On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student Setting
This provides a theoretical foundation for deep learning training dynamics, addressing a core problem for researchers in machine learning theory, though it is incremental as it builds on existing teacher-student frameworks.
The paper tackles the theoretical understanding of training two-layer ReLU neural networks in a teacher-student regression model, showing that with specific regularization and over-parameterization, gradient descent can identify the teacher's parameters with high probability despite non-convexity.
Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a teacher-student regression model, in which a student network learns an unknown teacher network through its outputs. We show that with a specific regularization and sufficient over-parameterization, the student network can identify the parameters of the teacher network with high probability via gradient descent with a norm dependent stepsize even though the objective function is highly non-convex. The key theoretical tool is the measure representation of the neural networks and a novel application of a dual certificate argument for sparse estimation on a measure space. We analyze the global minima and global convergence property in the measure space.