Group invariant machine learning by fundamental domain projections

Benjamin Aslan, Daniel Platt, David Sheard

Keywords: Group invariant, group equivariant, geometric deep learning, fundamental domain, geometric topology

TL;DR: We propose a geometric pre-processing step that renders any machine learning architecture group invariant.

Abstract: We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), in each case finding an improvement in accuracy versus others in the literature.