# The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networks

arXiv: https://arxiv.org/abs/1912.06987 · HTML: https://mlsanity.com/paper/1912.06987/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [Generalization Error of GAN from the Discriminator's Perspective](https://mlsanity.com/paper/2107.03633/) (2021)
- [A Mathematical Framework for Learning Probability Distributions](https://mlsanity.com/paper/2212.11481/) (2022)
- [One-pass Stochastic Gradient Descent in Overparametrized Two-layer Neural Networks](https://mlsanity.com/paper/2105.00262/) (2021)
- [Distribution Free Uncertainty for the Minimum Norm Solution of Over-parameterized Linear Regression](https://mlsanity.com/paper/2102.07181/) (2021)
- [Data-informed Deep Optimization](https://mlsanity.com/paper/2107.08166/) (2021)
- [Quantifying the Prediction Uncertainty of Machine Learning Models for Individual Data](https://mlsanity.com/paper/2412.07520/) (2024)

## Abstract (arXiv)

We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for all three models, the generalization error for the minimum-norm solution is comparable to the Monte Carlo rate, up to some logarithmic terms, as long as the models are sufficiently over-parametrized.