DisCal: Distribution-Aware Calibration for Mathematical Reasoning Under Character-Level Noisy Inputs
Bo Zhang, Jiawei Zhang, Cong Gao, Bingxu Han, Minghao Hu, Jun Zhang, Yunbo Cao, Zhunchen Luo, Wen Yao, Guotong Geng, Zhong Wang
Abstract
Although 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 (AU-ROC) by up to 31.44%.
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