# Perturbation Dose Responses in Recursive LLM Loops: Raw Switching, Stochastic Floors, and Persistent Escape under Append, Replace, and Dialog Updates

arXiv: https://arxiv.org/abs/2605.02236 · HTML: https://mlsanity.com/paper/2605.02236/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 20 of 20)

- [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)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Not what you've signed up for: Compromising Real-World LLM-Integrated Applications with Indirect Prompt Injection](https://mlsanity.com/paper/2302.12173/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Ignore Previous Prompt: Attack Techniques For Language Models](https://mlsanity.com/paper/2211.09527/) (2022)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [Benchmarking and Defending Against Indirect Prompt Injection Attacks on Large Language Models](https://mlsanity.com/paper/2312.14197/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [AgentDojo: A Dynamic Environment to Evaluate Prompt Injection Attacks and Defenses for LLM Agents](https://mlsanity.com/paper/2406.13352/) (2024)
- [Geometric Dynamics of Agentic Loops in Large Language Models](https://mlsanity.com/paper/2512.10350/) (2025)
- [Correlation Dimension of Auto-Regressive Large Language Models](https://mlsanity.com/paper/2510.21258/) (2025)
- [Generalization at the Edge of Stability](https://mlsanity.com/paper/2604.19740/) (2026)

## Abstract (arXiv)

Recursive language-model loops often settle into recognizable attractor-like patterns. The practical question is how much injected text is needed to move a settled loop somewhere else, and whether that move lasts. We study this in 30-step recursive loops by separating the model from the context-update rule: append, replace, and dialog updates expose different histories to the same generator. The main result is that persistent redirection in append-mode recursive loops is memory-policy-conditioned. Under a 12,000-character tail clip, destination-coherent persistence plateaus near 16 percent and retained source-basin escape near 36 percent at dose 400; neither crosses 50 percent. Under a full-history protocol, retained source-basin escape crosses 50 percent near 400 tokens and saturates at 75-80 percent by 1,500 tokens; destination-coherent persistence first reaches 0.50 near 1,500 tokens (Wilson 95 percent CI [0.41, 0.61]). A four-step falsification battery (heterogeneity control, granularity sweep with hierarchical macro-merge, transition-entropy diagnostic, and long-horizon trajectory continuation) recasts the high-dose destination-coherent dip as a finite-horizon, endpoint-definition-sensitive feature rather than a stable structural asymmetry. Half the canonical magnitude is endpoint timing; the residual drops 73 percent from -0.143 at step 29 to -0.039 at step 79 under the frozen canonical cluster basis, bootstrap interval straddling zero. Replace-mode raw switching is near-saturated under the default protocol but largely reflects state-reset overwrite: insert-mode probes drop it to 12-32 percent. We report 37 experiments on gpt-4o-mini with within-vendor replication on gpt-4.1-nano. Recursive-loop evaluations should distinguish transient movement from durable escape, subtract stochastic floors, and treat context-update rules as safety-relevant design choices.