Hyperbolic Neural Cellular Automata: A Geometric Framework for Emergent Complexity

Key Points

• The research aims to develop a framework for addressing capacity and temporal binding limitations in neural cellular automata.
• Introduced Hyperbolic Neural Cellular Automata situated on hyperbolic tessellations.
• Integrated phase-oscillator dynamics through H-AKOrN.
• Formulated H-NCA as a Riemannian dynamical system.
• Utilized Euler discretization of natural gradient flows.
• Achieved exponential capacity growth proportional to er.
• Established intrinsic temporal coherence within the system.
• Addressed the geometric capacity bottleneck effectively.