On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student Setting

Shunta Akiyama · Taiji Suzuki

[ Abstract ] [ Livestream: Visit Learning Theory 1 ] [ Paper ]
Wed 21 Jul 5:40 a.m. — 5:45 a.m. PDT
[ Paper ]

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.

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