# Heavy-Tailed Memory Traces in Long-Horizon Language Agents

arXiv: https://arxiv.org/abs/2610.00010 · HTML: https://mlsanity.com/paper/2610.00010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 27 of 27)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [LongMemEval: Benchmarking Chat Assistants on Long-Term Interactive Memory](https://mlsanity.com/paper/2410.10813/) (2024)
- [Zep: A Temporal Knowledge Graph Architecture for Agent Memory](https://mlsanity.com/paper/2501.13956/) (2025)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)
- [Scale-free networks are rare](https://mlsanity.com/paper/1801.03400/) (2018)

## Abstract (arXiv)

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. Motivated by this audit, we propose Core--Tail World Model (CTWM), a rank-based memory controller that allocates prompt budget with a single exponent τ while retaining a summarized tail. On Synthetic Graph World, CTWM preserves full state and transition coverage, reduces prompt tokens by 5.9%, and lowers bottom-half tail prediction error by 13.6% relative to a graph-memory baseline. The same paired comparison gives consistent token savings on ALFWorld and a 24.48% token reduction on LongMemEval with aggregate accuracy parity. These results suggest that heavy-tailed memory traces are not only a diagnostic of finite retrieval, but also a practical control signal for token-efficient agent world models.