# Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization

arXiv: https://arxiv.org/abs/2309.00508 · HTML: https://mlsanity.com/paper/2309.00508/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 33 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 4 of 4)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances](https://mlsanity.com/paper/2105.12221/) (2021)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [The Global Landscape of Neural Networks: An Overview](https://mlsanity.com/paper/2007.01429/) (2020)

## Built on by (most cited first, 4 of 4)

- [Towards Understanding Adam Convergence on Highly Degenerate Polynomials](https://mlsanity.com/paper/2603.09581/) (2026)
- [Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks](https://mlsanity.com/paper/2405.17501/) (2024)
- [Disentangle Sample Size and Initialization Effect on Perfect Generalization for Single-Neuron Target](https://mlsanity.com/paper/2405.13787/) (2024)
- [Linear Independence of Generalized Neurons and Related Functions](https://mlsanity.com/paper/2410.03693/) (2024)

## Abstract (arXiv)

Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate: (i) how global minima with zero generalization error become geometrically separated from other global minima as the sample size grows; and (ii) the local convergence properties and rate of gradient flow dynamics. Our results indicate that two-layer neural networks can be locally recovered in the regime of overparameterization.