mlsanityData to 7 Oct 2026

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

arXiv 2002.06262 ↗First posted 14 Feb 2020cs.LG stat.MLcited by 60

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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.

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

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Citing papers per year: 2021: 17; 2022: 15; 2023: 15; 2024: 8; 2025: 5.

60 papers.

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  1. 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
  2. 2023What can a Single Attention Layer Learn? A Study Through the Random Features Lenscited by 39
  3. 2021A Fully Spiking Hybrid Neural Network for Energy-Efficient Object Detectioncited by 31
  4. 2022Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initializationcited by 30
  5. 2022An Empirical Study of Implicit Regularization in Deep Offline RLcited by 24
  6. 2021A Neural Tangent Kernel Perspective of GANscited by 21
  7. 2021Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networkscited by 20
  8. 2023Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networkscited by 18
  9. 2023Neural (Tangent Kernel) Collapsecited by 18
  10. 2021Shift Invariance Can Reduce Adversarial Robustnesscited by 16
  11. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  12. 2021Neural Tangent Kernel Maximum Mean Discrepancycited by 15
38 more
  1. 2021Generalization Guarantees for Neural Architecture Search with Train-Validation Splitcited by 14
  2. 2022Generalization Properties of NAS under Activation and Skip Connection Searchcited by 14
  3. 2023On the Convergence of Encoder-only Shallow Transformerscited by 13
  4. 2022Wide and Deep Neural Networks Achieve Optimality for Classificationcited by 12
  5. 2022A Kernel Perspective of Skip Connections in Convolutional Networkscited by 12
  6. 2021On the Convergence of Shallow Neural Network Training with Randomly Masked Neuronscited by 11
  7. 2023The Interpolating Information Criterion for Overparameterized Modelscited by 11
  8. 2022Generalization Through The Lens Of Leave-One-Out Errorcited by 10
  9. 2022Dynamical systems' based neural networkscited by 10
  10. 2023Controlling the Inductive Bias of Wide Neural Networks by Modifying the Kernel's Spectrumcited by 9
  11. 2021Uniform Convergence, Adversarial Spheres and a Simple Remedycited by 8
  12. 2023Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approachcited by 8
  13. 2021Provable Convergence of Nesterov's Accelerated Gradient Method for Over-Parameterized Neural Networkscited by 7
  14. 2022Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Studycited by 7
  15. 2023On the Neural Tangent Kernel of Equilibrium Modelscited by 7
  16. 2021Deep Networks Provably Classify Data on Curvescited by 6
  17. 2021On the Provable Generalization of Recurrent Neural Networkscited by 6
  18. 2021An Interpretive Constrained Linear Model for ResNet and MgNetcited by 6
  19. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  20. 2023Field theory for optimal signal propagation in ResNetscited by 6
  21. 2023Better NTK Conditioning: A Free Lunch from (ReLU) Nonlinear Activation in Wide Neural Networkscited by 6
  22. 2024Robust NAS under adversarial training: benchmark, theory, and beyondcited by 6
  23. 2022How You Start Matters for Generalizationcited by 5
  24. 2023Generalization Ability of Wide Residual Networkscited by 5
  25. 2024Fast and Exact Enumeration of Deep Networks Partitions Regionscited by 5
  26. 2021A Convergence Theory Towards Practical Over-parameterized Deep Neural Networkscited by 4
  27. 2021A Neural Tangent Kernel Perspective of Infinite Tree Ensemblescited by 4
  28. 2022Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysiscited by 4
  29. 2024Cross-Space Adaptive Filter: Integrating Graph Topology and Node Attributes for Alleviating the Over-smoothing Problemcited by 4
  30. 2024Can Kernel Methods Explain How the Data Affects Neural Collapse?cited by 4
  31. 2024Generalization of Scaled Deep ResNets in the Mean-Field Regimecited by 3
  32. 2025Divergence of Empirical Neural Tangent Kernel in Classification Problemscited by 3
  33. 2021Experiments with Rich Regime Training for Deep Learningcited by 2
  34. 2022Analyzing Tree Architectures in Ensembles via Neural Tangent Kernelcited by 2
  35. 2023Towards Reliable Colorectal Cancer Polyps Classification via Vision Based Tactile Sensing and Confidence-Calibrated Neural Networkscited by 2
  36. 2023MALIBO: Meta-learning for Likelihood-free Bayesian Optimizationcited by 2
  37. 2022Convergence Analysis of Deep Residual Networkscited by 1
  38. 2022Pit-Pattern Classification of Colorectal Cancer Polyps Using a Hyper Sensitive Vision-Based Tactile Sensor and Dilated Residual Networkscited by 1

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