mlsanityData to 14 Oct 2026

Probing Equivariance and Symmetry Breaking in Convolutional Networks

arXiv 2501.01999 ↗First posted 1 Jan 2025cs.CV cs.AI cs.LGcited by 12

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Abstract (arXiv)

In this work, we explore the trade-offs of explicit structural priors, particularly group equivariance. We address this through theoretical analysis and a comprehensive empirical study. To enable controlled and fair comparisons, we introduce textttRapidash, a unified group convolutional architecture that allows for different variants of equivariant and non-equivariant models. Our results suggest that more constrained equivariant models outperform less constrained alternatives when aligned with the geometry of the task, and increasing representation capacity does not fully eliminate performance gaps. We see improved performance of models with equivariance and symmetry-breaking through tasks like segmentation, regression, and generation across diverse datasets. Explicit textitsymmetry breaking via geometric reference frames consistently improves performance, while textitbreaking equivariance through geometric input features can be helpful when aligned with task geometry. Our results provide task-specific performance trends that offer a more nuanced way for model selection.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 56 of its 67 references that are in the map. First posted on arXiv 1 Jan 2025.

Builds on

56 of 67 references.

References · 56

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38 more
  1. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
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  3. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
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  15. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  16. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  17. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
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  19. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
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  24. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
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  26. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 91
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  28. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 73
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  30. 2024Does equivariance matter at scale?cited by 52
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50 most cited of 56 All 56 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 6.

12 papers.

  1. 2025Platonic Transformers: A Solid Choice For Equivariancecited by 10
  2. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  3. 2025Transformers Discover Molecular Structure Without Graph Priorscited by 7
  4. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  5. 2026ToolMol: Evolutionary Agentic Framework for Multi-objective Drug Discoverycited by 3
  6. 2025AdS-GNN -- a Conformally Equivariant Graph Neural Networkcited by 2
  7. 2025Learning Generalizable Shape Completion with SIM(3) Equivariancecited by 2
  8. 2026Recursive Flow Matchingcited by 1
  9. 2026Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fieldscited by 0
  10. 2026Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Spacecited by 0
  11. 2026When Does Equivariance Help? Canonical Alignment in Neural Fluid Surrogatescited by 0
  12. 2026Sample Complexity of Equivariant Reinforcement Learningcited by 0