Lessons from the Rademacher complexity for deep learning

Understanding the generalization properties of deep learning models is critical for successful applications, especially in the regimes where the number of training samples is limited. We study the generalization properties of deep neural networks via the empirical Rademacher complexity and show that it is easier to control the complexity of convolutional networks compared to general fully connected networks. In particular, we justify the usage of small convolutional kernels in deep networks as they lead to a better generalization error. Moreover, we propose a representation based regularization method that allows to decrease the generalization error by controlling the coherence of the representation. Experiments on the MNIST dataset support these foundations.