# Universality of Gradient Descent Neural Network Training

arXiv: https://arxiv.org/abs/2007.13664 · HTML: https://mlsanity.com/paper/2007.13664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [An in-depth look at approximation via deep and narrow neural networks](https://mlsanity.com/paper/2510.07202/) (2025)

## Abstract (arXiv)

It has been observed that design choices of neural networks are often crucial for their successful optimization. In this article, we therefore discuss the question if it is always possible to redesign a neural network so that it trains well with gradient descent. This yields the following universality result: If, for a given network, there is any algorithm that can find good network weights for a classification task, then there exists an extension of this network that reproduces these weights and the corresponding forward output by mere gradient descent training. The construction is not intended for practical computations, but it provides some orientation on the possibilities of meta-learning and related approaches.