Beyond ECE: Calibrated Size Ratio, Risk Assessment, and Confidence-Weighted Metrics

When providing forecasted probabilities with a predictive model, the ideal model offers perfect calibration: the true probability of the outcome (i.e., the probability that $Y=1$) exactly matches the forecasted probability $f(X)$. In practice, models inevitably exhibit calibration error, and it is therefore important to be able to measure this miscalibration to assess a model's reliability. The Expected Calibration Error (ECE) is the most widely used measure of miscalibration, but is known to be impossible to estimate the ECE with guaranteed accuracy in an assumption-free setting. In this work, we propose an alternative measure, the rankECE, that is based on comparing points with neighboring values of the predicted probability $f(X)$. Our theoretical guarantees and empirical results establish that rankECE provides a better proxy for ECE as compared to binned approximations to ECE, which are the most commonly-used approximations in practice.

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.

Reliable probability estimates by classifiers are essential in high-risk applications. In practice, however, predicted probabilities are often miscalibrated, and many existing post-hoc calibration methods typically lack guarantees that a specific notion of calibration is achieved after the correction procedure is applied. We introduce a set-based perspective on calibration through the notion of cumulative mass calibration and the corresponding error measures. We propose a new calibration procedure based on conformal prediction that forms cumulative probabilities with guaranteed marginal coverage. We introduce an adaptive temperature scaling algorithm, with the temperature tuned for each input to satisfy the conformal coverage constraint. As we show, this procedure can be efficiently implemented. Across image classification tasks, particularly in settings with many classes, our method improves newly introduced calibration error measures (CMCE and $α$-CMCE) and standard metrics (such as ECE, cw-ECE, MCE) over the existing baselines.