Analytic function approximation by path norm regularized deep networks
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Abstract (arXiv)
We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on 1/varepsilon can varepsilon-approximate functions that are analytic on certain regions of mathbbCd.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 10 of its 24 references that are in the map. First posted on arXiv 5 Apr 2021.
Builds on
10 of 24 references.
References · 10
- 2016Error bounds for approximations with deep ReLU networkscited by 567
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
- 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
- 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
- 2015Norm-Based Capacity Control in Neural Networkscited by 299
- 2018Exponential Convergence of the Deep Neural Network Approximation for Analytic Functionscited by 38
- 2020Statistical Guarantees for Regularized Neural Networkscited by 25
- 2018Approximation and Estimation for High-Dimensional Deep Learning Networkscited by 22
- 2020Piecewise linear activations substantially shape the loss surfaces of neural networkscited by 19
- 2018Capacity Control of ReLU Neural Networks by Basis-path Normcited by 10
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Citing papers per year: 2021: 1; 2022: 1; 2023: 0; 2024: 0; 2025: 0; 2026: 1.
3 papers.