Long-horizon language agents are becoming increasingly important for tasks that require persistent interaction, planning, and reasoning over extended trajectories. External memory plays a central role in these agents by preserving past states, transitions, and experiences beyond the limited context window. Existing memory systems, however, are typically evaluated mainly by task success and token cost, with much less attention to how memory usage is distributed across stored information. We show that repeated retrieval can produce heavy-tailed memory usage, where a small set of states is accessed frequently while many others are rarely retrieved and more prone to prediction errors. We study this phenomenon through a systematic tail audit across retrieval policies and graph structures. We find that memory concentration is reproducible but strongly policy-dependent, ranging from log-normal-compatible patterns under random walks to truncated-power-law-compatible heavy tails under semantic LLM policies. Motivated by these findings, we propose Core-Tail Memory Controller (CTMC), a rank-based memory controller that allocates prompt budget with a single exponent $τ$ while preserving summarized information from the tail. Across Synthetic Graph World and ALFWorld, CTMC substantially reduces memory usage while preserving performance, and on LongMemEval it reduces prompt tokens by 24.48% while maintaining aggregate accuracy. These results show that heavy-tailed memory usage is both a measurable property of long-horizon agent memory and a practical signal for improving memory efficiency.
Long-horizon LLM agents must maintain and update a world model over extended sequences of observations, actions, decisions and tool calls. We study the dynamics of long horizon agents from three perspectives: self-organized criticality, weak chaos, and metastable belief dynamics. Through extensive experiments on controlled puzzles, tool-use tasks, embodied environments, multi-hop retrieval, general-assistant reasoning, and Game of Life, we study how world-model errors develop over long interactions. We find that externally increased task pressure can sharply raise the probability of collapse, while naturally occurring pressure is only a modest predictor of later failure. Errors are temporally correlated rather than independent, and their propagation changes with dependency depth while remaining bounded in finite tasks. We also find that locally valid actions can continue after the agent's overall task state has become incorrect, that error structure depends on task topology and horizon, and that belief states in embodied tasks are shallow rather than strongly trapped in incorrect states. Larger horizons allow larger error cascades, but their scale remains constrained by the task and the model's capability. Overall, we observe power-law behavior, bounded divergence consistent with weak chaos, and metastable belief dynamics across long-horizon agent interactions. We call this perspective world model science: the empirical study of self organized criticality in long-horizon agent world models.
LLM agents increasingly operate in modular systems, where planning requires coordinating multiple functional components whose actions can causally change downstream states and behaviors. This makes intervention-aware prediction essential: an agent must anticipate not only what is likely to happen next, but what will happen as a consequence of its own actions. We find that purely observational world models can incur irreducible intervention-time error in such systems, even when they accurately model observational trajectories. To address this limitation, we propose CausalCompose, a causal world-model framework that equips modular LLM agents with causal structure for intervention-aware prediction and planning. We theoretically show that causal composition can overcome this intervention gap with sufficient evidence and controlled local error. Experiments across diverse modular agent environments validate these results: incorporating causal structure consistently improves intervention-sensitive reasoning and planning, with particularly clear gains in structured tool-use systems where causal dependencies directly govern action execution. Our results show when causal world models help modular LLM agents: when causal dependencies are identifiable and actionable for planning.