Revisiting Uncertainty Estimation and Calibration of Large Language Models
Linwei Tao, Yi-Fan Yeh, Minjing Dong, Tao Huang, Philip Torr, Chang Xu
cs.CL, cs.AI, cs.LG
2025-05-29
An 80-model sweep finds linguistic verbal uncertainty beats token-probability and numeric self-scores by about 10% on both AUROC and ECE.
In high-stakes use, a model has to be right and also know when it might be wrong. Calibration asks whether uncertainty tracks actual accuracy. Selective classification asks whether uncertainty ranks correct answers above incorrect ones. The toolkit is already large: token probabilities, hidden states, multi-sample agreement, numeric self-scores, and hedging language. What was missing is a single sweep across the current model zoo.
Researchers at the University of Sydney, City University of Hong Kong, Shanghai Jiao Tong University, and Oxford evaluate 80 models: open and closed, dense and Mixture-of-Experts, reasoning and non-reasoning, quantized and full precision, from 0.6B to 671B parameters. They keep only black-box, single-pass estimators: token-probability uncertainty (TPU), numerical verbal uncertainty (NVU), and linguistic verbal uncertainty (LVU). The testbed is MMLU-Pro.
Uncertainty is a scalar in [0, 1], with 0 meaning fully certain. TPU is one minus the length-normalized geometric mean of token probabilities. NVU prompts the model, with chain-of-thought, to emit a numeric score beside the answer. LVU does not ask for a number; a separate judge, LLaMA-4-Maverick-17B-128E-Instruct, scores hedges such as "probably" and "might". Calibration uses 10-bin expected calibration error (ECE). Ranking uses AUROC. White-box internals and multi-sample semantic entropy are left out on purpose: they are often unavailable or too expensive in deployment.
Averaged over 80 models, LVU beats the next-best method by about 10% on both AUROC and ECE. Accuracy is a poor proxy for uncertainty quality. GPT-4.1, LLaMA-4-Maverick, and LLaMA-3.1-405B are highly accurate yet poorly calibrated under TPU. Qwen3-235B-A22B in reasoning mode scores only 67% accuracy, about 15 points behind DeepSeek-R1 and GPT-4.1, but lands in the top tier on all three uncertainty methods.
Scale, post-training, and reasoning mode all help. On Qwen3 from 0.6B to 32B, larger models get lower ECE and higher AUROC, with gains flattening around 8B; 0.6B and 1.7B are close to chance. Instruct variants beat Base on all three methods. Reasoning mode cuts highly overconfident errors by more than 20%, and Qwen3-4B Think matches GPT-4.1 on uncertainty. Qwen3-30B-A3B (MoE, 3B active) beats the similar-size dense Qwen3-32B under LVU, though comparable MoE–dense pairs are scarce. AUROC is more than 10% higher on reasoning subjects (math, biology, physics) than on knowledge-heavy ones (law, history). FP8 and AWQ usually hurt uncertainty by about 5%. Multi-sample Consistency reaches ECE 0.08 on Qwen3-32B, better than single-pass methods and more expensive. About 17% of responses fail format extraction and are dropped.
ECE and AUROC correlate weakly, nearly zero for LVU. A well-calibrated score need not rank errors well.
If the constraint is black-box access and one generation, hedging language is a better signal than self-reported numbers or perplexity. Post-training and reasoning mode change how uncertainty is expressed, not only how often the answer is right. Do not treat accuracy as a stand-in for calibration.
LVU depends on a judge model; the paper itself calls the judge study small-scale. Small models follow instructions poorly, and the judge marks non-compliant outputs as highly uncertain, so AUROC can be inflated by "messy equals wrong" rather than genuine uncertainty expression. Everything is multiple-choice MMLU-Pro; open-ended generation is untested. The MoE edge rests on one near-matched pair. Dropping 17% of malformed answers may systematically favor models that follow the template.