# A priori estimates for classification problems using neural networks

arXiv: https://arxiv.org/abs/2009.13500 · HTML: https://mlsanity.com/paper/2009.13500/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2020.

## Built on by (most cited first, 5 of 5)

- [Optimal Approximation Rate of ReLU Networks in terms of Width and Depth](https://mlsanity.com/paper/2103.00502/) (2021)
- [Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons](https://mlsanity.com/paper/2107.02397/) (2021)
- [Nonlocal techniques for the analysis of deep ReLU neural network approximations](https://mlsanity.com/paper/2504.04847/) (2025)
- [Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks](https://mlsanity.com/paper/2103.16355/) (2021)
- [Dimension-independent learning rates for high-dimensional classification problems](https://mlsanity.com/paper/2409.17991/) (2024)

## Abstract (arXiv)

We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and direct approximation theorems to obtain a priori error estimates for regularized loss functionals.