Related papers: Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks

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

URL: http://arxiv.org/abs/2606.02758v1
Date: Mon, 01 Jun 2026 18:23:34 GMT
Title: Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
Abstract summary: Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers.<n>We show that each of the aforementioned layers is a special case of recently introduced admissible category-equivariant layers.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We introduce Lie groupoid equivariant neural networks as a specialization of recently proposed topological category-equivariant neural networks to the differentiable setting. Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers, and we show how for suitable Lie groupoids they are equivalent to certain Lie algebroid-equivariant neural networks. We additionally describe groupoid invariant global pooling as a generalization of group invariant global pooling. Furthermore, we show that each of the aforementioned layers is a special case of recently introduced admissible category-equivariant layers by demonstrating that they define continuous natural transformations between continuous feature functors.

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