This paper presents a margin-based multiclass generalization bound for neural
networks that scales with their margin-normalized "spectral complexity": their
Lipschitz constant, meaning the product of the spectral norms of the weight
matrices, times a certain correction factor. This bound is empirically
investigated for a standard AlexNet network trained with SGD on the mnist and
cifar10 datasets, with both original and random labels; the bound, the
Lipschitz constants, and the excess risks are all in direct correlation,
suggesting both that SGD selects predictors whose complexity scales with the
difficulty of the learning task, and secondly that the presented bound is
sensitive to this complexity.

本文提出了一种基于边界的多类神经网络概化界限，其与神经网络谱规范化的 “谱复杂度” 成比例，谱规范化的含义是权重矩阵谱范数的乘积与一定的校正因子。在 mnist 和 cifar10 数据集上，使用 SGD 训练标准的 AlexNet 网络进行了实验研究，同时使用原始标签和随机标签，结果显示：界限、Lipschitz 常数和超限风险都直接相关，这表明 SGD 选择的预测器的复杂度与学习任务的难度成比例。