On Random Kernels of Residual Architectures

Etai Littwin, Tomer Galanti, Lior Wolf

Research output: Contribution to journalConference articlepeer-review


We analyze the finite corrections to the neural tangent kernel (NTK) of residual and densely connected networks, as a function of both depth and width. Surprisingly, our analysis reveals that given a fixed depth, residual networks provide the best tradeoff between the parameter complexity and the coefficient of variation (normalized variance), followed by densely connected networks and vanilla MLPs. While in networks that do not use skip connections, convergence to the NTK requires one to fix the depth, while increasing the layers’ width. Our findings show that in ResNets, convergence to the NTK may occur when depth and width simultaneously tend to infinity, provided with a proper initialization. In DenseNets, however, the convergence of the NTK to its limit as the width tends to infinity is guaranteed, at a rate that is independent of both the depth and scale of the weights. Our experiments validate the theoretical results and demonstrate the advantage of deep ResNets and DenseNets for kernel regression with random gradient features.

Original languageEnglish
Pages (from-to)897-907
Number of pages11
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event37th Conference on Uncertainty in Artificial Intelligence, UAI 2021 - Virtual, Online
Duration: 27 Jul 202130 Jul 2021


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