Local Recovery of Two-layer Neural Networks at Overparameterization

Under mild assumptions, we investigate the structure of loss landscape of two-layer neural networks near global minima, determine the set of parameters which recovers the target function, and characterize the gradient flows around it. With novel techniques, our work uncovers some simple aspects of the complicated loss landscape and reveals how model, target function, samples and initialization affect the training dynamics differently. These results concludes that two-layer neural networks can be recovered locally at overparameterization.