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.

翻译：现代神经网络虽能实现高精度，却往往校准不良，产生的置信度估计与实际正确性不匹配。然而，校准常被视为事后属性。我们采取不同视角：将校准作为小规模视觉任务上的训练阶段现象进行研究，探究能否通过干预训练过程可靠地获得校准解。我们识别出深度网络在多种基于梯度的训练方法下，校准、曲率与间隔之间存在紧密耦合。实验表明，预期校准误差（ECE）在整个优化过程中紧密追踪基于曲率的锐度。数学上，我们证明ECE与高斯-牛顿曲率均受相同轨迹上间隔相关指数尾函数控制（仅取决于问题相关常数）。受此机制启发，我们提出一种间隔感知训练目标，显式优化鲁棒间隔尾部与局部平滑性，在不牺牲精度的前提下跨优化器提升样本外校准性能。