DisCal: Distribution-Aware Calibration for Mathematical Reasoning Under Character-Level Noisy Inputs

AbstractAlthough large reasoning models (LRMs) exhibit exceptional mathematical reasoning capabilities on clean inputs, their reasoning accuracy drops substantially in the presence of character-level noise such as typographical errors. Critically, their confidence estimates fail to reflect the corresponding decline in reasoning accuracy. While confidence calibration offers a principled solution, existing methods predominantly target clean inputs, leaving noisy scenarios largely unexplored. To address this gap, we propose DisCal (Distribution-aware Calibration), a confidence calibration framework for character-level noisy inputs. DisCal extracts uncertainty signals from both the empirical answer distribution and the model’s predictive distribution, and integrates them via a learned calibrator to produce well-calibrated confidence. Experiments across multiple mathematical reasoning benchmarks demonstrate that DisCal consistently outperforms existing calibration methods under noisy inputs, reducing Expected Calibration Error (ECE) by up to 39.21% and improving Area Under the Receiver Operating Characteristic Curve (AUROC) by up to 31.44%.