DirEAG is proposed, a Dirichlet Evidence Aggregation method that converts each elicited answer-confidence observation into calibrated soft evidence over generated candidate answers and an additional null state, allowing the model to represent cases where none of the candidates is correct.
Abstract
Reliable confidence estimation is essential for using large language models in mathematical reasoning, but black-box verbalized confidence is difficult to calibrate. When the same problem is queried under multiple confidence-steering prompts, the resulting answer-confidence observations contain useful uncertainty information, yet their scales may shift across steering levels, models, and datasets. Existing black-box uncertainty methods often rely on answer agreement, sample consistency, or entropy, which describe output variation but do not model the numerical meaning of self-reported confidence. Conversely, direct averaging or heuristic aggregation of elicited confidence cannot learn prompt- and task-dependent bias. We propose DirEAG, a Dirichlet Evidence Aggregation method that converts each elicited answer-confidence observation into calibrated soft evidence over generated candidate answers and an additional null state, allowing the model to represent cases where none of the candidates is correct. Experiments on GSM8K, SVAMP, and GSM-Hard with Qwen, Mistral, and Gemma models show that, compared with direct confidence averaging and heuristic confidence-steering aggregation, DirEAG often achieves better calibration while maintaining competitive answer selection. Ablations further reveal that evidence aggregation and final binary calibration address distinct parts of the calibration problem.
This work instantiate this framework with p, a hybrid estimator that combines verbal confidence with spectral answer diversity computed from the negative von Neumann entropy of sampled answer embeddings, and achieves higher average AUROC than verbal confidence and sampling-based uncertainty while using half as many samples as Vn10 sampling.
Rounak Sharma, Ananya B. Sai, Soumyabrata Pal· 0 citations
As generative artificial intelligence enters scientific and professional work, its uncertainty must be defined on the states that matter for inference and decision-making. Language models assign probabilities to words, whereas applications require uncertainty over meaningful states such as diagnoses, hypotheses or operational conditions. We introduce a \emph{semantic map}: a prespecified, testable bridge from probabilities over verbal responses to a posterior over declared finite states. The language distribution remains unrestricted; held-out calibration connects it to a reference posterior. We derive posterior-error bounds and conditions for existence, conditional uniqueness, presentation stability and stable inverse recovery. This distinction matters because language probabilities depend on prompt wording, while the target posterior should not change under information-equivalent rewording. Experiments use professional market text compiled from Federal Reserve economic and financial series, together with controlled simulations having exact posteriors. Across two fitted language models, language-derived probabilities outperform printed numerical confidence, recover held-out posteriors with valid uncertainty coverage, remain largely stable under paraphrase and respond appropriately to altered evidence. \textbf{Prompt engineering optimises a wording-dependent response; robust scientific use requires validated stability of application-relevant meaning.} The proposed map turns semantic uncertainty in generative systems into an identifiable and testable statistical measurement problem and, when its acceptance conditions hold, yields an auditable posterior estimate.
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.
M. ffrench-Constant, Daniel Yang, Xinmeng Huang et al.· arXiv.org· 1 citation· ⚡1
Confidence estimation for large language models (LLMs) aims to estimate the probability that a generated answer is correct, while calibration aligns these estimates with empirical accuracy. Prior work has shown that token probabilities are often overconfident, we investigate whether these readily available signals can nevertheless provide well-calibrated confidence estimation for mathematical question answering. We compare single-pass estimators, which reuse token probabilities from the original generation, with multi-pass estimators, which obtain additional confidence signals through verification or stochastic forward passes. While individual token probabilities can be highly saturated, we find that aggregating token probabilities over the full sequence captures small but consistent differences between correct and incorrect generations, yielding more informative confidence estimates. Multi-pass methods can yield calibrated confidence estimates. We study two such approaches: self-verification through re-prompting, including a lower-cost in-situ variant, and Monte Carlo Dropout, which derives confidence from variation across stochastic forward passes. We further evaluate two post-hoc calibration methods, Platt scaling and isotonic regression, both of which substantially reduce in-domain calibration error. However, their data efficiency varies with dataset difficulty, and the calibration mappings often transfer asymmetrically across datasets and models.
A. Ma, Lorne Schell, Vin Bhaskara et al.· 0 citations
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
Regression analyses show that distributional properties of confidence scores explain much of the observed alignment pattern, with model metadata playing a smaller role after controls, and support a lossy-channel view of linguistic confidence.
Hefan Zhang, Bing-Quan Zhang, Ming Cheng et al.· 0 citations
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