Symmetry Discovery

Latest papers

21 papers4 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

Learning Operators for Symmetry Discovery: From Lie Groups to Local Symmetry Geometry
Oct 12, 2026Pavan Karjol, Scindhiya Laxmi, Prathosh APSymmetry Discovery Operator Learning
Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India · Department of Mathematics and Computing, IIT (ISM) Dhanbad, India
KASALv2: Fully Automatic 3D Rotational Symmetry Classification and Axis Localization
Oct 7, 2026Mengxin Zhang, Yulin Wang, Chen Luo +2Symmetry Discovery Symmetry-Aware Object Pose Estimation
School of Mechanical Engineering, Southeast University Nanjing, China
LieDiscover: Adaptive Symbolic Library Construction for Explicit Open-form Symmetry Discovery
Sep 27, 2026Xinxin Li, Jianming Ma, Xingyu Cui +3Lie Group Methods Symmetry Discovery
East China Normal University · Shanghai Jiao Tong University · Institute of Applied Physics and Computational Mathematics +2
Discovering Symmetries in Neural Network Parameter Spaces
Sep 27, 2026Bo Zhao, Nima Dehmamy, Robin Walters +1Scientific Discovery Symmetry Discovery
Harvard University · IBM Research · Northeastern University +1
Emergent Intelligence: Resonant Oscillators Produce Proactive Adaptive Behavior
Sep 18, 2026Alex Fedosov, Maxim Yakimenko, Sander StepanovSymmetry Discovery Oscillatory Neural Networks
FoundAItion Inc · FoundAItion Inc.
Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurements
Sep 11, 2026Zeyu ChenSymmetry Discovery Quantum Machine Learning
Efficient Learning and Symmetry Discovery under Exact Invariances
Sep 7, 2026Ashkan Soleymani, Behrooz Tahmasebi, Patrick Jaillet +1Symmetry Discovery Invariant Representation Learning
MIT Laboratory for Information and Decision Systems (LIDS) · Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA · Technical University of Munich (CIT, MCML, MDSI) and MIT Computer Science and Artificial Intelligence Laboratory (CSAIL)
Adaptive Symmetry Discovery for Dynamical System Identification
Aug 8, 2026Behrooz Tahmasebi, Melanie WeberDynamical Systems Nonlinear System Identification
Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems
Aug 3, 2026Shida Liu, Abhishek Gupta, Sumit Sinha +1Stochastic Differential Equations Lie Group Methods
School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA, USA. · Tracelink, Wilmington, MA, USA. · SEAS, Physics and OEB, Harvard University, Cambridge, MA, USA.
Observable- and Positional-Encoding-Dependent Symmetry Readout from Neural Network Weights
Jul 3, 2026Naoya Chiba, Satoshi Sugiyama, Yuki UranishiNeural Representation Geometry Implicit Neural Representations
D3 Center, The Unversity of Osaka
Blind Recovery of Latent Domains via Unsupervised Symmetry Discovery
Jun 16, 2026Onur Efe, Arkadas OzakinSymmetry Discovery Inverse Problems
Physics Department, Bogazici University
Attention-based optimizer for symmetry finding
May 28, 2026Shreya Banerjee, Vinodh Raj Rajagopal Muthu, Charlie Nation +5Set Transformer Quantum Many-Body Physics
Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom · Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada · QuAOS collaboration
Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules
May 19, 2026Paulina Hoyos, Shashanka Ubaru, Dongsung Huh +5Scientific Discovery Symmetry Discovery
UT Austin · IBM Research · Independent +2
Mapping Uncharted Symmetries: Machine Discovery in Combinatorics
May 18, 2026Eugenio Cainelli, Lorenzo Luccioli, Alessandro Iraci +2Symmetry Discovery
University of Bologna · Pegaso University · University of Pisa
The Symmetries of Three-Layer ReLU Networks
May 18, 2026Johanna Marie Gegenfurtner, Moritz Grillo, Guido MontúfarParameter Identifiability ReLU Neural Networks
Technical University of Denmark · Max Planck Institute for Mathematics in the Sciences · UCLA and MPI MiS
Prism: Structural Symmetry Scanning via Duality-Constrained Laplacian Projection
May 18, 2026Jiatong XieGraph Clustering Spectral Methods
Independent researcher.
ArchSym: Detecting 3D-Grounded Architectural Symmetries in the Wild
Apr 24, 2026Hanyu Chen, Ruojin Cai, Steve Marschner +13D Scene Understanding Symmetry Discovery
Cornell University · Kempner Institute, Harvard University
Disentangled Representation Learning through Unsupervised Symmetry Group Discovery
Mar 12, 2026Barthélémy Dang-Nhu, Louis Annabi, Sylvain ArgentieriDisentangled Representation Learning Unsupervised Representation Learning
Sorbonne Universit´e, CNRS, Institut des Syst`emes Intelligents et de Robotique, ISIR, F-75005 Paris, France
Spectral Discovery of Continuous Symmetries via Generalized Fourier Transforms
Mar 7, 2026Pavan Karjol, Kumar Shubham, Prathosh APSymmetry Discovery Spectral Methods
Department of Electrical Communication Engineering , Indian Institute of Science , Bengaluru, Karnataka
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.
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

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Learning Operators for Symmetry Discovery: From Lie Groups to Local Symmetry Geometry

Pavan Karjol, Scindhiya Laxmi, Prathosh AP

Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India · Department of Mathematics and Computing, IIT (ISM) Dhanbad, India

Symmetry Discovery Operator Learning Lie Group Methods

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Continuous symmetry discovery is typically formulated as a separate estimation problem for each function or dataset. We instead investigate whether the map from a function to its symmetry structure can be learned across a family of functions from finite observations. Using the infinitesimal differential characterization of continuous symmetries, we formulate this map as an inverse symmetry operator, analogous to an inverse PDE problem. For global Lie-group symmetries, we establish a representation-theoretic population characterization: the symmetry Lie algebra is the nullspace of a positive-semidefinite operator constructed from representation coefficients and the infinitesimal group action. We also show that the inverse symmetry operator is equivariant under coordinate changes through the adjoint action. This characterization separates the geometric symmetry map from finite-sample estimation, motivating a hybrid approach that amortizes statistically difficult components while retaining analytic structure. On SO(5) benchmarks, amortized equivariant estimation of harmonic coefficients improves symmetry recovery from sparse observations, whereas ordinary least squares suffices for SL(2,R). We extend this viewpoint to local symmetries, where symmetry directions form smoothly varying tangent distributions rather than a fixed Lie algebra. Under the Lie-bracket consistency condition, Frobenius' theorem guarantees local integral submanifolds along which observables remain unchanged. We recover this geometry using a hybrid estimator that learns observation weights while preserving analytic differential and geometric recovery. Across global, non-compact, local, and physically motivated synthetic benchmarks, our results support learning the statistically difficult finite-sample components while preserving the known geometric structure of symmetry recovery.