Heavy-Tailed Memory Traces in Long-Horizon Language Agents

Language agents that operate over extended periods increasingly rely on external memory to model their environment, yet evaluations typically focus only on task success rates or token consumption. The study argues that the distribution of memory usage warrants closer scrutiny. In constrained contexts with repeated retrievals, information tends to cluster in a small core, while infrequent states populate a long tail that accumulates prediction errors. By auditing this tail carefully, the authors show that the concentration is reproducible and depends on the agent’s policy. Random‑walk agents produce retrieval patterns that fit a log‑normal distribution, whereas language models with semantic policies exhibit core‑tail traces better described by a truncated power law. Building on these findings, the authors propose the Core‑Tail World Model (CTWM) memory controller, which allocates prompt budget using a single exponent and maintains a summary of the tail. In the synthetic Graph World environment, CTWM fully covers states and transitions, reduces token usage by 5.9 % and cuts prediction error in the lower half of the tail by 13.6 % compared with a graph‑based memory model. Similar results appear in ALFWorld and LongMemEval, achieving a 24.48 % token reduction without sacrificing overall accuracy. This research demonstrates that heavy‑tailed memory patterns can serve as useful indicators for designing more token‑efficient agent world models, which is relevant for advancing AI applications that require prolonged reasoning while conserving computational resources.

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