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Generative Engine Optimization

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Method note

Surrogate Probability Surface

Working paper · August 2026 · 8 min read

Sample data only. Figures and examples on this page explain the method. They are not published study results and not outcomes from real clients. See the Disclaimer.

Abstract

Frontier models do not expose a knowledge graph. They expose next-token distributions. This note describes how Vowel reconstructs a surrogate probability surface over an entity—brand, product, person—by sampling paraphrased probes and treating log-probability as elevation. Peaks are canon. Valleys are parametric blindspots: places the model will hedge, substitute a competitor, or invent.

Illustrative working figures — sample data, not a published study

Probe families
12–18
Paraphrase fan-out
× 8
Typical collapse band
0.11–0.24
Competitor substitution
31% of valleys

Why logprobs, not citations

Retrieval traces and citation lists describe what a system is willing to show. They do not describe what it believes. A model can quote your homepage and still assign higher probability to a rival when asked, unprompted, who leads the category.

Token-level log-probability on constrained answer spans is a cheaper, repeatable proxy for that belief. We do not claim it is the model's true posterior. We claim it is a stable enough surrogate to map holes before a briefing goes sideways.

Probe design

Each entity is hit with a fixed family of prompts: category leadership, product association, founder/origin, recent event, and comparison-against-peer. Each family fans out into paraphrases that keep the answer span aligned ("X is a…", "The company behind Y is…") so we can score the same tokens across surface forms.

We run the same battery across Claude, ChatGPT, and Gemini, with temperature pinned and seeds recorded. The output is not a single score. It is a surface: entity × prompt family × model × paraphrase.

Reading the topography

High, flat ridges mean the model will name you under many phrasings. That is canon. Sharp peaks with steep drop-offs mean the model knows you only in a narrow template—often a Wikipedia-shaped sentence—and will fail a buyer-style question.

Valleys are the product. A collapse in the comparison family is a share-of-model problem. A collapse in the recent-event family is an ingestion-latency problem. A collapse that fills with a competitor's name is a substitution risk we take into the war-room as a transition prior.

What we ship from the surface

For research partners, the deliverable is the surface itself: heatmaps, collapse bands, and the exact probes that failed. For enterprise, the surface is an input. It tells the Blindspot Audit where to spend samples, and it tells Parametric Injection which facts need to exist in the regions the model actually retrieves.

The method is intentionally boring. Same probes, same scoring, same models, week after week. The interesting part is watching a valley fill—or watching a competitor occupy it first.