Frequency-Histogram Coarse Graining in Elementary and 2-Dimensional Cellular Automata

2024-05-22

Nordic Machine Intelligence

AI Summary

Identifying the key computational processes driving emergent complexity in large-scale discrete dynamical systems remains a fundamental challenge. Method: We propose a multi-scale coarse-graining framework for cellular automata (CA) based on frequency histograms, integrating macrostate block clustering, statistical dimensionality reduction, and interactive visualization to efficiently characterize macroscopic behavior in both one-dimensional elementary CA and two-dimensional CA. This approach systematically reduces state-space dimensionality while preserving essential dynamical features. Contribution/Results: By unifying frequency statistics with hierarchical filtering, our method constructs interpretable coarse-graining pathways that explicitly reveal mechanisms underlying self-organization and open-ended evolution. It not only captures the formation of complex spatiotemporal structures but also establishes a novel, computationally grounded paradigm for analyzing emergence in AI systems—particularly neural cellular automata—and for modeling the evolution of general intelligence.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Machine Learning: Evolutionary Learning
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial intelligence, thanks to their propensity to support properties such as self-organization, emergence, and open-endedness. However, understanding emergent complexity in large scale systems is an open challenge. How can the important computations leading to emergent complex structures and behaviors be identified? In this work, we systematically investigate a form of dimensionality reduction for 1-dimensional and 2-dimensional cellular automata based on coarse-graining of macrostates into smaller blocks. We discuss selected examples and provide the entire exploration of coarse graining with different filtering levels in the appendix (available also digitally at this link: https://s4nyam.github.io/eca88/. We argue that being able to capture emergent complexity in AI systems may pave the way to open-ended evolution, a plausible path to reach artificial general intelligence.

Problem

• Identify key computations in emergent complex structures
• Develop dimensionality reduction for cellular automata systems
• Capture emergent complexity to enable open-ended evolution

Innovation

• Frequency-histogram coarse graining technique
• Dimensionality reduction in cellular automata
• Macrostate filtering for emergent complexity