# Self-Cleaning and Captured Anyway: One Measured Primitive for Error in a Store an Agent Writes to Itself, and What a Falling Score Actually Measures

arXiv: https://arxiv.org/abs/2609.25052 · HTML: https://mlsanity.com/paper/2609.25052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 48 of its 77 references that are in the map.
- First posted on arXiv 6 Sep 2026.

## Builds on (most cited first, 30 of 48)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [AgentPoison: Red-teaming LLM Agents via Poisoning Memory or Knowledge Bases](https://mlsanity.com/paper/2407.12784/) (2024)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [Memory Injection Attacks on LLM Agents via Query-Only Interaction](https://mlsanity.com/paper/2503.03704/) (2025)
- [Measuring what Matters: Construct Validity in Large Language Model Benchmarks](https://mlsanity.com/paper/2511.04703/) (2025)
- [The Curious Decline of Linguistic Diversity: Training Language Models on Synthetic Text](https://mlsanity.com/paper/2311.09807/) (2023)
- [Large Language Models Suffer From Their Own Output: An Analysis of the Self-Consuming Training Loop](https://mlsanity.com/paper/2311.16822/) (2023)
- [How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse](https://mlsanity.com/paper/2404.05090/) (2024)
- [Chinchilla Scaling: A replication attempt](https://mlsanity.com/paper/2404.10102/) (2024)
- [Memory for Autonomous LLM Agents:Mechanisms, Evaluation, and Emerging Frontiers](https://mlsanity.com/paper/2603.07670/) (2026)
- [Beyond a Million Tokens: Benchmarking and Enhancing Long-Term Memory in LLMs](https://mlsanity.com/paper/2510.27246/) (2025)
- [STALE: Can LLM Agents Know When Their Memories Are No Longer Valid?](https://mlsanity.com/paper/2605.06527/) (2026)
- [A Survey of Agent Memory in the Second Half: Towards Self-Evolving and Long-Horizon Agents](https://mlsanity.com/paper/2602.06052/) (2026)
- [Self-Correcting Self-Consuming Loops for Generative Model Training](https://mlsanity.com/paper/2402.07087/) (2024)
- [From Agent Traces to Trust: A Survey of Evidence Tracing and Execution Provenance in LLM Agents](https://mlsanity.com/paper/2606.04990/) (2026)
- [Fluid Language Model Benchmarking](https://mlsanity.com/paper/2509.11106/) (2025)
- [Reliability without Validity: A Systematic, Large-Scale Evaluation of LLM-as-a-Judge Models Across Agreement, Consistency, and Bias](https://mlsanity.com/paper/2606.19544/) (2026)
- [Universality of the π2/6 Pathway in Avoiding Model Collapse](https://mlsanity.com/paper/2410.22812/) (2024)
- [Adaptive Memory Admission Control for LLM Agents](https://mlsanity.com/paper/2603.04549/) (2026)
- [Unable to Forget: Proactive Interference Reveals Working Memory Limits in LLMs Beyond Context Length](https://mlsanity.com/paper/2506.08184/) (2025)
- [Supersede: Diagnosing and Training the Memory-Update Gap in LLM Agents](https://mlsanity.com/paper/2606.27472/) (2026)
- [From Lossy to Verified: A Provenance-Aware Tiered Memory for Agents](https://mlsanity.com/paper/2602.17913/) (2026)
- [A Theoretical Perspective: How to Prevent Model Collapse in Self-consuming Training Loops](https://mlsanity.com/paper/2502.18865/) (2025)
- [MemMark: State-Evolution Attribution Watermarking for Agent Long-Term Memory Systems](https://mlsanity.com/paper/2605.25002/) (2026)
- [Belief Memory: Agent Memory Under Partial Observability](https://mlsanity.com/paper/2605.05583/) (2026)

## Abstract (arXiv)

"An agent that writes its conclusions into a store it later retrieves from closes a loop usually reported as one-way contamination. Taking the loop to the infinite-tenure limit against an append-only store gives a different picture: because writing never deletes, the reachable state space has a hard upper edge at (n-1)/n, so the outcome is a choice between two edges rather than a decay. At f0 = 0.9 the interval between the two modes holds 3.6% of 220 runs where a uniform spread would put 20.6%, and is strictly empty on the first 15; the pooled mean describes 8.2% of the runs it summarises, the median 68.2%. Everything the model contributes is carried by one measured primitive with no fitted parameter, the copy function γ(φ): on 36 Wikidata facts, sign(hatγ - γcrit), with γcrit = 1/k at r = 0, w = 1, predicts the direction of drift on 353 of 360 real-fact runs (39 of 40 synthetic in the same batch). Scale does not rescue the store: pooled frontier capture is 0.850, with claude-sonnet-4.5 captured on 20 of 20 seeds against our registered prediction of <0.5. What the interval tests is distinguishability rather than count: on the real facts, multi-valued runs have 6.4x its occupancy of the rest. It survives at f0 in 0.1, 0.3, 0.5, capture peaks at f0 = 0.5, and of four interventions with criteria frozen first, timing dominates fraction at matched budget while a consistency gate drives every model to 0.993. The resampling unit is the seed, at a design effect of 3.75 on a pooled level: under a 44-seed control the ordering supporting claim 4 collapses from Spearman +0.98 at three seeds to +0.31-0.80 at forty-four, while claim 2's ordering is exact there (+1.00, p = 0.017). All 87 graded rows are in Appendix W, 37 of them graded withdrawn, failed, self-correcting, undecidable or an acknowledged limit, against 50 that are not."