Diverse Neural Network Learns True Target Functions

Understand

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications.

• Despite their practical success, there is a paucity of results that provide theoretical guarantees on why they are so effective.
• Lying in the center of the problem is the difficulty of analyzing the non-convex loss function with potentially numerous local minima and saddle points.
• Can neural networks corresponding to the stationary points of the loss function learn the true target function? If yes, what are the key factors contributing to such nice optimization properties? In this paper, we answer these questions by analyzing one-hidden-layer neural networks with ReLU activation, and show that despite the non-convexity, neural networks with diverse units have no spurious local minima.