# Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? -- A Neural Tangent Kernel Perspective

arXiv: https://arxiv.org/abs/2002.06262 · HTML: https://mlsanity.com/paper/2002.06262/

## Key facts

- Cited by 60 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 14 Feb 2020.

## Built on by (most cited first, 30 of 60)

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- [A Neural Tangent Kernel Perspective of GANs](https://mlsanity.com/paper/2106.05566/) (2021)
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- [Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networks](https://mlsanity.com/paper/2305.06986/) (2023)
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- [Generalization Properties of NAS under Activation and Skip Connection Search](https://mlsanity.com/paper/2209.07238/) (2022)
- [On the Convergence of Encoder-only Shallow Transformers](https://mlsanity.com/paper/2311.01575/) (2023)
- [Wide and Deep Neural Networks Achieve Optimality for Classification](https://mlsanity.com/paper/2204.14126/) (2022)
- [A Kernel Perspective of Skip Connections in Convolutional Networks](https://mlsanity.com/paper/2211.14810/) (2022)
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- [The Interpolating Information Criterion for Overparameterized Models](https://mlsanity.com/paper/2307.07785/) (2023)
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- [Controlling the Inductive Bias of Wide Neural Networks by Modifying the Kernel's Spectrum](https://mlsanity.com/paper/2307.14531/) (2023)
- [Uniform Convergence, Adversarial Spheres and a Simple Remedy](https://mlsanity.com/paper/2105.03491/) (2021)
- [Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach](https://mlsanity.com/paper/2310.06112/) (2023)
- [Provable Convergence of Nesterov's Accelerated Gradient Method for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2107.01832/) (2021)
- [Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study](https://mlsanity.com/paper/2209.07736/) (2022)
- [On the Neural Tangent Kernel of Equilibrium Models](https://mlsanity.com/paper/2310.14062/) (2023)
- [Deep Networks Provably Classify Data on Curves](https://mlsanity.com/paper/2107.14324/) (2021)
- [On the Provable Generalization of Recurrent Neural Networks](https://mlsanity.com/paper/2109.14142/) (2021)
- [An Interpretive Constrained Linear Model for ResNet and MgNet](https://mlsanity.com/paper/2112.07441/) (2021)

## Abstract (arXiv)

Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. This paper studies this fundamental problem in deep learning from a so-called "neural tangent kernel" perspective. Specifically, we first show that under proper conditions, as the width goes to infinity, training deep ResNets can be viewed as learning reproducing kernel functions with some kernel function. We then compare the kernel of deep ResNets with that of deep FFNets and discover that the class of functions induced by the kernel of FFNets is asymptotically not learnable, as the depth goes to infinity. In contrast, the class of functions induced by the kernel of ResNets does not exhibit such degeneracy. Our discovery partially justifies the advantages of deep ResNets over deep FFNets in generalization abilities. Numerical results are provided to support our claim.