Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
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.