Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata

2025-08-21

AI Summary

This study investigates whether robust memory dynamics beyond the Toom rule exist in two-dimensional nonequilibrium systems—specifically, whether other local, noise-stable many-body mechanisms can retain initial information over thermodynamic timescales. Method: Integrating rigorous mathematical analysis, neuro-inspired cellular automata modeling, machine-learning-driven dynamical search, and interactive visualization-based validation, the work systematically characterizes the two-dimensional nonequilibrium memory phase space. Contribution/Results: We discover several original error-correction mechanisms—including fluctuation-induced stabilization of ordered phases and noise-assisted information storage—establishing novel memory paradigms. Our findings demonstrate that two-dimensional memory behavior is significantly richer than previously assumed, enabling multiple physically realizable, robust information storage protocols. To support reproducibility and exploration, we release an open-source, dynamic interactive visualization platform.

Technology Category

• Intelligent Robots: Other Foundations and Applications
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

We investigate the landscape of many-body memories: families of local non-equilibrium dynamics that retain information about their initial conditions for thermodynamically long time scales, even in the presence of arbitrary perturbations. In two dimensions, the only well-studied memory is Toom's rule. Using a combination of rigorous proofs and machine learning methods, we show that the landscape of 2D memories is in fact quite vast. We discover memories that correct errors in ways qualitatively distinct from Toom's rule, have ordered phases stabilized by fluctuations, and preserve information only in the presence of noise. Taken together, our results show that physical systems can perform robust information storage in many distinct ways, and demonstrate that the physics of many-body memories is richer than previously realized. Interactive visualizations of the dynamics studied in this work are available at https://memorynca.github.io/2D.

Problem

• Exploring non-equilibrium memories in many-body dynamics
• Investigating robust information storage under perturbations
• Discovering diverse error correction mechanisms in 2D systems

Innovation

• Machine learning discovers diverse 2D memory dynamics
• Error correction mechanisms distinct from Toom's rule
• Noise-dependent information preservation in non-equilibrium systems