  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.
