Despite the impressive generalization capabilities of deep neural networks, they have been repeatedly shown to poorly estimate their predictive uncertainty - in other words, they are frequently overconfident when they are wrong. Fixing this issue is known as model calibration, and has consequently received much attention in the form of modified training schemes and post-training calibration procedures. In this work, we present a significant hurdle to the calibration of modern models: deep neural networks have large neighborhoods of almost certain confidence around their training points. We demonstrate in our experiments that this phenomenon consistently arises (in the context of image classification) across many model and dataset pairs. Furthermore, we prove that when this phenomenon holds, for a large class of data distributions with overlaps between classes, it is not possible to obtain a model that is asymptotically better than random (with respect to calibration) even after applying the standard post-training calibration technique of temperature scaling. On the other hand, we also prove that it is possible to circumvent this defect by changing the training process to use a modified loss based on the Mixup data augmentation technique.

翻译：尽管深度神经网络具有令人瞩目的泛化能力，但它们反复被证明无法准确估计其预测的不确定性——换言之，当它们出错时，常常过度自信。修复这一问题被称为模型校准，并因此通过改进训练方案和训练后校准程序得到了广泛关注。在本文中，我们指出现代模型校准面临一个显著障碍：深度神经网络在其训练点周围存在大范围几乎确定的置信区域。我们的实验表明，这一现象在多种模型与数据集组合的图像分类上下文中始终出现。此外，我们证明当这一现象成立时，对于一类具有类别间重叠的广泛数据分布，即使应用标准的训练后校准技术（温度缩放），也无法获得在校准方面渐近优于随机模型的模型。另一方面，我们还证明可以通过改变训练过程，使用基于Mixup数据增强技术的修正损失函数来规避这一缺陷。