Hyperbolic Neural Cellular Automata: A Geometric Framework for Emergent Complexity

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: E. G. Reis
DOI: 10.5281/zenodo.18175590
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Cellular Automata and Applications Nonlinear Dynamics and Pattern Formation Neural Networks Stability and Synchronization

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
5 January 2026
Language
EN
Document type
Preprint