# Global Convergence of Sobolev Training for Overparameterized Neural Networks

arXiv: https://arxiv.org/abs/2006.07928 · HTML: https://mlsanity.com/paper/2006.07928/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 2 of 2)

- [Sobolev acceleration for neural networks](https://mlsanity.com/paper/2509.19773/) (2025)
- [DeepLight: A Sobolev-trained Image-to-Image Surrogate Model for Light Transport in Tissue](https://mlsanity.com/paper/2601.09439/) (2026)

## Abstract (arXiv)

Sobolev loss is used when training a network to approximate the values and derivatives of a target function at a prescribed set of input points. Recent works have demonstrated its successful applications in various tasks such as distillation or synthetic gradient prediction. In this work we prove that an overparameterized two-layer relu neural network trained on the Sobolev loss with gradient flow from random initialization can fit any given function values and any given directional derivatives, under a separation condition on the input data.