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Generalization bounds for deep convolutional neural networks

arXiv 1905.12600 ↗First posted 29 May 2019cs.LG cs.AI cs.NEcited by 58

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Abstract (arXiv)

We prove bounds on the generalization error of convolutional networks. The bounds are in terms of the training loss, the number of parameters, the Lipschitz constant of the loss and the distance from the weights to the initial weights. They are independent of the number of pixels in the input, and the height and width of hidden feature maps. We present experiments using CIFAR-10 with varying hyperparameters of a deep convolutional network, comparing our bounds with practical generalization gaps.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 May 2019.

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Citing papers per year: 2021: 15; 2022: 14; 2023: 13; 2024: 9; 2025: 6; 2026: 1.

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  1. 2021Inductive Biases and Variable Creation in Self-Attention Mechanismscited by 144
  2. 2022Leveraging Unlabeled Data to Predict Out-of-Distribution Performancecited by 141
  3. 2021Deep Learning Through the Lens of Example Difficultycited by 139
  4. 2021Information-Theoretic Generalization Bounds for Stochastic Gradient Descentcited by 84
  5. 2021Skew Orthogonal Convolutionscited by 67
  6. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  7. 2021Improved Regularization and Robustness for Fine-tuning in Neural Networkscited by 45
  8. 2023Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusioncited by 39
  9. 2021Learning with Multiclass AUC: Theory and Algorithmscited by 35
  10. 2022Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guaranteescited by 34
  11. 2021Generalization bounds via distillationcited by 33
  12. 2023GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentationcited by 29
38 more
  1. 2023A Unified Perspective for Loss-Oriented Imbalanced Learning via Localizationcited by 24
  2. 2023Theoretical Analysis of Inductive Biases in Deep Convolutional Networkscited by 21
  3. 2021On the Equivalence between Neural Network and Support Vector Machinecited by 17
  4. 2022Bounding the Rademacher Complexity of Fourier neural operatorscited by 16
  5. 2023(Almost) Provable Error Bounds Under Distribution Shift via Disagreement Discrepancycited by 16
  6. 2022Optimizing Two-way Partial AUC with an End-to-end Frameworkcited by 15
  7. 2024DirMixE: Harnessing Test Agnostic Long-tail Recognition with Hierarchical Label Variationscited by 15
  8. 2024On the hardness of learning under symmetriescited by 13
  9. 2023Robust low-rank training via approximate orthonormal constraintscited by 12
  10. 2024Generalization Bound and New Algorithm for Clean-Label Backdoor Attackcited by 11
  11. 2022The Sample Complexity of One-Hidden-Layer Neural Networkscited by 10
  12. 2022On Measuring Excess Capacity in Neural Networkscited by 9
  13. 2022Optimizing Partial Area Under the Top-k Curve: Theory and Practicecited by 9
  14. 2022MaxMatch: Semi-Supervised Learning with Worst-Case Consistencycited by 9
  15. 2022The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithmcited by 9
  16. 2022Improved techniques for deterministic l2 robustnesscited by 9
  17. 2023Generalization Guarantees of Gradient Descent for Multi-Layer Neural Networkscited by 9
  18. 2024Improved Diversity-Promoting Collaborative Metric Learning for Recommendationcited by 9
  19. 2022Few-Shot Learning by Dimensionality Reduction in Gradient Spacecited by 8
  20. 2023Amortised Invariance Learning for Contrastive Self-Supervisioncited by 8
  21. 2021Visualizing the Emergence of Intermediate Visual Patterns in DNNscited by 7
  22. 2022Meta Mirror Descent: Optimiser Learning for Fast Convergencecited by 7
  23. 2023Norm-based Generalization Bounds for Compositionally Sparse Neural Networkscited by 7
  24. 2023Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applicationscited by 7
  25. 2023On Size-Independent Sample Complexity of ReLU Networkscited by 6
  26. 2021Robust Generalization of Quadratic Neural Networks via Function Identificationcited by 5
  27. 2024Role of Locality and Weight Sharing in Image-Based Tasks: A Sample Complexity Separation between CNNs, LCNs, and FCNscited by 5
  28. 2021Trap of Feature Diversity in the Learning of MLPscited by 4
  29. 2024The Price of Implicit Bias in Adversarially Robust Generalizationcited by 4
  30. 2021Perturbated Gradients Updating within Unit Space for Deep Learningcited by 3
  31. 2022CNNs Avoid Curse of Dimensionality by Learning on Patchescited by 3
  32. 2025Generalization Analysis for Supervised Contrastive Representation Learning under Non-IID Settingscited by 3
  33. 2024How to Collaborate: Towards Maximizing the Generalization Performance in Cross-Silo Federated Learningcited by 2
  34. 2024A Margin-based Multiclass Generalization Bound via Geometric Complexitycited by 2
  35. 2026Bound to Disagree: Generalization Bounds via Certifiable Surrogatescited by 2
  36. 2024Top-K Pairwise Ranking: Bridging the Gap Among Ranking-Based Measures for Multi-Label Classificationcited by 1
  37. 2025Generalization Bound for a General Class of Neural Ordinary Differential Equationscited by 1
  38. 2021Compression Implies Generalizationcited by 0

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