Fast, Expressive SE$(n)$ Equivariant Networks through Weight-Sharing in Position-Orientation Space

arXiv:2310.02970v3 Announce Type: replace
Abstract: Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning …

abstract arxiv cs.lg edge framework functions math.gr networks notion space spaces theory through type