Learning to predict a reliable characteristic orientation of 3D point clouds is an important yet challenging problem, as unordered point clouds of the same class may have largely varying appearances. In this work, we introduce CORes, a novel method to decouple the shape geometry and semantics of the input point cloud to achieve both stability and consistency. In particular, we integrate shape-geometry-based SO(3)-equivariant learning and shape-semantics-based SO(3)-invariant residual learning, w…