# Generalization Bounds for Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1910.01487 · HTML: https://mlsanity.com/paper/1910.01487/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 21 of 21)

- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [Sequence Length Independent Norm-Based Generalization Bounds for Transformers](https://mlsanity.com/paper/2310.13088/) (2023)
- [Theoretical Analysis of Inductive Biases in Deep Convolutional Networks](https://mlsanity.com/paper/2305.08404/) (2023)
- [Generalization Error Bounds for Deep Neural Networks Trained by SGD](https://mlsanity.com/paper/2206.03299/) (2022)
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- [On Measuring Excess Capacity in Neural Networks](https://mlsanity.com/paper/2202.08070/) (2022)
- [Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications](https://mlsanity.com/paper/2311.05116/) (2023)
- [Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networks](https://mlsanity.com/paper/2105.00292/) (2021)
- [Analysis of convolutional neural network image classifiers in a rotationally symmetric model](https://mlsanity.com/paper/2205.05500/) (2022)
- [Exploring the Complexity of Deep Neural Networks through Functional Equivalence](https://mlsanity.com/paper/2305.11417/) (2023)
- [CNNs Avoid Curse of Dimensionality by Learning on Patches](https://mlsanity.com/paper/2205.10760/) (2022)
- [Generalization Bounds in Hybrid Quantum-Classical Machine Learning Models](https://mlsanity.com/paper/2504.08456/) (2025)
- [Analysis of convolutional neural network image classifiers in a hierarchical max-pooling model with additional local pooling](https://mlsanity.com/paper/2106.05233/) (2021)
- [On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descent](https://mlsanity.com/paper/2312.17007/) (2023)
- [Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Data](https://mlsanity.com/paper/2402.15284/) (2024)
- [Bound to Disagree: Generalization Bounds via Certifiable Surrogates](https://mlsanity.com/paper/2602.23128/) (2026)
- [Under-Counted Tensor Completion with Neural Incorporation of Attributes](https://mlsanity.com/paper/2306.03273/) (2023)
- [A Theory for Conditional Generative Modeling on Multiple Data Sources](https://mlsanity.com/paper/2502.14583/) (2025)
- [On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversion](https://mlsanity.com/paper/2111.14220/) (2021)
- [Data-Adaptive Discriminative Feature Localization with Statistically Guaranteed Interpretation](https://mlsanity.com/paper/2211.10061/) (2022)
- [Statistically guided deep learning](https://mlsanity.com/paper/2504.08489/) (2025)

## 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.