World-Model Collapse as a Phase Transition

Abstract: Water looks unchanged as it warms, then at a critical point it boils. We ask whether long-horizon language agents show an analogous transition in their implicit world models. In some parameter settings, changing state load by a small amount, or adding a single step of horizon, leaves behavior nearly unchanged; near a critical boundary, the same small change causes a sudden world collapse. We study this effect in a deterministic task family with exact per-step gold state. A large grid search over state cardinality, dependency density, horizon, branching, observation mode, and mutation rate reveals a phase diagram: a solved plateau, a narrow transition band, and a collapse floor. Per-step traces show the mechanism: world-state fidelity fails before action validity, so the agent is not merely choosing a bad action; it is acting from a corrupted world. Stronger models translate the critical boundary but do not remove the qualitative transition. These results make world-model collapse a measurable bottleneck for long-horizon agents.

• The paper demonstrates a sharp, capacity-induced collapse in long-horizon agents, revealing a plateau-transition-floor performance structure.
• The controlled experiments in structured environments isolate state cardinality and dependency density as critical parameters defining the collapse boundary.
• The analysis shows that world-model representational failures precede erroneous actions, underlining the need for enhanced diagnostic and memory architectures.

World-Model Collapse in Long-Horizon Language Agents: Evidence for a Phase Transition

Introduction

The paper "World-Model Collapse as a Phase Transition" (2606.31399) investigates a non-gradual, phase-transition-like failure mode in long-horizon LLM agents. The central claim is that task difficulty, modulated via state cardinality (sc) and dependency density (dd), does not induce a smooth decline in agent performance as typically assumed. Instead, the empirical results indicate a plateau-transition-floor structure in performance, with abrupt collapse once world-model capacity is exceeded. The authors primarily utilize the controlled "StatefulPuzzle" environment, with a fully instrumented agent loop that enables per-step analysis of world-state fidelity and action validity.

Problem Formulation and Theoretical Perspective

The study frames long-horizon agent failures using statistical physics terminology, considering sc and dd as control parameters and final task success as the order parameter. The crucial mechanistic element is that the agent's world-state representation degrades before invalid actions manifest, exposing a temporal precursor to overall plan failure. This structure is formalized via operational grid bracketing and per-step diagnostics, allowing for precise localization of the transition boundary.

Figure 1: Conceptual phase diagram for world-model collapse in the $(sc,dd)$ plane, separating solved, transition, and collapsed regimes.

Methodology

Controlled Environment Design

Three deterministic environments are constructed for isolating the effect of structural parameters:

• GraphNav: Navigation in graphs with keys/switches.
• ToolDAG: Tool-call sequencing under increasing variable namespace.
• StatefulPuzzle: The main environment, manipulating objects over rooms, containers, and items, allowing orthogonal control over sc and dd.

The key innovation is the explicit separation of world-state accuracy from action validity by exposing gold world states at each step.

Agent Architecture

A three-call Planner/Updater/Self-Diag loop maintains and updates a structured explicit world-state memory, which is critical for deconvolving representational failures from policy/execution errors.

Figure 2: Stepwise agent loop separating planning, world-state updates, and self-diagnosis under fine-grained control of stressors.

Stress Grid and Evaluation Protocol

A $4\times4$ grid on $(sc, dd)$ is evaluated, with $n=100$ episodes per cell, under fixed horizon and other nuisance parameters. The choice of axes and environment follows locked, preregistered pilot criteria ensuring monotonicity and diagnostic validity.

Numerical Results and Phase Structure

Empirical Phase Diagram

Task success heatmaps show that:

• At low sc and dd, the agent maintains near-perfect performance;
• Increasing sc, especially in conjunction with high dd, causes a sharply localized drop (transition band) to a regime of consistent failure (collapse floor);
• Increasing dd at fixed sc only induces collapse near the transition; away from the boundary, its effect is limited.

  Figure 3: Success-rate heatmap demonstrates plateau, transition, and collapse under systematic variation of state and dependency size.

  

  Figure 4: Cross-sectional profiles reveal the sharpness of the transition, localized to a narrow range on the sc axis.

World-model fidelity is empirically shown to decay before action validity, meaning the observed actions are made under an already inconsistent state, not simply as a result of transient planning noise.

Single-Axis Ablations

The role of secondary factors is systematically evaluated:

• Horizon: Acts as an enabler; insufficient $T$ can block completion, but increasing $T$ alone does not shift the critical boundary.
• Branching: Minimal effect, ruling out search-space explosion as the main failure driver.
• Observation noise: Hiding state slots (partial observability) is more damaging than adding irrelevant distractors.
• Mutation rate: Lacks coherent, directional effect; treated as descriptive.

  Figure 5: Ablations confirm the main phase boundary is insensitive to horizon, branching, and mutation except in enabling/visibility roles.

Cross-Model and Fine-Grained Analysis

Boundary Localization

Fine-grained scans along sc sharpen the critical point to $sc^\star\approx 13.5$ (claude-haiku-4-5). In contrast, no direct horizon analog is observed; $T$ modifies feasibility but not the critical world-model load boundary.

Figure 6: Critical-point analysis; the SC axis exposes a narrow transition, absent on the $T$ axis, confirming structural, not horizon-driven, collapse.

Robustness Across Foundation Models

Comparative experiments with GPT-4o-mini, GPT-4o, and Llama-3 70B show:

• The qualitative phase-structure is preserved; each model exhibits the same plateau-band-floor geometry.
• Model strength primarily translates the critical boundary outward (higher sc and dd tolerances) but does not abolish the sharp transition.

  Figure 7: Cross-model grids confirm boundary translation under increased model capability with phase diagram geometry unchanged.

Theoretical and Practical Implications

The results explicitly falsify gradual-drift models of agent failure, e.g., canonical path-deviation frameworks (Lee, 22 Feb 2026), and instead reveal a sharp capacity-induced cliff. This is analogous to statistical mechanics phase transitions but operationalized at finite grid resolution rather than in the thermodynamic limit.

The critical implication for agent-design and evaluation:

• Final step success is not diagnostic; failures are typically representational, not merely local action noise.
• Agent harnesses and memory architectures must be assessed not only for total score but for when ($\tau_W$) the world model loses coherence.
• Structured and externalized memory mechanisms, planner/memory hybrids, and explicit causal state tracking are the most direct targets for extending world-model capacity.

Future research should integrate per-step instrumentation of world-state fidelity, avoid conflating structural and horizon/branching stressors, and employ controlled grids to complement ecological benchmarks. Scaling or scaffolding that merely increases context length without state support is insufficient for reliable long-horizon operation.

Conclusion

"World-Model Collapse as a Phase Transition" demonstrates that LLM-agent failures in long-horizon tasks are governed by an abrupt, quantifiable capacity boundary in their implicit world-models, not by smooth drift or local error accumulation (2606.31399). Empirical analysis in controlled settings, with multiple model families, exposes a plateau-transition-floor structure in task success with collapse first manifesting as a representational failure. Capability increases shift the boundary but do not remove it. These findings direct methodological attention toward explicit diagnostics of world-model fidelity, agent design with externalized or structured state representations, and evaluation protocols sensitive to the existence and location of structural collapse boundaries.