Summarizing “Conversational Capture: A Trajectory-Level Framework for Evaluating Generative Engine Optimization in Multi-turn Human-Agent Interaction”: A Hamsterdam Research Post

By Ethan Lazuk

Welcome to another edition of Hamsterdam Research! 🐹

This is where we look at recent AI research papers to learn what they’re talking about and explore their hypothetical implications for the future of search and SEO/GEO strategies.

This time, we’ll look at research called, “Conversational Capture: A Trajectory-Level Framework for Evaluating Generative Engine Optimization in Multi-turn Human-Agent Interaction.”

It was submitted to arXiv on September 30, 2026, and its authors are Junwei Yu, Jieyu Zhou, Mufeng Yang, Yepeng Ding, and Hiroyuki Sato.

First off, why should SEO/GEO professionals care about this research?

This research questions the basic way AI visibility is usually measured. GEO measurement commonly treats a prompt almost like a traditional search query by running the query, looking at the answer, recording which brands or sources appear, then repeating the process with another prompt. But the authors argue that that process misses what makes conversational search different.

In AI search, the answer can influence the second question a user asks, and the conversation history can also influence what the system retrieves next. Therefore, each turn isn’t necessarily independent.

The author’s key concept is conversational capture, where if a source gets cited early, it may become more likely to appear again through one of two mechanisms: either the AI assistant’s conversation history can favor the source in subsequent retrieval or the user may begin asking follow-up questions shaped by what they just saw. This means there’s an early visibility advantage that could potentially compound over the rest of the conversation.

That early visibility advantage matters to SEO/GEO practitioners in a few ways:

• Our visibility metrics may be incomplete. A source’s value may not just be whether it appears for Prompt A, but whether appearing for Prompt A changes what happens in Prompts B, C, and D. The authors therefore argue for measuring cumulative visibility across the whole conversational trajectory rather than isolated answers.
• The first few turns may matter disproportionately. In the authors’ theoretical model, early advantages can persist because later retrieval and questioning build on what happened earlier.
• A tactic that looks strongest in a one-prompt test may not be strongest over a conversation. The authors’ model shows that rankings of GEO methods can change when you evaluate an entire trajectory instead of a single response.
• It changes what “AI visibility” could mean. Instead of simply measuring mention rate or citation rate, GEO measurement may eventually need concepts like persistence, compounding, and the probability that one citation leads to another. The authors recommend that GEO audits move toward trajectory-level measures.

In summary, there’s a difference between winning the answer and winning the conversation.

Caveat: this paper is primarily theoretical. The authors didn’t test conversational capture on real ChatGPT, Gemini, Perplexity, etc., and they didn’t conduct a human-user experiment. Their numerical examples come from their mathematical model, and they say empirical validation is the next step.

Let’s start by reviewing the paper’s abstract.

This is worth a read in full, particularly the first half:

“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. This persistence can be independent of the source’s current relevance. We formalize the interaction as a two-layer closed-loop system and derive computable trajectory-level constructs: cumulative conversational visibility; a decomposition of trajectory gain into a single-turn “direct” term and a closed-loop “feedback” term; a nested counterfactual 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 (Pólya-urn) theory, we prove that the feedback term is identically 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 the single-turn and trajectory rankings of GEO methods agree only weakly (Kendall’s $\tau =0.4$). Thus, single-turn evaluation can select the wrong method. We connect the human channel to information foraging, trust calibration, and Bayesian persuasion, and discuss design implications for answer engines.”

Next, let’s break down the paper’s key vocabulary terms:

• Generative Engine Optimization (GEO): The practice of shaping or optimizing content to increase the likelihood that an AI answer engine will surface or cite it.
• Conversational Capture: The phenomenon where a source cited early in a conversation becomes more likely to be cited again in later turns, even as the user’s information need changes.
• Cumulative Conversational Visibility (CCV): The total visibility a source receives across an entire multi-turn conversation rather than in a single response.
• Trajectory Gain: The total increase in a source’s visibility across the full conversational path when GEO is applied.
• Direct Term: The visibility gain produced by GEO itself when the conversation path is held constant and feedback effects are excluded.
• Feedback Term: The additional visibility created because GEO changes later queries, dialogue history, or both. This is the part single-turn evaluation misses.
• Machine-Side Capture (M1): The tendency for a previously cited source to appear again because retrieval and generation are conditioned on the conversation history.
• Human-Side Capture (M2): The effect where an AI answer influences what the user asks next, steering later queries toward a previously mentioned source.
• Capture Coefficient: A measure of how much a previous citation increases the probability that the same source will be cited again on the next turn.
• Compounding Ratio: A measure comparing the actual visibility gained across a conversation with what would have been predicted by simply multiplying single-turn visibility by the number of turns. A value above 1 indicates compounding.

Esta bien. Let’s take a deeper look at the research paper’s contents now.

If you want to follow along, you can grab a PDF or the HTML version on arXiv.

The paper has 11 main sections.

We’ll focus on the most relevant ones below.

Introduction

“Existing work measures GEO’s impact in a single-turn setting: it fixes a query, runs the engine, and scores the prominence of a target source in that answer using position-adjusted word count, an LLM-judged impression score, or a related metric,” write the authors. “This approach assumes that the query is exogenous, meaning that it is supplied independently of the system, and that turns are independent.”

“These assumptions do not hold in a conversation,” they continue.

“Human-agent information seeking forms a closed loop: the user asks a question, reads the answer, and adjusts the next question in response. The agent’s reply thus influences rather than merely answers the next query. A GEO bias toward a source can propagate by steering the user’s follow-up toward that source and by conditioning subsequent retrieval on a history that already privileges it. The resulting advantage can compound over turns.”

Next they introduce their thesis:

“Single-turn visibility metrics systematically misestimate the true impact of GEO because they ignore the human-agent feedback loop intrinsic to multi-turn dialogue. The real return to GEO is not single-turn exposure, but its cumulative, path-dependent influence on the user’s sequence of interactions.”

“We name the central phenomenon conversational capture: in multi-turn generative retrieval, a source cited in earlier turns has a substantially higher probability of being cited in later ones, and this persistence can be decoupled from its relevance to the user’s current need, which may have narrowed or shifted,” they write.

“Capture has two distinct causes that we keep separate throughout the paper. On the machine side, retrieval and generation condition on the dialogue history, so a previously cited source can resurface regardless of the user. On the human side, a GEO-shaped answer directs the user’s next question toward the captured source.”

Motivation: Why Single-Turn GEO Evaluation Fails

Current GEO measurement is based on two assumptions, they explain:

“The GEO literature operationalizes “impact” as a single-turn visibility lift (Aggarwal et al., 2024; Kumar and Lakkaraju, 2024). The standard procedure samples a query $q$ from a distribution, runs the engine with and without the optimized content, and reports the difference in a visibility score, such as position-adjusted word count or an LLM-judged impression. Averaging over independently sampled queries yields the reported estimate. Two assumptions support this procedure: queries are exogenous (drawn from a fixed distribution unaffected by the engine), and turns are independent (each query is scored in isolation).”

But “Neither assumption holds in a conversation.”

For instance, “The user’s next question is shaped by the agent’s last answer.”

Therefore, “Queries are endogenous, and turns are coupled.”

They explain this as conversational capture: “In multi-turn generative retrieval, once a source is cited in earlier turns, its probability of being cited in later turns is significantly elevated; this persistence may be independent of the source’s relevance to the user’s current (narrowed or drifted) information need.”

In short, “A source that gains an early advantage can retain that advantage throughout the conversation.”

Discussion: Implications for Answer-Engine Design

“Single-turn GEO competes for one answer, whereas multi-turn GEO competes for a trajectory,” they write.

Consequently, “GEO audits, answer-engine benchmarks, and platform-side abuse detection should report trajectory-level quantities ($L_T$, $L_T^{\mathrm{feedback}}$, $\rho$, $\kappa$) and the single-turn/trajectory misranking $\tau$, not single-turn visibility alone.”

Basically what the authors are saying is that GEO may need to be evaluated across an entire conversation, not just one prompt-response pair.

A trajectory means the whole sequence of interactions, including the first question, the answer, the user’s follow-up, the next answer, and so on. The authors’ argument is that appearing in the first answer can affect what happens later because the system retains conversational context and because users may ask follow-up questions based on what they were just shown.

So instead of measuring only, “Did this source appear for this prompt?”, they want GEO measurement to ask, “What happened to this source’s visibility over the entire conversation?”

Conclusion

“GEO is currently evaluated as if a conversation were a sequence of independent search queries, although an answer engine influences the user’s next question. An initial GEO advantage can therefore propagate through a human-agent feedback loop and compound. We call this phenomenon conversational capture. We formalized the loop, separated its machine-side and human-side channels, and defined trajectory-level evaluation constructs. The feedback term $L_T^{\mathrm{feedback}}$ is identically zero under single-turn evaluation. Reinforcement-process theory shows the dynamics are non-ergodic (early turns decide the outcome) and that cumulative GEO gain grows superlinearly with conversation length while capture develops. Single-turn extrapolation therefore underestimates the gain by a margin that widens with the conversation. A model-derived computation shows that the feedback term can dominate the direct term and that single-turn and trajectory rankings of GEO methods can diverge. Single-turn evaluation can consequently select the wrong method. Evaluation should instead measure trajectories, while answer engines should re-ground, diversify, and explain persistent citations. The next step is to validate the human-side channel empirically with conversational corpora and real users.”

Knowing what we do now, why should SEO/GEO professionals care about “Conversational Capture: A Trajectory-Level Framework for Evaluating Generative Engine Optimization in Multi-turn Human-Agent Interaction”?

Once again, this research challenges a common assumption about AI visibility measurement, which is that each prompt can be evaluated in isolation.

The paper argues that conversational search is path-dependent, meaning that once a brand or source appears early in a conversation, that visibility may influence both what the system retrieves next and what the user asks next. Suffice to say, an early citation can potentially create a feedback loop that increases its chances of being cited again later. The author’s call this conversational capture.

Conversational capture has a major implication for GEO measurement: if a tool only reports whether a brand appeared for a single prompt, it may miss part of the picture. According to this research, the more meaningful question may be whether a brand’s visibility persists, compounds, or changes the direction of the conversation over multiple turns. Thus, the authors argue that GEO should be evaluated across conversational trajectories, not just individual answers.

This could also change how we as practitioners think about optimization. According to the paper’s model, a GEO method that performs best on one isolated response is not necessarily the method that produces the most visibility over a full conversation. That means there’s a difference between winning the answer and winning the conversation.

For SEO/GEO professionals, a practical takeaway is that AI visibility may have momentum. Based on the concept of conversational capture, getting cited early could be more valuable than a single mention because initial visibility may influence the rest of the user’s journey.

Outro

This research suggests we may be measuring AI visibility at the wrong level. Instead of asking whether a brand won a single answer, we may need to measure whether it gained enough early visibility to influence and persist across the rest of the conversation.

I hope you’ve enjoyed this edition of Hamsterdam Research! 🐹

Feel free to comment below or contact me with your feedback.

Stay tuned for another new article, hopefully next week, or check out related research posts below.

Until next time, enjoy the vibes:

Thanks for reading. Happy optimizing!