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Generalization Bounds for Convolutional Neural Networks

arXiv 1910.01487 ↗First posted 3 Oct 2019stat.ML cs.LGcited by 21

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Abstract (arXiv)

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization ability of neural networks mostly focuses on fully connected neural networks (FNNs), regarding CNNs as a special case of FNNs without taking into account the special structure of convolutional layers. In this work, we propose a tighter generalization bound for CNNs by exploiting the sparse and permutation structure of its weight matrices. As the generalization bound relies on the spectral norm of weight matrices, we further study spectral norms of three commonly used convolution operations including standard convolution, depthwise convolution, and pointwise convolution. Theoretical and experimental results both demonstrate that our bounds for CNNs are tighter than existing bounds.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Oct 2019.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 8; 2024: 1; 2025: 3; 2026: 1.

21 papers.

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  1. 2023What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalizationcited by 112
  2. 2023Sequence Length Independent Norm-Based Generalization Bounds for Transformerscited by 28
  3. 2023Theoretical Analysis of Inductive Biases in Deep Convolutional Networkscited by 21
  4. 2022Generalization Error Bounds for Deep Neural Networks Trained by SGDcited by 14
  5. 2023Deep Learning From Crowdsourced Labels: Coupled Cross-entropy Minimization, Identifiability, and Regularizationcited by 12
  6. 2022On Measuring Excess Capacity in Neural Networkscited by 9
  7. 2023Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applicationscited by 7
  8. 2021Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networkscited by 4
  9. 2022Analysis of convolutional neural network image classifiers in a rotationally symmetric modelcited by 4
  10. 2023Exploring the Complexity of Deep Neural Networks through Functional Equivalencecited by 4
  11. 2022CNNs Avoid Curse of Dimensionality by Learning on Patchescited by 3
  12. 2025Generalization Bounds in Hybrid Quantum-Classical Machine Learning Modelscited by 3
9 more
  1. 2021Analysis of convolutional neural network image classifiers in a hierarchical max-pooling model with additional local poolingcited by 2
  2. 2023On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descentcited by 2
  3. 2024Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Datacited by 2
  4. 2026Bound to Disagree: Generalization Bounds via Certifiable Surrogatescited by 2
  5. 2023Under-Counted Tensor Completion with Neural Incorporation of Attributescited by 1
  6. 2025A Theory for Conditional Generative Modeling on Multiple Data Sourcescited by 1
  7. 2021On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversioncited by 0
  8. 2022Data-Adaptive Discriminative Feature Localization with Statistically Guaranteed Interpretationcited by 0
  9. 2025Statistically guided deep learningcited by 0