Constructs G-equivariant ViTs for arbitrary discrete G ≤ O(2), proves H ≤ G implies G-models embed into H-models and single-head equivariant attention realizes all ordinary G-equivariant maps, introduces D6 hexagonal model, and reports preliminary accuracy gains on PatternNet in low-data regimes.
On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including graphs and data lying on manifolds. In this paper we give a rigorous, theoretical treatment of convolution and equivariance in neural networks with respect to not just translations, but the action of any compact group. Our main result is to prove that (given some natural constraints) convolutional structure is not just a sufficient, but also a necessary condition for equivariance to the action of a compact group. Our exposition makes use of concepts from representation theory and noncommutative harmonic analysis and derives new generalized convolution formulae.
verdicts
UNVERDICTED 4representative citing papers
RGFlow uses flow-based neural networks to learn bijective real-space RG transformations for the 2D phi^4 theory, identifying a Wilson-Fisher-like critical point and estimating the correlation length exponent.
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
Velocityformer achieves 35% higher velocity correlation than linear theory by matching graph transformer inductive bias to the line-of-sight broken symmetry and conditioning on long-wavelength physics, while training efficiently on only four low-fidelity simulations.
citing papers explorer
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A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of $\mathrm{O}(2)$
Constructs G-equivariant ViTs for arbitrary discrete G ≤ O(2), proves H ≤ G implies G-models embed into H-models and single-head equivariant attention realizes all ordinary G-equivariant maps, introduces D6 hexagonal model, and reports preliminary accuracy gains on PatternNet in low-data regimes.
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Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory
RGFlow uses flow-based neural networks to learn bijective real-space RG transformations for the 2D phi^4 theory, identifying a Wilson-Fisher-like critical point and estimating the correlation length exponent.
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SurReal: Fr\'echet Mean and Distance Transform for Complex-Valued Deep Learning
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
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Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction
Velocityformer achieves 35% higher velocity correlation than linear theory by matching graph transformer inductive bias to the line-of-sight broken symmetry and conditioning on long-wavelength physics, while training efficiently on only four low-fidelity simulations.