Geometric Control Manifolds for Hyperbolic Self-Organizing Intelligence
Geometric Control Manifolds for Hyperbolic Self-Organizing Intelligence
We present an architectural specification resolving the Geometric Capacity Bottle-neck through precise geometric alignment between computational substrate and informationstructure. Neural dynamics within a Lorentzian hyperbolic manifold (Ln ) leverage constantnegative curvature for exponential volume growth (V ∝ eζr ). The Geometric ControlManifold (GCM) is defined as a differentiable manifold induced on the system’s statespace, characterized by joint optimization of Integration, Coherence, and Differentiation.The computational substrate consists of H-NCA on pentagrid tessellations coupled withH-AKOrN for temporal binding. Differentiable proxies (Persistence Landscapes) enableclosed-loop topological regularization.
topological data analysis, Lorentz manifold, geometric deep learning, Riemannian optimization, Hyperbolic neural networks
topological data analysis, Lorentz manifold, geometric deep learning, Riemannian optimization, Hyperbolic neural networks
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