Robust Large Margin Deep Neural Networks

Jure Sokolić*, Raja Giryes, Guillermo Sapiro, Miguel R.D. Rodrigues

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The generalization error of deep neural networks via their classification margin is studied in this paper. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary nonlinearities and pooling layers, and to networks with different architectures such as feed forward networks and residual networks. Our analysis leads to the conclusion that a bounded spectral norm of the network's Jacobian matrix in the neighbourhood of the training samples is crucial for a deep neural network of arbitrary depth and width to generalize well. This is a significant improvement over the current bounds in the literature, which imply that the generalization error grows with either the width or the depth of the network. Moreover, it shows that the recently proposed batch normalization and weight normalization reparametrizations enjoy good generalization properties, and leads to a novel network regularizer based on the network's Jacobian matrix. The analysis is supported with experimental results on the MNIST, CIFAR-10, LaRED, and ImageNet datasets.

Original languageEnglish
Article number7934087
Pages (from-to)4265-4280
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number16
StatePublished - 15 Aug 2017


FundersFunder number
National Science Foundation
Office of Naval Research
Army Research Office
Engineering and Physical Sciences Research CouncilEP/K033166/1, Ep/K033166/1
German-Israeli Foundation for Scientific Research and Development


    • Deep learning
    • deep neural networks
    • generalization error
    • robustness


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