On Rademacher Complexity-based Generalization Bounds for Deep Learning

Lan V. Truong

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arXiv · 2208.04284

On Rademacher Complexity-based Generalization Bounds for Deep Learning

Lan V. Truong

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Abstract

We show that the Rademacher complexity-based framework can establish non-vacuous generalization bounds for Convolutional Neural Networks (CNNs) in the context of classifying a small set of image classes. A key technical advancement is the formulation of novel contraction lemmas for high-dimensional mappings between vector spaces, specifically designed for general Lipschitz activation functions. These lemmas extend and refine the Talagrand contraction lemma across a broader range of scenarios. Our Rademacher complexity bound provides an enhancement over the results presented by Golowich et al. for ReLU-based Deep Neural Networks (DNNs). Moreover, while previous works utilizing Rademacher complexity have primarily focused on ReLU DNNs, our results generalize to a wider class of activation functions.

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Lan V. Truong. 2022-08-08. On Rademacher Complexity-based Generalization Bounds for Deep Learning. https://arxiv.org/abs/2208.04284

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