# Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learning

arXiv: https://arxiv.org/abs/2307.16203 · HTML: https://mlsanity.com/paper/2307.16203/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 30 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [Deep vs. shallow networks : An approximation theory perspective](https://mlsanity.com/paper/1608.03287/) (2016)
- [Provable approximation properties for deep neural networks](https://mlsanity.com/paper/1509.07385/) (2015)
- [Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks](https://mlsanity.com/paper/1610.09887/) (2016)
- [Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks](https://mlsanity.com/paper/1903.10047/) (2019)
- [Equivalence of approximation by convolutional neural networks and fully-connected networks](https://mlsanity.com/paper/1809.00973/) (2018)
- [Universal Consistency of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2106.12498/) (2021)
- [Depth Selection for Deep ReLU Nets in Feature Extraction and Generalization](https://mlsanity.com/paper/2004.00245/) (2020)
- [Generalization and Expressivity for Deep Nets](https://mlsanity.com/paper/1803.03772/) (2018)
- [Deep Neural Networks for Rotation-Invariance Approximation and Learning](https://mlsanity.com/paper/1904.01814/) (2019)
- [Realization of spatial sparseness by deep ReLU nets with massive data](https://mlsanity.com/paper/1912.07464/) (2019)

## Built on by (most cited first, 4 of 4)

- [Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach](https://mlsanity.com/paper/2503.07976/) (2025)
- [Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks](https://mlsanity.com/paper/2308.03259/) (2023)
- [Component-based Sketching for Deep ReLU Nets](https://mlsanity.com/paper/2409.14174/) (2024)
- [Feature Qualification by Deep Nets: A Constructive Approach](https://mlsanity.com/paper/2503.18676/) (2025)

## Abstract (arXiv)

This paper studies the performance of deep convolutional neural networks (DCNNs) with zero-padding in feature extraction and learning. After verifying the roles of zero-padding in enabling translation-equivalence, and pooling in its translation-invariance driven nature, we show that with similar number of free parameters, any deep fully connected networks (DFCNs) can be represented by DCNNs with zero-padding. This demonstrates that DCNNs with zero-padding is essentially better than DFCNs in feature extraction. Consequently, we derive universal consistency of DCNNs with zero-padding and show its translation-invariance in the learning process. All our theoretical results are verified by numerical experiments including both toy simulations and real-data running.