This work introduces the first toolkit around path-norms that is fully able to encompass general DAG ReLU networks with biases, skip connections and max pooling. This toolkit notably allows us to establish generalization bounds for real modern neural networks that are not only the most widely applicable path-norm based ones, but also recover or beat the sharpest known bounds of this type. These extended path-norms further enjoy the usual benefits of path-norms: ease of computation, invariance under the symmetries of the network, and improved sharpness on feedforward networks compared to the product of operators' norms, another complexity measure most commonly used. The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.

通过使用支持一般DAG ReLU网络的路径范数工具包，该研究建立了适用于现代神经网络的泛化界限，该工具包不仅可以恢复或超越已知的界限，而且还具有计算简便、对网络对称性不变以及相对于算符范数的优化尖锐度等路径范数的优点。该工具包的多功能性和易于实施性使我们能够在ImageNet上对ResNets的最尖锐的已知界限进行数值评估，从而挑战基于路径范数的泛化界限的具体承诺。

现代网络的路径-范数工具包：后果、承诺和挑战