Symmetry Breaking

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Overview

Symmetry breaking examines how systems that are unchanged under transformations select or develop distinct states, from structural phases in materials to features learned by neural networks. Researchers use group-theoretic analysis, equivariant models with controlled symmetry-breaking inputs or initializations, and diagnostics such as Hessian spectra to understand these changes; symmetry reduction also helps combinatorial search. Applications include crystal structure prediction, graph explanations, and learning representations that identify latent variables or generalize beyond symmetric training data. A central tension is that preserving symmetry can improve efficiency and consistency, while breaking it can enable selection and identification but may introduce arbitrary choices or instability.

Latest papers

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27 papers3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. Symmetry Breaking Is the Price of Finite Capacity

    Oct 26, 2026Maggie Chlon, Leon ChlonSymmetry Breaking

    Hassana Labs.

  2. Quantifying the failure of symmetry learning in linear diffusion models due to initialization and finite-sample effects

    Oct 26, 2026John J. Vastola, Kanaka RajanSymmetry BreakingDiffusion Models

    Department of Neurobiology, Harvard Medical School · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University

  3. Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems

    Oct 8, 2026Anna Zimmel, Fleur Hendriks, Markus Holzleitner +4Generative ModelingDynamical Systems

    ELLIS Unit, LIT AI Lab, Institute for Machine Learning, JKU Linz · Department of Mechanical Engineering, Eindhoven University of Technology · DIFFER – Dutch Institute for Fundamental Energy Research +2

  4. Eigenvalues of the Hessian in Deep Learning: The Origin of Symmetry and Its Breaking

    Oct 7, 2026Yossi ArjevaniSymmetry BreakingDeep Learning Optimization

    Yossi Arjevani

  5. Broken scale symmetries in undercomplete linear autoencoders

    Oct 2, 2026Farhad Pashakhanloo, Jacob A. Zavatone-VethNeural Network Training DynamicsSymmetry Breaking

    Center for Brain Science Harvard University · Center for Brain Science and Society of Fellows Harvard University

  6. Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurements

    Sep 11, 2026Zeyu ChenSymmetry DiscoveryQuantum Machine Learning

  7. Symmetry-Breaking De Novo Crystal Generation via Markovian Jump Diffusion

    Aug 13, 2026Van Khoa Nguyen, Alexandros KalousisSymmetry BreakingMaterials Science

    HES-SO Geneva · University of Geneva

  8. LeanCSP: A Framework for Certifying Constraint Reformulation and Solving in Lean

    Jul 30, 2026Pablo Manrique, Stefan SzeiderSymmetry BreakingFormal Verification

    Algorithms and Complexity Group TU Wien, Vienna, Austria

  9. Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks

    Jul 28, 2026Xin Xu, Siru Tao, Kaizhen TanGradient-Based AttributionSymmetry Breaking

    Carnegie Mellon University

  10. Beyond ICA: Identifiability by Symmetry Breaking

    Jul 25, 2026Pengzhou WuLatent Variable ModelsRepresentation Identifiability

    SANKEN, University of Osaka

  11. Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks

    Jul 8, 2026Marcel Kühn, Bernd RosenowReLU Neural NetworksSymmetry Breaking

    Institut für Theoretische Physik, Universität Leipzig, 04103 Leipzig, Germany · ScaDS.AI Dresden/Leipzig, Universität Leipzig, 04105 Leipzig, Germany

  12. Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry

    Jun 24, 2026Luoning Zhang, Xu Zhuang, Tianhao Wang +1Symmetry BreakingCombinatorial Optimization

    Department of Mathematics, University of California, Irvine

  13. Gated MLPs as Symmetry-Broken Rank-1 Bilinear Attention

    Jun 20, 2026Nathan BreslowMultilayer PerceptronsSymmetry Breaking

  14. Analyzing Stream Collapse in Hyper-Connections: From Diagnosis to Mitigation

    Jun 2, 2026Ekaterina Alimaskina, Gleb Molodtsov, Aleksandr BeznosikovTransformerHyper-Connections

    1MIRAI, Moscow, Russia · 2BRAIn Lab, Moscow, Russia · 3Yandex Research, Moscow, Russia +1

  15. Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway

    May 29, 2026Hee-Sung Kim, Sungyoon LeeEdge of StabilitySymmetry Breaking

    Department of Computer Science, Hanyang University, Seoul, Korea.

  16. Solving Combinatorial Counting Problems with Weighted First-Order Model Counting

    May 24, 2026Yuanhong Wang, Juhua Pu, Yuxu Zhou +2Symmetry Breaking

    School of Artificial Intelligence, Jilin University, Changchun, China · State Key Laboratory of Complex & Critical Software Environment, Beihang University, China · National Research Center for Educational Materials, China +3

  17. Feature Lottery? A Bifurcation Theory of Concept Emergence

    May 22, 2026Fuming YangDynamical SystemsRepresentation Learning

    MIT

  18. Learning Developmental Scaffoldings to Guide Self-Organisation

    May 14, 2026Milton L. Montero, Elias Najarro, Jakob Schauser +1Neural Cellular AutomataSymmetry Breaking

    IT University of Copenhagen, Denmark · University of Copenhagen, Denmark · Sakana AI, Japan

  19. Spontaneous symmetry breaking and Goldstone modes for deep information propagation

    May 14, 2026Nabil Iqbal, T. Anderson Keller, Yue Song +2Symmetry BreakingEquivariant Neural Networks

    Dept. of Mathematical Sciences, Durham University · Kempner Institute, Harvard University · College of AI, Tsinghua University +2

  20. Broken-symmetry shape discrimination on a driven Duffing ring

    May 8, 2026Kaspar Anton SchindlerDynamical SystemsSymmetry Breaking

    Sleep-Wake-Epilepsy-Center, Department of Neurology, Inselspital, Bern University Hospital, University of Bern, Bern, Switzerland

  21. Why Geometric Continuity Emerges in Deep Neural Networks: Residual Connections and Rotational Symmetry Breaking

    May 6, 2026Kyungwon Jeong, Won-Gi Paeng, Honggyo SuhSymmetry BreakingGeometric Representation Learning

    Hyntel

  22. Concurrence of Symmetry Breaking and Nonlocality Phase Transitions in Diffusion Models

    May 6, 2026Yifan F. Zhang, Fangjun Hu, Guangkuo Liu +2Diffusion TransformerSymmetry Breaking

    Department of Electrical and Computer Engineering Princeton University Princeton, NJ 08544, USA · QuEra Computing Inc. 1284 Soldiers Field Road, Boston, MA 02135, USA · JILA and Department of Physics University of Colorado Boulder Boulder, CO 80309, USA +1

  23. Rank, Head-Channel Non-Identifiability, and Symmetry Breaking: A Precise Analysis of Representational Collapse in Transformers

    Apr 26, 2026Giansalvo CirrincioneTransformer InterpretabilityRepresentation Collapse

    aLaboratoire LTI, Université de Picardie Jules Verne, Chemin du Thil, 80025 Amiens, France

  24. Continuous PT-Symmetry Breaking as a Design Variable for Giant Altermagnetic Spin Splitting

    Apr 11, 2026Kichan Chun, Gunn KimMaterials ScienceSymmetry Breaking

    Department of Physics, Sejong University, Seoul 05006, Korea

  25. Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels

    Mar 31, 2026Marcel Tomàs Bernal, Neil Rohit Mallinar, Mikhail BelkinSymmetry BreakingKernel Methods

    CFIS UPC · UC San Diego

  26. Any-Subgroup Equivariant Networks via Symmetry Breaking

    Mar 19, 2026Abhinav Goel, Derek Lim, Hannah Lawrence +2Equivariant Neural NetworksEquivariant GNNs

    MIT · TUM · Flatiron Institute

  27. Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study

    Dec 19, 2025Shengdu Chai, Chen Lin, Xinyang Dong +4Variational Monte CarloCrystal Structure Prediction

    Interdisciplinary Center for Theoretical Physics and Information Sciences (ICTPIS), Fudan University, Shanghai 200433, China · Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China · Department of Engineering, University of Oxford, Oxford OX1 4BH, UK +4