Unifying transformers and convolutional networks as equivariant maps

Paper in proceeding, 2025

Motivated by the prevalence of equivariant machine learning models and the success of the framework of linear equivariant convolutional neural networks, we present in this work an extended framework that also includes non-linear equivariant models. More specifically, we represent these models as integral operators and derive conditions on the integrand for the operator to be equivariant. Further, we prove the generality of the proposed framework and show explicitly how common equivariant models, linear as well as non-linear, fit into the proposed formulation. This extended abstract summarises the central points of the preprint Nyholm et al. (2025), which is joint work together with Oscar Carlsson, Maurice Weiler and Daniel Persson.