Title: Exploring the Theoretical Foundations of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks

Original: arXiv:2606.02758v1 Announcement Type: Cross Abstract: This paper presents Lie groupoid equivariant neural networks, which serve as a differentiable adaptation of the recently introduced topological category-equivariant neural networks. These networks are constructed using Lie groupoid lifting convolutions and Lie groupoid convolution layers. We establish that, for appropriate Lie groupoids, these architectures are equivalent to certain Lie algebroid-equivariant neural networks. Additionally, we introduce groupoid invariant global pooling, which extends the concept of group invariant global pooling. Finally, we demonstrate that each of these layers constitutes a specific instance of the recently proposed admissible category-equivariant layers by proving that they represent continuous natural transformations between continuous feature functors.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC