mlsanityData to 7 Oct 2026

Geometric Clifford Algebra Networks

arXiv 2302.06594 ↗First posted 13 Feb 2023cs.LG cs.AI cs.CVcited by 37

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Abstract (arXiv)

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable textitgeometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 74 of its 130 references that are in the map. First posted on arXiv 13 Feb 2023.

Builds on

74 of 130 references.

References · 74

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50 most cited of 74 All 74 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 10; 2024: 11; 2025: 9; 2026: 7.

37 papers.

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  1. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  2. 2023Clifford Group Equivariant Neural Networkscited by 54
  3. 2024Does equivariance matter at scale?cited by 49
  4. 2023Geometric Algebra Transformercited by 46
  5. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  6. 2024Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physicscited by 36
  7. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  8. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  9. 2023AI Foundation Models for Weather and Climate: Applications, Design, and Implementationcited by 19
  10. 2023MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modelingcited by 14
  11. 2023Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networkscited by 12
  12. 2023Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogatescited by 9
25 more
  1. 2024Generating Highly Designable Proteins with Geometric Algebra Flow Matchingcited by 7
  2. 2025GAGrasp: Geometric Algebra Diffusion for Dexterous Graspingcited by 7
  3. 2024Differentiable and Learnable Wireless Simulation with Geometric Transformerscited by 5
  4. 2023Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networkscited by 4
  5. 2024Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networkscited by 4
  6. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  7. 2025Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learningcited by 3
  8. 2026Ananke: Contractive Torus Attractor Networkscited by 2
  9. 2024Randomized Geometric Algebra Methods for Convex Neural Networkscited by 1
  10. 2024Fully tensorial approach to hypercomplex-valued neural networkscited by 1
  11. 2024Geometric Algebra Meets Large Language Models: Instruction-Based Transformations of Separate Meshes in 3D, Interactive and Controllable Scenescited by 1
  12. 2026Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentialscited by 1
  13. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  14. 2024STAResNet: a Network in Spacetime Algebra to solve Maxwell's PDEscited by 0
  15. 2025Fast Clifford Neural Layerscited by 0
  16. 2025FoGE: Fock Space inspired encoding for graph promptingcited by 0
  17. 2025Conditional Clifford-Steerable CNNs for PDE Modelingcited by 0
  18. 2025Geometric Dynamics of Consumer Credit Cycles: A Multivector-based Linear-Attention Framework for Explanatory Economic Analysiscited by 0
  19. 2025Interaction as Interference: A Quantum-Inspired Aggregation Approachcited by 0
  20. 2025Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifoldscited by 0
  21. 2026On Lie Groups Preserving Subspaces of Degenerate Clifford Algebrascited by 0
  22. 2026Clifford Kolmogorov-Arnold Networkscited by 0
  23. 2026A Geometric Algebra-informed NeRF Framework for Generalizable Wireless Channel Predictioncited by 0
  24. 2026Recursive Binding on a Budget: Subspace Carving in Order-p Tensor Memoriescited by 0
  25. 2026Clifford Sheaf Neural Networkscited by 0