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Rademacher复杂度的方法能够为卷积神经网络（CNNs）在少量图像类别分类任务上生成非平凡的泛化界。本研究的关键技术贡献在于：针对函数空间之间的高维映射以及使用一般Lipschitz激活函数的CNNs，发展了新的Talagrand收缩引理。结果表明，对于采用特定类型激活函数（如ReLU、Leaky ReLU、参数化整流线性单元、Sigmoid和Tanh）的CNNs，其Rademacher复杂度不依赖于网络深度。