Discovering Symmetry Group Structures via Implicit Orthogonality Bias

arXiv:2402.17002v1 Announce Type: new
Abstract: We introduce the HyperCube network, a novel approach for autonomously discovering symmetry group structures within data. The key innovation is a unique factorization architecture coupled with a novel regularizer that instills a powerful inductive bias towards learning orthogonal representations. This leverages a fundamental theorem of representation theory that all compact/finite groups can be represented by orthogonal matrices. HyperCube efficiently learns general group operations from partially observed data, successfully recovering complete operation tables. Remarkably, the learned …

abstract architecture arxiv bias cs.lg data factorization inductive innovation key math.gr math.rt network novel representation symmetry the key theorem theory type via