POOL: Propagated Uncertainty Over Lookalikes

• URL: http://arxiv.org/abs/2608.23086v1
• Date: Mon, 24 Aug 2026 10:51:44 GMT
• Title: POOL: Propagated Uncertainty Over Lookalikes
• Abstract summary: textscPOOL (emphPropagated Uncertainty Over Lookalikes) is a cost-efficient framework that addresses this trade-off.<n>We instantiate this framework with textscHy@$p$, a hybrid estimator that combines verbal confidence with spectral answer diversity.<n>textscHy@5 achieves higher average AUROC than verbal confidence and textscVn@10 sampling while using half as many samples as textscVn@10.
• Score: 17.512476090072028
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Black-box large language models need confidence scores that can separate likely-correct from likely-incorrect outputs, enabling systems to prioritize human review, route uncertain cases to stronger models, or choose abstention thresholds on development data. Yet existing confidence estimators face a cost-quality trade-off: verbal confidence is cheap but is often overconfident, while sampling-based uncertainty is more informative but scales linearly with the number of samples per query. We propose \textsc{POOL} (\emph{Propagated Uncertainty Over Lookalikes}),a cost-efficient framework that addresses this trade-off taking inspiration from group-testing.\textsc{POOL} clusters query stems with overlaps, evaluates a base estimator on representative medoids, softly propagates confidence scores to nearby queries, and selectively evaluates high-disagreement cases. We instantiate this framework with \textsc{Hy@}$p$, a hybrid estimator that combines verbal confidence with spectral answer diversity computed from the negative von Neumann entropy of sampled answer embeddings.Across six domains from three datasets and five black-box LLMs, \textsc{Hy@}5 achieves higher average AUROC than verbal confidence and \textsc{Vn@}10 sampling while using half as many samples as \textsc{Vn@}10. \textsc{POOL}-\textsc{Hy@}5 retains 93.5--97.9\% of its AUROC while saving 19.3--39.3\% of generations. On paraphrase-dense workloads, generation savings rise to 73-76\%, showing that semantic redundancy can be leveraged to lower confidence-estimation costs.

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