This research introduces H-NCA to enhance capacity and coherence in geometric systems, highlighting broad implications.
We introduce Hyperbolic Neural Cellular Automata (H-NCA), addressing the GeometricCapacity Bottleneck and Temporal Binding Problem. By situating cellular automata onhyperbolic tessellations (pentagrid {5, 4}) and integrating phase-oscillator dynamics via H-AKOrN, we achieve exponential capacity growth (∝ er ) and intrinsic temporal coherence.H-NCA is formalized as a Riemannian dynamical system with Euler discretization of naturalgradient flows on Lorentz manifolds.
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E. G. Reis (2026) studied this question.
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