# Optimization Landscapes of Wide Deep Neural Networks Are Benign

arXiv: https://arxiv.org/abs/2010.00885 · HTML: https://mlsanity.com/paper/2010.00885/

## Key facts

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

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

- [Neural Spectrahedra and Semidefinite Lifts: Global Convex Optimization of Polynomial Activation Neural Networks in Fully Polynomial-Time](https://mlsanity.com/paper/2101.02429/) (2021)
- [Manifold Regularization for Memory-Efficient Training of Deep Neural Networks](https://mlsanity.com/paper/2305.17119/) (2023)

## Abstract (arXiv)

We analyze the optimization landscapes of deep learning with wide networks. We highlight the importance of constraints for such networks and show that constraint -- as well as unconstraint -- empirical-risk minimization over such networks has no confined points, that is, suboptimal parameters that are difficult to escape from. Hence, our theories substantiate the common belief that wide neural networks are not only highly expressive but also comparably easy to optimize.