# Conversational Capture: A Trajectory-Level Framework for Evaluating Generative Engine Optimization in Multi-turn Human-Agent Interaction

arXiv: https://arxiv.org/abs/2609.40069 · HTML: https://mlsanity.com/paper/2609.40069/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agentic RAG, agents and memory, one of 15 directions in Retrieval-augmented generation.
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- Retrieval-augmented generation / [Agentic RAG, agents and memory](https://mlsanity.com/rag/agentic-rag-agents-and-memory/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 9 of 9)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [LMSYS-Chat-1M: A Large-Scale Real-World LLM Conversation Dataset](https://mlsanity.com/paper/2309.11998/) (2023)
- [Open-Domain Question Answering Goes Conversational via Question Rewriting](https://mlsanity.com/paper/2010.04898/) (2020)
- [Open-Retrieval Conversational Question Answering](https://mlsanity.com/paper/2005.11364/) (2020)
- [Manipulating Large Language Models to Increase Product Visibility](https://mlsanity.com/paper/2404.07981/) (2024)

## Abstract (arXiv)

Generative Engine Optimization (GEO) shapes content to increase its likelihood of being cited by answer engines built on retrieval-augmented large language models. GEO is typically evaluated as a single-turn property: for a fixed query, an evaluator measures a source's visibility in one answer. We argue that the single answer is an inadequate unit of analysis. Human-agent information seeking forms a closed loop: the agent's answer changes the user's beliefs and therefore the next question, which in turn determines what the agent retrieves. We introduce conversational capture, a phenomenon in which a source cited early becomes substantially more likely to be cited again. Capture operates through a machine-side channel, history-conditioned retrieval, and a human-side channel, follow-up questions directed toward the captured source. We formalize the interaction as a two-layer closed-loop system and derive trajectory-level constructs: cumulative conversational visibility; a direct/feedback decomposition of trajectory gain; a nested split of the feedback term into machine-side and human-side channels; a capture coefficient; a compounding ratio; and a misranking diagnostic. Using reinforcement-process (P'olya-urn) theory, we prove that the feedback term is zero under single-turn evaluation and that GEO's cumulative payoff grows superlinearly with conversation length while capture develops. A model-derived illustration shows that the feedback term can exceed the direct term, the compounding ratio exceeds two within ten turns, and single-turn and trajectory rankings agree only weakly (Kendall's τ = 0.4). We connect the human channel to information foraging, trust calibration, and Bayesian persuasion, and discuss design implications for answer engines.