mlsanityData to 7 Oct 2026

Equivariant Hamiltonian Flows

arXiv 1909.13739 ↗First posted 30 Sep 2019stat.ML cs.LGcited by 39

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Abstract (arXiv)

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt, as well as how the addition of symmetry invariance constraints can improve data efficiency and generalisation. Finally, we make connections to disentangled representation learning and show how this work relates to a recently proposed definition.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Sep 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 14; 2022: 5; 2023: 9; 2024: 5; 2025: 3; 2026: 3.

39 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2021E(n) Equivariant Normalizing Flowscited by 165
  3. 2023Equivariant flow matchingcited by 131
  4. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  5. 2023Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamicscited by 62
  6. 2023Equivariant Flow Matching with Hybrid Probability Transportcited by 59
  7. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  8. 2024Transferable Boltzmann Generatorscited by 43
  9. 2022Data-driven emergence of convolutional structure in neural networkscited by 29
  10. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  11. 2022Symmetry-Based Representations for Artificial and Biological General Intelligencecited by 26
  12. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
27 more
  1. 2021Equivariant Manifold Flowscited by 20
  2. 2021Riemannian Convex Potential Mapscited by 16
  3. 2025Space Group Equivariant Crystal Diffusioncited by 15
  4. 2023Sample Complexity of Probability Divergences under Group Symmetrycited by 13
  5. 2021Physics-aware, probabilistic model order reduction with guaranteed stabilitycited by 12
  6. 2026EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environmentscited by 12
  7. 2021Equivariant Finite Normalizing Flowscited by 11
  8. 2023Spatial Attention Kinetic Networks with E(n)-Equivariancecited by 11
  9. 2021Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descentcited by 10
  10. 2021Implicit Riemannian Concave Potential Mapscited by 10
  11. 2021The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learningcited by 9
  12. 2023Task-Equivariant Graph Few-shot Learningcited by 8
  13. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  14. 2023Symmetry Preservation in Hamiltonian Systems: Simulation and Learningcited by 6
  15. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  16. 2025HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passingcited by 5
  17. 2023Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexitycited by 4
  18. 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
  19. 2024Noether's razor: Learning Conserved Quantitiescited by 4
  20. 2021Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modelingcited by 3
  21. 2022Grassmann Manifold Flows for Stable Shape Generationcited by 3
  22. 2024Equivariant Manifold Neural ODEs and Differential Invariantscited by 2
  23. 2026SLayerGen: a Crystal Generative Model for all Space and Layer Groupscited by 2
  24. 2021Augmenting Imitation Experience via Equivariant Representationscited by 1
  25. 2022A tradeoff between universality of equivariant models and learnability of symmetriescited by 1
  26. 2025Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equationscited by 1
  27. 2026Folded Transport MCMC: Eliminating Label Switching by Sampling on a Fundamental Domaincited by 0