Kernel-Based Smoothness Analysis of Residual Networks

Tom Tirer, Joan Bruna, Raja Giryes

Research output: Contribution to journalConference articlepeer-review


A major factor in the success of deep neural networks is the use of sophisticated architectures rather than the classical multilayer perceptron (MLP). Residual networks (ResNets) stand out among these powerful modern architectures. Previous works focused on the optimization advantages of deep ResNets over deep MLPs. In this paper, we show another distinction between the two models, namely, a tendency of ResNets to promote smoother interpolations than MLPs. We analyze this phenomenon via the neural tangent kernel (NTK) approach. First, we compute the NTK for a considered ResNet model and prove its stability during gradient descent training. Then, we show by various evaluation methodologies that for ReLU activations the NTK of ResNet, and its kernel regression results, are smoother than the ones of MLP. The better smoothness observed in our analysis may explain the better generalization ability of ResNets and the practice of moderately attenuating the residual blocks.

Original languageEnglish (US)
Pages (from-to)921-954
Number of pages34
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event2nd Mathematical and Scientific Machine Learning Conference, MSML 2021 - Virtual, Online
Duration: Aug 16 2021Aug 19 2021


  • kernel methods
  • multilayer perceptron
  • Neural tangent kernel
  • residual networks

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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