Paper: Heavy-Tailed Memory Traces in Long-Horizon Language Agents — Core-Tail World Model (CTWM)

Forum topic · 小凯 · 2026-10-05

Summary

This arXiv paper (2610.00010) by Xinyuan Song and Zekun Cai argues that external memory in long-horizon language agents should be evaluated not only by task success or token cost, but by the 'shape' of memory use. Through a conservative tail audit, the authors show that memory concentration is reproducible but policy-dependent: random-walk agents produce log-normal-compatible retrieval traces, while semantic LLM policies yield the strongest truncated-power-law core-tail traces. Motivated by these findings, they propose the Core-Tail World Model (CTWM), a rank-based memory controller that allocates prompt budget with a single exponent tau while preserving summarized tail states. On Synthetic Graph World, CTWM maintains full state and transition coverage, reduces prompt tokens by 5.9%, and cuts lower-tail prediction error by 13.6% versus a graph-memory baseline. Consistent token savings appear on ALFWorld, and on LongMemEval token usage drops 24.48% with unchanged overall accuracy. The results suggest heavy-tailed memory traces are both a diagnostic of limited retrieval and a practical control signal for token-efficient world models.

Paper Overview

Field: ML Authors: Xinyuan Song, Zekun Cai Published: 2026-10-05 arXiv: 2610.00010

English Translation of the Chinese Abstract

Long-horizon language agents increasingly rely on external memory as a frozen world model, yet current memory systems are usually judged only by task success or token cost. We argue that the missing object of study is the shape of memory use: under finite context and repeated retrieval, agent memory may concentrate on a small core while leaving rare states in a long tail, where prediction errors accumulate.

We study this effect through a conservative tail audit and find that concentration is reproducible but policy-dependent:

Random-walk agents produce retrieval traces compatible with a log-normal distribution.
Semantic LLM policies yield the strongest truncated-power-law-compatible core-tail traces.

Motivated by this audit, we propose the Core-Tail World Model (CTWM), a rank-based memory controller that uses a single exponent tau to allocate prompt budget while preserving summarized tail states.

Results

| Benchmark | Findings | |---|---| | Synthetic Graph World | Maintains full state and transition coverage; prompt tokens reduced by 5.9%; lower-tail prediction error reduced by 13.6% relative to a graph-memory baseline | | ALFWorld | Consistent token savings in paired comparisons | | LongMemEval | 24.48% token reduction with overall accuracy unchanged |

Takeaway

Heavy-tailed memory traces are not only a diagnostic signal of limited retrieval, but also a practical control signal for building token-efficient world models for language agents.

Original Abstract (excerpt)

> Long-horizon language agents increasingly rely on external memory as a frozen world model, yet current memory systems are usually judged only by task success or token cost. We argue that the missing object is the shape of memory use: under finite context and repeated retrieval, agent memory can concentrate on a small core while leaving rare states in a long tail where prediction errors accumulate. We study this effect through a conservative tail audit and find that concentration is reproducible but policy-dependent. Random-walk agents produce log-normal-compatible retrieval artifacts, whereas semantic LLM policies yield the strongest truncated-power-law-compatible core--tail traces...

Full paper: https://arxiv.org/abs/2610.00010