On Rademacher Complexity-based Generalization Bounds for Deep Learning

Lan V. Truong

Keywords: Deep Learning, CNN, Generalisation Errors

Abstract: 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 contraction lemmas for high-dimensional mappings between vector spaces for general Lipschitz activation functions is a key technical contribution. These lemmas extend and improve the Talagrand contraction lemma in a variety of cases. Our generalisation bounds are based on the infinity norm of the weight matrices, distinguishing them from previous works that relied on different norms. Furthermore, while prior works that use the Rademacher complexity-based approach primarily focus on ReLU DNNs, our results extend to a broader class of activation functions.

Primary Area: learning theory

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Submission Number: 7720