Clifford Space Networks: Sub-Quadratic Non-Abelian Lie Rotor Scans for Geometric Sequence Modeling and Physical Systems

Clifford Space Networks (CSN) is a geometric deep learning framework that replaces Euclidean linear transitions with continuous, non-abelian Lie rotor scans over multivector Clifford algebras Cl(p, q). By evaluating recurrent state evolution via rational Cayley transforms on Spin(n), CSN couples sub-quadratic O(L log L) runtime with an asymmetric O(D^3) state interaction density versus O(D^2) per-step transition compute.