# Too Sharp, Too Sure: When Calibration Follows Curvature Source: [Too Sharp, Too Sure: When Calibration Follows Curvature]() Collection index: [llms.txt]() Data updated: 2026-04-24T05:00:14.774Z Authors: Alessandro Morosini, Matea Gjika, Tomaso Poggio, Pierfrancesco Beneventano Published: 2026-04-22T14:28:52.000Z ## Abstract Modern neural networks can achieve high accuracy while remaining poorly calibrated, producing confidence estimates that do not match empirical correctness. Yet calibration is often treated as a post-hoc attribute. We take a different perspective: we study calibration as a training-time phenomenon on small vision tasks, and ask whether calibrated solutions can be obtained reliably by intervening on the training procedure. We identify a tight coupling between calibration, curvature, and margins during training of deep networks under multiple gradient-based methods. Empirically, Expected Calibration Error (ECE) closely tracks curvature-based sharpness throughout optimization. Mathematically, we show that both ECE and Gauss--Newton curvature are controlled, up to problem-specific constants, by the same margin-dependent exponential tail functional along the trajectory. Guided by this mechanism, we introduce a margin-aware training objective that explicitly targets robust-margin tails and local smoothness, yielding improved out-of-sample calibration across optimizers without sacrificing accuracy. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR-10 90/10 (val)](): Image Classification; CIFAR-10 90/10 (val); Accuracy: 85.8. ## Original sources and implementation [Original paper]() [PDF]()