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

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.

@article{zhang2025_2309.00508,
  title={ Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization },
  author={ Leyang Zhang and Yaoyu Zhang and Tao Luo },
  journal={arXiv preprint arXiv:2309.00508},
  year={ 2025 }
}