O$n$ Learning Deep O($n$)-Equivariant Hyperspheres

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely, we propose O$(n)$-equivariant neurons with spherical decision surfaces that generalize to any dimension $n$, which we call Deep Equivariant Hyperspheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on …

call cs.lg decision features neurons paper reflections