There has been considerable effort to better understand the generalization
capabilities of deep neural networks both as a means to unlock a theoretical
understanding of their success as well as providing directions for further
improvements. In this paper, we investigate margin-based multiclass
generalization bounds for neural networks which rely on a recent complexity
measure, the geometric complexity, developed for neural networks. We derive a
new upper bound on the generalization error which scales with the
margin-normalized geometric complexity of the network and which holds for a
broad family of data distributions and model classes. Our generalization bound
is empirically investigated for a ResNet-18 model trained with SGD on the
CIFAR-10 and CIFAR-100 datasets with both original and random labels.

通过对深度神经网络的一种复杂性度量，即几何复杂性，进行研究，我们提出了一种新的上界推导出的泛化误差，该泛化误差与网络的几何复杂性的边际归一化相关，并适用于广泛的数据分布和模型类。同时，我们对 ResNet-18 模型在 CIFAR-10 和 CIFAR-100 数据集上进行实验证明该广义化界是准确的。