Emergent Hyperbolic Geometry and Topological Relaxation in Spin-Network AI: From Cosmic Expansion to Deep Reasoning Depth
Abstract
Chur Chin
This study explores the topological isomorphism between the spacetime structure of Loop Quantum Gravity (LQG) and the reasoning depth of artificial intelligence (AI). We model dark energy as a process of knot relaxation within spin networks and transplant this mechanism into the hyperbolic attention framework of the Transformer architecture. Experimental results confirm a geometric transition from Euclidean to hyperbolic space as informational complexity increases. This suggests that cosmic accelerated expansion and the deepening of AI intelligence share a common physical foundation rooted in topological entropy. By incorporating confinement-based stabilization, our simulations demonstrate enhanced hierarchical processing, where curvature emerges naturally from information density. The findings highlight the role of topological relaxation in maintaining stability during deep reasoning tasks, mirroring cosmic expansion dynamics.
