mlsanityData to 7 Oct 2026

Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks

arXiv 2007.02005 ↗First posted 4 Jul 2020cs.LG cond-mat.dis-nn physics.comp-phcited by 30

Not on the map. Why?

Abstract (arXiv)

Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them". We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions into simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry-breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jul 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 3; 2024: 6; 2025: 6; 2026: 6.

30 papers.

Sort:

By area:

  1. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  2. 2022e3nn: Euclidean Neural Networkscited by 171
  3. 2021Geometric Deep Learning on Molecular Representationscited by 113
  4. 2022Equivariance with Learned Canonicalization Functionscited by 106
  5. 2023Geometric Clifford Algebra Networkscited by 37
  6. 2021Applications and Techniques for Fast Machine Learning in Sciencecited by 32
  7. 2022Equivariant Networks for Crystal Structurescited by 24
  8. 2023Symmetry Breaking and Equivariant Neural Networkscited by 24
  9. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 19
  10. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  11. 2021Equivariant Filters for Efficient Tracking in 3D Imagingcited by 17
  12. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 15
18 more
  1. 2025E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Productscited by 12
  2. 2022Towards out of distribution generalization for problems in mechanicscited by 11
  3. 2025Learning (Approximately) Equivariant Networks via Constrained Optimizationcited by 10
  4. 2024Equivariant Symmetry Breaking Setscited by 9
  5. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 9
  6. 2024Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Modelscited by 7
  7. 2024Relaxed Equivariant Graph Neural Networkscited by 7
  8. 2024R2Det: Exploring Relaxed Rotation Equivariance in 2D object detectioncited by 4
  9. 2025When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approachcited by 3
  10. 2024Deconstructing equivariant representations in molecular systemscited by 2
  11. 2026Spontaneous symmetry breaking and Goldstone modes for deep information propagationcited by 1
  12. 2022U(1) Symmetry-breaking Observed in Generic CNN Bottleneck Layerscited by 0
  13. 2025Energy Loss Functions for Physical Systemscited by 0
  14. 2026Cross-Chirality Generalization by Axial Vectors for Hetero-Chiral Protein-Peptide Interaction Designcited by 0
  15. 2026Any-Subgroup Equivariant Networks via Symmetry Breakingcited by 0
  16. 2026Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networkscited by 0
  17. 2026Reducing Symmetry Increase in Equivariant Neural Networkscited by 0
  18. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0