Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules
cs.LG, cs.AI, math.RA
Submitted: 2026-05-19
Updated: 2026-10-12
Code: https://github.com/leanprover-community/mathlib4
Terminology
Sources
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
- Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
- Quasitubal Tensor Algebra Over Separable Hilbert Spaces
- Sufficient and Necessary Conditions for Eckart-Young like Result for Tubal Tensors
- Demystifying Tubal Tensor Algebra
- Tensor-Tensor Products, Group Representations, and Semidefinite Programming
- Representation Learning for Equivariant Inference with Guarantees
- VN-Transformer: Rotation-Equivariant Attention for Vector Neurons
- Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group
- The Lie Derivative for Measuring Learned Equivariance
- Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
- A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction
- Revisiting the Canonicalization for Fast and Accurate Crystal Tensor Property Prediction
- Efficient Equivariant High-Order Crystal Tensor Prediction via Cartesian Local-Environment Many-Body Coupling
- Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution
- A Unified Framework for Discovering Discrete Symmetries
- Bispectral Neural Networks
- The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
- Measurability and continuity of parametric low-rank approximation in Hilbert spaces: linear operators and random variables
- Representations of the symmetry groups of infinite crystals
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