ConfidenceBench, a calibration benchmark that evaluates verbalized confidence estimates in 15 frontier LLMs using the Brier score, a proper scoring rule that incentivises truthful probability reporting shows that verbalized confidence calibration is a distinct and practically important axis of LLM reliability, complementary to standard accuracy-based evaluation.
Abstract
Large language models (LLMs) are increasingly deployed in settings where fluent but incorrect answers can be costly. In these settings, accuracy alone is insufficient: models must also know when they are likely to be wrong. We present ConfidenceBench, a calibration benchmark that evaluates verbalized confidence estimates in 15 frontier LLMs using the Brier score, a proper scoring rule that incentivises truthful probability reporting. Confidence is elicited via prompting, requiring no access to model logits and making the framework applicable to both closed-source and open-source systems. The benchmark comprises 200 private multiple-choice questions across four categories: spatial reasoning, high-precision mathematics, word lookup, and unknowable questions. Across three independent runs, Claude Opus 4.6 and Gemini 3.1 Pro Preview achieve the lowest Brier scores, both reported as 0.103. Both substantially outperform the calibrated-random baseline of 0.1875, while Gemini 3.1 Flash-Lite scores 0.367, indicating severe miscalibration. Accuracy and calibration diverge substantially across model families: the most accurate model is not the best-calibrated, and several models perform worse than the calibrated-random Brier baseline despite reasonable accuracy. These results show that verbalized confidence calibration is a distinct and practically important axis of LLM reliability, complementary to standard accuracy-based evaluation.
Claim-level decomposition combined with post-hoc calibration reduces expected calibration error on factual questions while exposing failure modes on adversarial false-premise questions where decision-makers most need reliable uncertainty estimates.
Toghrul Abbasli, Kentaroh Toyoda, Yuan Wang et al.· 0 citations
This work proposes answer instability, defined as the variability of a model’s final answer across repeated stochastic generations of the same prompt, as a simple, label-free, and black-box uncertainty signal, and demonstrates its utility for selective prediction and targeted repair, improving reliability without access to internal probabilities or additional training.
J. M. Araña, Kristine Ann M. Carandang, Ethan Robert A. Casin et al.· Annual Meeting of the Associ...· 0 citations
Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level $\alpha$, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least $1-\delta$ that the selected threshold, if non-null, controls the error rate among accepted answers at level $\alpha$. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.
It is shown that prior scores, even when included only as context metadata, anchor judgments and systematically shift ratings toward their values, and effective mitigation must be validated for the intended model and task or domain.
A. Kapetanović, Kemal Altwlkany, Andro Merćep et al.· 0 citations
A consensus-based evaluation framework that measures relative preference among model-generated responses rather than absolute correctness rather than absolute correctness is introduced, offering an alternative perspective on response quality in scenarios where multiple valid answers exist.
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.
Rounak Sharma, Ananya B. Sai, Soumyabrata Pal· 0 citations
