Intelligence at the Edge of Chaos
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 14 of its 56 references that are in the map. First posted on arXiv 3 Oct 2024.
Builds on
14 of 56 references.
References · 14
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2023GPT-4 Technical Reportcited by 18,132
- 2020Scaling Laws for Neural Language Modelscited by 6,411
- 2022Training Compute-Optimal Large Language Modelscited by 2,927
- 2022Emergent Abilities of Large Language Modelscited by 2,483
- 2019Similarity of Neural Network Representations Revisitedcited by 1,695
- 2021A Survey of Data Augmentation Approaches for NLPcited by 408
- 2023What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuningcited by 354
- 2019Selection via Proxy: Efficient Data Selection for Deep Learningcited by 337
- 2023A Preliminary Study of the Intrinsic Relationship between Complexity and Alignmentcited by 33
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Citing papers per year: 2025: 7; 2026: 6.
13 papers.
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- 2026Training Language Models via Neural Cellular Automatacited by 15
- 2026Procedural Pretraining: Warming Up Language Models with Abstract Datacited by 10
- 2025Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoningcited by 9
- 2025Can You Learn to See Without Images? Procedural Warm-Up for Vision Transformerscited by 8
- 2025Advancing the Scientific Method with Large Language Models: From Hypothesis to Discoverycited by 7
- 2025Cognitive Activation and Chaotic Dynamics in Large Language Models: A Quasi-Lyapunov Analysis of Reasoning Mechanismscited by 1
- 2025Small Models, Smarter Learning: The Power of Joint Task Trainingcited by 1
- 2025Intuition emerges in Maximum Caliber models at criticalitycited by 0
- 2025Complexity-Regularized Proximal Policy Optimizationcited by 0
- 2026Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Trainingcited by 0
- 2026Procedural Core: A Compact Recurrent Initialization for Vision Transformerscited by 0
- 2026Lasting Effects of Abstract Pretraining Beyond Perplexitycited by 0
1 more
- 2026Bellman Meets Lyapunov: Unsupervised Reinforcement Learning via Mastering Chaos1 Oct 2026
- 2026Lasting Effects of Abstract Pretraining Beyond Perplexity30 Sep 2026
- 2026Procedural Core: A Compact Recurrent Initialization for Vision Transformers29 Sep 2026
- 2026Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Training13 Apr 2026
- 2026Training Language Models via Neural Cellular Automata9 Mar 2026
- 2026Procedural Pretraining: Warming Up Language Models with Abstract Data29 Jan 2026
- 2025Can You Learn to See Without Images? Procedural Warm-Up for Vision Transformers17 Nov 2025
- 2025Complexity-Regularized Proximal Policy Optimization24 Sep 2025
- 2025Intuition emerges in Maximum Caliber models at criticality8 Aug 2025
- 2025Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning28 May 2025
- 2025Small Models, Smarter Learning: The Power of Joint Task Training23 May 2025
- 2025Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery22 May 2025
- 2026Training Language Models via Neural Cellular Automatacited by 15
- 2026Procedural Pretraining: Warming Up Language Models with Abstract Datacited by 10
- 2025Can You Learn to See Without Images? Procedural Warm-Up for Vision Transformerscited by 8
- 2025Advancing the Scientific Method with Large Language Models: From Hypothesis to Discoverycited by 7
- 2025Small Models, Smarter Learning: The Power of Joint Task Trainingcited by 1
- 2025Intuition emerges in Maximum Caliber models at criticalitycited by 0
- 2025Complexity-Regularized Proximal Policy Optimizationcited by 0
- 2026Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Trainingcited by 0
- 2026Procedural Core: A Compact Recurrent Initialization for Vision Transformerscited by 0
- 2026Lasting Effects of Abstract Pretraining Beyond Perplexitycited by 0
- 2026Bellman Meets Lyapunov: Unsupervised Reinforcement Learning via Mastering Chaoscited by 0
- 2026Bellman Meets Lyapunov: Unsupervised Reinforcement Learning via Mastering Chaos1 Oct 2026
- 2026Lasting Effects of Abstract Pretraining Beyond Perplexity30 Sep 2026
- 2026Procedural Core: A Compact Recurrent Initialization for Vision Transformers29 Sep 2026
- 2026Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Training13 Apr 2026
- 2026Training Language Models via Neural Cellular Automata9 Mar 2026
- 2026Procedural Pretraining: Warming Up Language Models with Abstract Data29 Jan 2026
- 2025Can You Learn to See Without Images? Procedural Warm-Up for Vision Transformers17 Nov 2025
- 2025Complexity-Regularized Proximal Policy Optimization24 Sep 2025
- 2025Intuition emerges in Maximum Caliber models at criticality8 Aug 2025
- 2025Small Models, Smarter Learning: The Power of Joint Task Training23 May 2025
- 2025Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery22 May 2025