Intelligence at the Edge of Chaos
Shiyang Zhang Aakash Patel Syed A Rizvi Nianchen Liu Sizhuang He Amin Karbasi Emanuele Zappala David van Dijk
We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular automata (ECA), simple yet powerful one-dimensional systems that generate behaviors ranging from trivial to highly complex. By training distinct Large Language Models (LLMs) on different ECAs, we evaluated the relationship between the complexity of the rules' behavior and the intelligence exhibited by the LLMs, as reflected in their performance on downstream tasks. Our findings reveal that rules with higher complexity lead to models exhibiting greater intelligence, as demonstrated by their performance on reasoning and chess move prediction tasks. Both uniform and periodic systems, and often also highly chaotic systems, resulted in poorer downstream performance, highlighting a sweet spot of complexity conducive to intelligence. We conjecture that intelligence arises from the ability to predict complexity and that creating intelligence may require only exposure to complexity.
Large Language Models (LLMs), Elementary Cellular Automata (ECA), Emergent Intelligence, Complex Systems, Complexity Theory
Training Large Language Models (LLMs) on elementary cellular automata (ECA) rules shows that models exposed to more complex rule behaviors perform better on downstream tasks.