We show that the Rademacher complexity-based approach can generate non-vacuous generalisation bounds on Convolutional Neural Networks (CNNs) for classifying a small number of classes of images. The development of new Talagrand's contraction lemmas for high-dimensional mappings between function spaces and CNNs for general Lipschitz activation functions is a key technical contribution. Our results show that the Rademacher complexity does not depend on the network length for CNNs with some special types of activation functions such as ReLU, Leaky ReLU, Parametric Rectifier Linear Unit, Sigmoid, and Tanh.

翻译：我们证明了基于拉德马赫复杂度的方法能够为用于少量图像类别分类的卷积神经网络（CNN）生成非平凡泛化界。本文的关键技术贡献在于，针对函数空间与一般Lipschitz激活函数CNN之间的高维映射，发展了新的Talagrand压缩引理。研究结果表明，对于采用ReLU、Leaky ReLU、参数化整流线性单元、Sigmoid和Tanh等特定类型激活函数的CNN，其拉德马赫复杂度不依赖于网络深度。