Sharp bounds for the Rademacher complexity and the generalization error are derived for the residual network model. The Rademacher complexity bound has no explicit dependency on the depth of the network, while the generalization bounds are comparable to the Monte Carlo error rates, suggesting that they are nearly optimal in the high dimensional setting. These estimates are achieved by constraining the hypothesis space with an appropriately defined path norm such that the constrained space is large enough for the approximation error rates to be optimal and small enough for the estimation error rates to be optimal at the same time. Comparisons are made with other norm-based bounds.

中文翻译：

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Rademacher复杂度和残差网络的泛化误差

对于残差网络模型，得出了Rademacher复杂度和泛化误差的尖锐界限。Rademacher复杂度边界与网络深度没有明确的依赖关系，而泛化边界与Monte Carlo错误率相当，这表明它们在高维环境中几乎是最佳的。通过用适当定义的路径范数约束假设空间来实现这些估计，以使约束空间足够大，可以使最佳近似误差率达到最佳，而足够小，可以使估计误差率同时达到最佳值。与其他基于规范的界限进行了比较。