes across chemistry through a mixture of experts routed by that prior and a charge-equilibration head as in self-consistent-charge tight binding. A projection bounds band shifts from the prior, suppressing spurious states and keeping downstream properties physical. We provide the fastest SO(2) tensor-product GPU kernels for the network. The variant UniTB-Flash assembles its prior from two-center tables at

O(N)

cost for

N

atoms, against

O(N\log N)

on a grid. Trained on 29,242 crystals, UniTB reaches a 0.48 meV matrix-element error on nonmagnetic test crystals spanning 68 elements. Without amorphous training data, both models agree with DFT optics and conductivity of amorphous Ge-Sb-Te. UniTB-Flash ranks candidates with no significant difference from UniTB, whose property values are more accurate; together they screen 16,195 crystals for five application domains of industrial relevance.