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arXiv · 2307.16203

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

Zhi Han·Baichen Liu·Shao-Bo Lin·Ding-Xuan Zhou
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Abstract

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.

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Zhi Han, Baichen Liu, Shao-Bo Lin, Ding-Xuan Zhou. 2023-07-30. Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learning. https://arxiv.org/abs/2307.16203

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