On Rademacher Complexity-based Generalization Bounds for Deep Learning

ICLR 2025 Conference Submission7720 Authors

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

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 7720