2019/01/01 by Zheng-Chu Guo, Lei Shi, Guo, Zheng-Chu +3 · 2 citations
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Artificial neural network #Computer science #Deep learning #Deep neural networks #Deep water #FOS: Computer and information sciences #Feature (linguistics) #Generative Adversarial Networks and Image Synthesis #Geology #Image and Signal Denoising Methods #Logarithm #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Neural Networks and Applications #Simple (philosophy) #Smoothness #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1901.00130
published in arXiv (Cornell University) (Cornell University) · 12 pages, 2 figures
arxiv created 2019/01/01 · openalex publication_date 2019/01/01 · arxiv updated 2019/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additional capacity costs. This verifies the advantage of deep nets in realizing complex features. On the other hand, to realize some simple data feature like the smoothness, we prove that, up to a logarithmic factor, the approximation rate of deep nets is asymptotically identical to that of shallow nets, provided that the depth is fixed. This exhibits a limitation of deep nets in realizing simple features.