# Analytic function approximation by path norm regularized deep networks

arXiv: https://arxiv.org/abs/2104.02095 · HTML: https://mlsanity.com/paper/2104.02095/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 5 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [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)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions](https://mlsanity.com/paper/1807.00297/) (2018)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Approximation and Estimation for High-Dimensional Deep Learning Networks](https://mlsanity.com/paper/1809.03090/) (2018)
- [Piecewise linear activations substantially shape the loss surfaces of neural networks](https://mlsanity.com/paper/2003.12236/) (2020)
- [Capacity Control of ReLU Neural Networks by Basis-path Norm](https://mlsanity.com/paper/1809.07122/) (2018)

## Built on by (most cited first, 3 of 3)

- [Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation](https://mlsanity.com/paper/2109.13359/) (2021)
- [Shallow neural network representation of polynomials](https://mlsanity.com/paper/2208.08138/) (2022)
- [Efficient Approximation to Analytic and Lp functions by Height-Augmented ReLU Networks](https://mlsanity.com/paper/2603.11128/) (2026)

## 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.