New neural network architecture leverages Lie groupoids for differentiable settings

This paper introduces Lie groupoid equivariant neural networks, a specialized form of topological category-equivariant neural networks for differentiable settings. The proposed networks utilize Lie groupoid lifting convolutions and Lie groupoid convolution layers, which are shown to be equivalent to certain Lie algebroid-equivariant neural networks for specific Lie groupoids. Additionally, the research details groupoid invariant global pooling as a generalization of group invariant global pooling and demonstrates that these layers are special cases of admissible category-equivariant layers. AI

IMPACT Introduces a novel theoretical framework for equivariant neural networks, potentially enabling more robust models in domains with underlying symmetry.

RANK_REASON This is a research paper detailing theoretical aspects of a new neural network architecture. [lever_c_demoted from research: ic=1 ai=1.0]

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• Lie algebroid
• Lie groupoid
• Topological category-equivariant neural networks

• paper
• other

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