# Attractor States Emerge in Multi-Turn LLM Conversations

arXiv: https://arxiv.org/abs/2606.30571 · HTML: https://mlsanity.com/paper/2606.30571/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [On the Conversational Persuasiveness of Large Language Models: A Randomized Controlled Trial](https://mlsanity.com/paper/2403.14380/) (2024)
- [Systematic Biases in LLM Simulations of Debates](https://mlsanity.com/paper/2402.04049/) (2024)
- [The Assistant Axis: Situating and Stabilizing the Default Persona of Language Models](https://mlsanity.com/paper/2601.10387/) (2026)
- [Beyond Single-Turn: A Survey on Multi-Turn Interactions with Large Language Models](https://mlsanity.com/paper/2504.04717/) (2025)
- [Measuring and Controlling Instruction (In)Stability in Language Model Dialogs](https://mlsanity.com/paper/2402.10962/) (2024)
- [LLM Agents in Interaction: Measuring Personality Consistency and Linguistic Alignment in Interacting Populations of Large Language Models](https://mlsanity.com/paper/2402.02896/) (2024)
- [TRUTH DECAY: Quantifying Multi-Turn Sycophancy in Language Models](https://mlsanity.com/paper/2503.11656/) (2025)
- [How LLMs Distort Our Written Language](https://mlsanity.com/paper/2603.18161/) (2026)
- [Corrupted by Reasoning: Reasoning Language Models Become Free-Riders in Public Goods Games](https://mlsanity.com/paper/2506.23276/) (2025)
- [Unveiling Attractor Cycles in Large Language Models: A Dynamical Systems View of Successive Paraphrasing](https://mlsanity.com/paper/2502.15208/) (2025)
- [Language-Driven Opinion Dynamics in Agent-Based Simulations with LLMs](https://mlsanity.com/paper/2502.19098/) (2025)
- [The Lock-in Hypothesis: Stagnation by Algorithm](https://mlsanity.com/paper/2506.06166/) (2025)
- [Beyond One-Way Influence: Bidirectional Opinion Dynamics in Multi-Turn Human-LLM Interactions](https://mlsanity.com/paper/2510.20039/) (2025)
- [Agent-to-Agent Theory of Mind: Testing Interlocutor Awareness among Large Language Models](https://mlsanity.com/paper/2506.22957/) (2025)
- [Geometric Dynamics of Agentic Loops in Large Language Models](https://mlsanity.com/paper/2512.10350/) (2025)
- [The Chameleon Nature of LLMs: Quantifying Multi-Turn Stance Instability in Search-Enabled Language Models](https://mlsanity.com/paper/2510.16712/) (2025)

## Built on by (most cited first, 6 of 6)

- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Testing Interchangeability in LLM Agent Teams](https://mlsanity.com/paper/2609.05279/) (2026)
- [Relational Positioning as a Measurable Risk Object: History-Carried Lock-in and Self-Confabulation in Multi-Turn Human-AI Dialogue](https://mlsanity.com/paper/2607.11437/) (2026)
- [If It's Not Buggy, Don't Fix It: On the Dynamics of Iterative Bug-fixing with LLMs](https://mlsanity.com/paper/2609.10123/) (2026)
- [ANIMASK: What the Model Contributes to Role Play in Simulated Story Worlds](https://mlsanity.com/paper/2609.16667/) (2026)
- [Towards Better Exploration in Sequential Test-Time Scaling](https://mlsanity.com/paper/2609.39632/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used in open-ended multi-agent settings, but the long-run dynamics of model--model interaction remain poorly understood. We study whether open-ended LLM discussions exhibit attractor-like behavior, i.e. topic-independent stable sets of behaviors which conversations settle into. Across 7 LLMs and 20 controversial topics, we compare self-play and mixed-play dyadic debates, tracking trajectories in representation space, discourse traits, and stances. We find self-play trajectories to be model-specific attractors that draw their conversation partners asymmetrically in mixed-play debates, influencing the other models' stylistic choices and behavior. For example, Claude Haiku is a strong attractor of other models in latent space, corresponding to other models taking on its traits like metacommentary, and models like GPT-4.1 nano are especially malleable. Our results suggest that open-ended LLM interactions are partially predictable from model-specific attractors, but shaped by structured and asymmetric partner influence. Overall, our analysis sheds some light on the complex behavior of open-ended multi-agent interaction, which we hope is helpful in designing, predicting, and monitoring autonomous agentic systems in the real world.