mlsanityData to 14 Oct 2026

Machine-learning hidden symmetries

arXiv 2109.09721 ↗First posted 20 Sep 2021cs.LG gr-qc physics.class-phcited by 31

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Abstract (arXiv)

We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painleve metric that manifests hidden translational symmetry in the Schwarzschild metric of non-rotating black holes, as well as Hamiltonicity, modularity and other simplifying traits not traditionally viewed as symmetries.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 13 of its 25 references that are in the map. First posted on arXiv 20 Sep 2021.

Builds on

13 of 25 references.

References · 13

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2021E(n) Equivariant Graph Neural Networkscited by 965
  4. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  5. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  6. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  7. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  8. 2020Lagrangian Neural Networkscited by 398
  9. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  10. 2020AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularitycited by 144
  11. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
  12. 2020Sampling using SU(N) gauge equivariant flowscited by 84
1 more
  1. 2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 6; 2023: 9; 2024: 5; 2025: 8; 2026: 1.

31 papers.

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  1. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  2. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  3. 2022AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equationscited by 20
  4. 2022Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computingcited by 20
  5. 2024Learning Infinitesimal Generators of Continuous Symmetries from Datacited by 17
  6. 2022Simplifying Polylogarithms with Machine Learningcited by 15
  7. 2024Symmetry-Informed Governing Equation Discoverycited by 15
  8. 2025Interpretable Machine Learning in Physics: A Reviewcited by 14
  9. 2021Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learningcited by 11
  10. 2023Metalearning generalizable dynamics from trajectoriescited by 9
  11. 2023Discovering Sparse Representations of Lie Groups with Machine Learningcited by 8
  12. 2023Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6cited by 6
19 more
  1. 2023Identifying the Group-Theoretic Structure of Machine-Learned Symmetriescited by 6
  2. 2024Governing equation discovery of a complex system from snapshotscited by 6
  3. 2023Oracle-Preserving Latent Flowscited by 5
  4. 2025Scaling Up Unbiased Search-based Symbolic Regressioncited by 5
  5. 2023The R-mAtrIx Netcited by 4
  6. 2021Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networkscited by 3
  7. 2022Data Science and Machine Learning in Educationcited by 3
  8. 2025Discovering Symmetry Groups with Flow Matchingcited by 3
  9. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  10. 2023Representation Learning in a Decomposed Encoder Design for Bio-inspired Hebbian Learningcited by 2
  11. 2025Learning finite symmetry groups of dynamical systems via equivariance detectioncited by 2
  12. 2022Machine-Learning the Classification of Spacetimescited by 1
  13. 2022Learning Linear Symmetries in Data Using Moment Matchingcited by 1
  14. 2024Scalable learning of potentials to predict time-dependent Hartree-Fock dynamicscited by 1
  15. 2025Do Two AI Scientists Agree?cited by 1
  16. 2025Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approachcited by 1
  17. 2025Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AIcited by 1
  18. 2025Deep Learning based discovery of Integrable Systemscited by 0
  19. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0