# World Model Science: Self-Organized Criticality, Weak Chaos, and Metastable Belief Dynamics in Long-Horizon LLM Agents

arXiv: https://arxiv.org/abs/2609.17419 · HTML: https://mlsanity.com/paper/2609.17419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 15 of 15)

- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [Measuring AI Ability to Complete Long Software Tasks](https://mlsanity.com/paper/2503.14499/) (2025)
- [Where LLM Agents Fail and How They can Learn From Failures](https://mlsanity.com/paper/2509.25370/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [Agent Drift: Quantifying Behavioral Degradation in Multi-Agent LLM Systems Over Extended Interactions](https://mlsanity.com/paper/2601.04170/) (2026)
- [SABER: Small Actions, Big Errors -- Safeguarding Mutating Steps in LLM Agents](https://mlsanity.com/paper/2512.07850/) (2025)
- [Hallucination Cascade: Analyzing Error Propagation in Multi-Agent LLM Systems](https://mlsanity.com/paper/2606.07937/) (2026)
- [Auditing Automated Evaluation, Error Propagation, and Runtime Mitigation in Tool-Using Language Agents](https://mlsanity.com/paper/2604.16706/) (2026)
- [Where Did It Go Wrong? Process-Level Evaluation of Web Agents with Semantic State Tracking](https://mlsanity.com/paper/2606.15673/) (2026)
- [When Planning Fails Despite Correct Execution: On Epistemic Calibration for LLM-Based Multi-Agent Systems](https://mlsanity.com/paper/2605.23414/) (2026)
- [Dissecting Failure Dynamics in Large Language Model Reasoning](https://mlsanity.com/paper/2604.14528/) (2026)

## Abstract (arXiv)

Long-horizon LLM agents must maintain task state across extended sequences of observations, actions, tool calls, and intermediate beliefs. We study these trajectories through three dynamical views: self-organized criticality, weak chaos, and metastable belief dynamics. Our framework aligns agent-implied states with benchmark-grounded states and measures stress accumulation, error avalanches, temporal dependence, local--global mismatch, bounded divergence, belief-basin transitions, and finite-size scaling under explicit null models. Across 22 experiments spanning controlled puzzles, tool use, embodied tasks, multi-hop retrieval, general-assistant reasoning, and Game of Life, we find that locally valid actions can persist after global state fidelity fails, stress can trigger abrupt collapse, error sequences exhibit long memory, dependency depth changes the propagation regime, and larger horizons support larger avalanches. At the same time, divergence remains bounded, belief states show metastable rather than fully chaotic behavior, and stronger claims of universal power laws, critical points, or shared intervention optima are not supported. These results suggest a science of agent world models based on trajectory-level dynamical diagnostics rather than terminal reward alone.