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arXiv · 2604.20614

Too Sharp, Too Sure: When Calibration Follows Curvature

Alessandro Morosini·Matea Gjika·Tomaso Poggio·Pierfrancesco Beneventano
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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.

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Alessandro Morosini, Matea Gjika, Tomaso Poggio, Pierfrancesco Beneventano. 2026-04-22. Too Sharp, Too Sure: When Calibration Follows Curvature. https://arxiv.org/abs/2604.20614

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