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

In this paper, we utilize hyperspheres and regular n-The orthogonal group O(n) fully encapsulates the symmetry simplexes and propose an approach to learning deep features structure of an nD sphere, including both rotational equivariant under the transformations of nD reflections and reflection symmetries. Integrating these symmetries and rotations, encompassed by the powerful group into a model as an inductive bias is often a crucial requirement of O(n). Namely, we propose O(n)-equivariant neurons for problems in natural sciences and the respective with spherical decision surfaces that generalize to applications, e.g., molecular analysis, protein design and any dimension n, which we call Deep Equivariant assessment, or catalyst design (Rupp et al., 2012; Ramakrishnan Hyperspheres. We demonstrate how to combine them et al., 2014; Townshend et al., 2021; Jing et al., 2021; in a network that directly operates on the basis of the input Lan et al., 2022).