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Lipschitz regularized Deep Neural Networks generalize and are adversarially robust

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arxiv 1808.09540 v4 pith:RHFY6JNJ submitted 2018-08-28 cs.LG cs.NAmath.NAstat.ML

Chris Finlay , Jeff Calder , Bilal Abbasi , Adam Oberman This is my paper · ORCID
classification cs.LGcs.NAmath.NAstat.ML
keywords regularizationadversarialnetworksdeepdemonstrategeneralizationgradientlipschitz
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In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networks. The adversarial robustness regularization combines adversarial training, which we show to be equivalent to Total Variation regularization, with Lipschitz regularization. We demonstrate empirically that the regularized models are more robust, and that gradient norms of images can be used for attack detection.

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Cited by 3 Pith papers

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    math.OC 2025-06 conditional novelty 5.0 of 10

    Consensus-based optimization matches or beats natural evolution strategies as a closed-box adversarial attack method in easier attack scenarios, and consensus hopping is shown to be a gradient-descent-like limit of CBO.

  2. A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

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    Alternating a shallow denoising CNN with an implicit heat equation step produces a tunable SAR despeckling network with improved robustness to adversarial perturbations.

  3. A New Formulation of Lipschitz Constrained With Functional Gradient Learning for GANs

    cs.CV 2025-01 reject novelty 4.0 of 10

    Li-CFG adds an ε-centered gradient penalty to the CFG GAN method and claims this enlarges the discriminator gradient norm, shrinking the latent neighborhood size and thereby increasing image diversity.

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