Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter counting. The current paper shows generalization bounds that're orders of magnitude better in practice. These rely upon new succinct reparametrizations of the trained net --- a compression that is explicit and efficient. These yield generalization bounds via a simple compression-based framework introduced here. Our results also provide some theoretical justification for widespread empirical success in compressing deep nets. Analysis of correctness of our compression relies upon some newly identified \textquotedblleft noise stability\textquotedblright properties of trained deep nets, which are also experimentally verified. The study of these properties and resulting generalization bounds are also extended to convolutional nets, which had eluded earlier attempts on proving generalization.

本论文通过新的简洁再参数化方法的引入和新的“噪声稳定性”属性的发现，提供了一种基于压缩的框架来估计神经网络的泛化性能边界，并将此方法拓展到卷积神经网络中。

通过压缩方法增强深度网络的泛化界限