Calibration as a First-Class Criterion in LLM Evaluation

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem$_1$-ECE, the same-sample self-consistency score, and Sem$_2$-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem$_2$ achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

LLM confidence calibration is often evaluated by comparing two signals: token-probability scores and verbalized confidence. These signals are sometimes treated as direct readouts of model uncertainty, but their comparison depends on measurement choices that are rarely made explicit. In the main analysis, we hold the verbalized-confidence elicitation fixed: a single prompt template, probability scale, and output format. We then vary the measurement axes that define the verbalized-vs-token comparison: which answer string receives the token-probability score, how that score is read from the answer tokens, and under which conditioning context it is measured. We evaluate this design on four QA benchmarks across three open 7--8B base/Instruct model families, with larger Qwen2.5 variants as same-family robustness checks. The resulting comparison is sensitive to these choices: conditioning context changes the sign or magnitude of the ECE gap across settings, token readout produces smaller but still sign-moving changes, and changing the ECE estimator has little effect. Under the default generated-answer, bare-context protocol, Instruct settings are close to parity rather than showing a large calibration gain for verbalized confidence. In a separate supplied-answer analysis, surface-plausible wrong answers receive nearly the same confidence as supplied gold answers, suggesting that verbalized confidence also reflects answer plausibility and provenance rather than correctness alone. We argue that both confidence signals should be treated as protocol-dependent behavioral measurements, and provide a reporting checklist covering elicitation provenance, scored answer, token-probability readout, and conditioning context.

As language models improve and become increasingly deployed to solve a variety of tasks, trustworthiness becomes essential. Calibration is a good proxy for trust: well-calibrated confidence estimates help inform the risk versus reward tradeoff when trusting a specific model output. Unfortunately, even as models improve, they remain poorly calibrated, often biasing towards overconfidence. Additionally, calibration can be gamed: a policy that always predicts the base rate is perfectly calibrated, but completely uninformative. To resolve this, we develop a new metric, expected utility renormalized by the oracle (EURO), that balances calibration and informativeness. We also propose a general-purpose activation-based confidence, utility, and trust estimation protocol (ACUTE) to appropriately adjudicate uncertainty. The ACUTE protocol provides flexible, sample-efficient, and compute-efficient confidence estimators for 3 tasks including multiple choice question answering, tool-calling, and scientific document summarization across 6 models from 4 model families. ACUTE outperforms strong baselines on EURO, while maintaining low calibration error. Taken together, our work shows that equipping LLMs with the ACUTE protocol can improve calibration, utility, and trustworthiness in numerous settings.