From Stochastic to Stable: Rank Stability and Structural Sufficiency in AI Visibility Measurement

• URL: http://arxiv.org/abs/2607.10341v1
• Date: Sat, 11 Jul 2026 14:50:02 GMT
• Title: From Stochastic to Stable: Rank Stability and Structural Sufficiency in AI Visibility Measurement
• Abstract summary: We introduce a sequential convergence framework based on two complementary criteria.<n>Rank stability evaluates whether the rank-correlation trajectory has reached a structural plateau.<n> structural sufficiency evaluates whether the spread of citation shares among established domains exceeds the uncertainty of those estimates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: AI visibility measurement is comparative: practitioners want to know which domains generative search engines cite most often and whether observed differences are large enough to support decisions. Yet the industry lacks a principled way to determine whether enough data has been collected. Collection budgets vary widely across studies and platforms, and conclusions are often drawn from rankings whose stability and precision are unknown. We introduce a sequential convergence framework based on two complementary criteria: rank stability evaluates whether the rank-correlation trajectory has reached a structural plateau, while structural sufficiency evaluates whether the spread of citation shares among established domains -- those whose confidence intervals exclude zero -- exceeds the uncertainty of those estimates. Together, these criteria distinguish rankings that have merely stabilized from those sufficiently resolved to support inference. Both are derived from regularities in the observed citation distribution, including its rank structure, uncertainty profile, and the boundary between observed and established domains. The framework retains a small number of structural constants but requires no externally specified query count, correlation target, or confidence-interval width target; stopping is driven by observed measurement uncertainty and remains robust across a range of sufficiency thresholds. Applied across 30 platform-topic combinations spanning Gemini, SearchGPT, and Perplexity, the framework adapts to platform- and topic-specific citation distributions. Results show that no fixed collection budget can be justified across contexts and that convergence can instead be evaluated from the structure of the observed distribution. The framework provides a practical basis for determining when AI visibility measurements are ready to support comparative analysis.

Related papers

• Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations [55.76952683833966]
  This paper proposes weighted CONCH (W-CONCH) and weighted CROC (W-CROC) to reduce confidence set size when data may be corrupted.<n>Experiments on image-based and real-world changepoint and root-cause benchmarks show that uncertainty-based weighting substantially reduces confidence set size.
  arXiv  Detail & Related papers  (2026-07-29T05:16:59Z)
• A general estimation framework for continuous-variable systems [32.505127447635864]
  We show that informational completeness does not guarantee statistically stable reconstruction from finite measurement data.<n>We develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame.
  arXiv  Detail & Related papers  (2026-07-21T16:58:41Z)
• Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty [5.839104770457067]
  Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently.<n>We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings.
  arXiv  Detail & Related papers  (2026-06-15T21:39:47Z)
• Uncertainty-DTW for Sequences and Visual Tokens [43.798398689900075]
  We introduce uncertainty-aware alignment, a probabilistic framework that models correspondences with heteroscedastic uncertainty and performs structured matching along alignment paths.<n>We generalize this framework from temporal sequences to tokenized visual representations, enabling structured matching over sets of visual tokens.<n>These findings establish uncertainty-aware alignment as a general, robust, and interpretable framework for learning from structured data.
  arXiv  Detail & Related papers  (2026-05-24T14:49:43Z)
• Coverage, Not Averages: Semantic Stratification for Trustworthy Retrieval Evaluation [3.4588983513116065]
  Retrieval quality is the primary bottleneck for accuracy and robustness in retrieval-augmented generation (RAG)<n>We formalize evaluation as a statistical estimation problem, showing that metric reliability is fundamentally limited by the evaluation-set construction.<n>This yields (1) formal coverage guarantees across retrieval semantic regimes and (2) interpretable visibility into retrieval failure modes.
  arXiv  Detail & Related papers  (2026-04-22T16:49:30Z)
• ERA: Evidence-based Reliability Alignment for Honest Retrieval-Augmented Generation [19.616905640490252]
  We propose a new framework called ERA (Evidence-based Reliability Alignment) to enhance abstention behavior in RAG systems.<n>Our approach significantly outperforms baselines, optimizing the trade-off between answer coverage and abstention with superior calibration.
  arXiv  Detail & Related papers  (2026-02-24T01:45:51Z)
• Uncertainty in Federated Granger Causality: From Origins to Systemic Consequences [3.122408196953971]
  Granger Causality (GC) provides a rigorous framework for learning causal structures from time-series data.<n> Federated GC algorithms only yield deterministic point estimates of causality and neglect uncertainty.<n>This paper establishes the first methodology for rigorously quantifying uncertainty.
  arXiv  Detail & Related papers  (2026-02-13T15:12:18Z)
• Benchmarking Corruption Robustness of LVLMs: A Discriminative Benchmark and Robustness Alignment Metric [49.393713730706445]
  We introduce Bench-C, a benchmark emphasizing discriminative samples for assessing corruption robustness.<n>We propose the Robustness Alignment Score (RAS), a unified metric that measures degradation in logit-level prediction structure.
  arXiv  Detail & Related papers  (2025-11-24T12:07:56Z)
• Uncertainty Awareness on Unsupervised Domain Adaptation for Time Series Data [49.36938105983916]
  Unsupervised domain adaptation methods seek to generalize effectively on unlabeled test data.<n>We propose incorporating multi-scale feature extraction and uncertainty estimation to improve the model's generalization and robustness across domains.
  arXiv  Detail & Related papers  (2025-08-26T03:13:08Z)
• SConU: Selective Conformal Uncertainty in Large Language Models [59.25881667640868]
  We propose a novel approach termed Selective Conformal Uncertainty (SConU)<n>We develop two conformal p-values that are instrumental in determining whether a given sample deviates from the uncertainty distribution of the calibration set at a specific manageable risk level.<n>Our approach not only facilitates rigorous management of miscoverage rates across both single-domain and interdisciplinary contexts, but also enhances the efficiency of predictions.
  arXiv  Detail & Related papers  (2025-04-19T03:01:45Z)
• Distribution-free binary classification: prediction sets, confidence intervals and calibration [106.50279469344937]
  We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting. We derive confidence intervals for binned probabilities for both fixed-width and uniform-mass binning. As a consequence of our 'tripod' theorems, these confidence intervals for binned probabilities lead to distribution-free calibration.
  arXiv  Detail & Related papers  (2020-06-18T14:17:29Z)
• GenDICE: Generalized Offline Estimation of Stationary Values [108.17309783125398]
  We show that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions. The resulting algorithm, GenDICE, is straightforward and effective.
  arXiv  Detail & Related papers  (2020-02-21T00:27:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.