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.

翻译：本研究通过探究基于规则的系统复杂性如何影响训练用于预测这些规则的模型能力，来探索人工系统中智能行为的涌现。我们的研究聚焦于基本元胞自动机（ECA），这是一种简单而强大的一维系统，能够产生从平凡到高度复杂的行为。通过在不同的ECA上训练不同的大型语言模型（LLM），我们评估了规则行为的复杂性与LLM所展现的智能之间的关系，这反映在它们在下游任务上的表现。我们的研究结果表明，具有更高复杂性的规则会导致模型展现出更强的智能，这体现在它们在推理和国际象棋走子预测任务上的表现。无论是均匀系统还是周期系统，甚至常常是高度混沌的系统，都导致了较差的下游性能，突显了一个有利于智能涌现的复杂性“最佳点”。我们推测，智能源于预测复杂性的能力，并且创造智能可能只需要接触复杂性。