mlsanityData to 7 Oct 2026

Clifford-Steerable Convolutional Neural Networks

arXiv 2402.14730 ↗First posted 22 Feb 2024cs.LG cs.AIcited by 24

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Abstract (arXiv)

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p, q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces ℝp,q. They cover, for instance, E(3)-equivariance on ℝ3 and Poincar'e-equivariance on Minkowski spacetime ℝ1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 40 of its 67 references that are in the map. First posted on arXiv 22 Feb 2024.

Builds on

40 of 67 references.

References · 40

  1. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  2. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  4. 2018Group Normalizationcited by 1,514
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 2019General E(2)-Equivariant Steerable CNNscited by 441
  7. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  8. 2016Steerable CNNscited by 298
  9. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  10. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  11. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  12. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
28 more
  1. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  2. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  3. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  4. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  5. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 123
  6. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  7. 2021CKConv: Continuous Kernel Convolution For Sequential Datacited by 117
  8. 2019Deep Scale-spaces: Equivariance Over Scalecited by 113
  9. 2019Scale-Equivariant Steerable Networkscited by 110
  10. 2019B-Spline CNNs on Lie Groupscited by 97
  11. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
  12. 2022Clifford Neural Layers for PDE Modelingcited by 91
  13. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  14. 2023Clifford Group Equivariant Neural Networkscited by 54
  15. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  16. 2023Geometric Algebra Transformercited by 46
  17. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  18. 2023Geometric Clifford Algebra Networkscited by 37
  19. 2022PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physicscited by 26
  20. 2019Scale Steerable Filters for Locally Scale-Invariant Convolutional Neural Networkscited by 22
  21. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  22. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  23. 2018Scale equivariance in CNNs with vector fieldscited by 20
  24. 2019Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filterscited by 18
  25. 2022Implicit Convolutional Kernels for Steerable CNNscited by 9
  26. 2020Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Seriescited by 5
  27. 2020Computing Representations for Lie Algebraic Networkscited by 3
  28. 2022Similarity Equivariant Linear Transformation of Joint Orientation-Scale Space Representationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 8; 2025: 10; 2026: 6.

24 papers.

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  1. 2024Does equivariance matter at scale?cited by 49
  2. 2024Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physicscited by 36
  3. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  4. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  5. 2025Platonic Transformers: A Solid Choice For Equivariancecited by 9
  6. 2024Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networkscited by 4
  7. 2024Learning Color Equivariant Representationscited by 4
  8. 2024TASI Lectures on Physics for Machine Learningcited by 4
  9. 2025Equivariant Neural Networks for General Linear Symmetries on Lie Algebrascited by 4
  10. 2024ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3Dcited by 3
  11. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  12. 2025Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoderscited by 3
12 more
  1. 2026Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materialscited by 3
  2. 2025AdS-GNN -- a Conformally Equivariant Graph Neural Networkcited by 2
  3. 2025GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebrascited by 2
  4. 2024On the VC dimension of deep group convolutional neural networkscited by 1
  5. 2025Flow Equivariant Recurrent Neural Networkscited by 1
  6. 2026Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AIcited by 1
  7. 2026Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentialscited by 1
  8. 2025FoGE: Fock Space inspired encoding for graph promptingcited by 0
  9. 2025Conditional Clifford-Steerable CNNs for PDE Modelingcited by 0
  10. 2026On Lie Groups Preserving Subspaces of Degenerate Clifford Algebrascited by 0
  11. 2026Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Groupcited by 0
  12. 2026Distillation of Foundation Models for Time-dependent PDEscited by 0