María Jiménez (UC3M-ICMAT)

Groupoid equivariant neural networks: An approach for steerable CNNs on bounded domains

Thursday the 22nd of October, 2026, 14:00, Room 2.2.D08

Equivariance is a powerful inductive bias in machine learning, allowing neural networks to incorporate known symmetries of the data directly into their architecture. In this talk, we present a groupoid-based framework for constructing equivariant neural networks, in which symmetries can act locally and may have domains of definition with boundaries. We develop the mathematical framework underlying these networks using groupoid representations and introduce the notion of local rigid bisections, which provide coherent transformations between regions of the domain. We then illustrate the framework through an example involving the action groupoid of the Euclidean group on the plane, restricted to a domain with boundary. By explicitly taking the boundary structure into account, the resulting tangent-cone groupoid may have several connected components, leading to additional constraints on the structure of the equivariant channels. Joint work with prof. Alberto Ibort and prof. Juan Manuel Pérez Pardo. arXiv:2609.25987