How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks

• URL: http://arxiv.org/abs/2406.01766v2
• Date: Mon, 04 Nov 2024 23:02:25 GMT
• Title: How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks
• Authors: Mo Zhou, Rong Ge,
• Abstract summary: The ability of learning useful features is one of the major advantages of neural networks. Recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning.
• Score: 18.809547338077905
• License:
• Abstract: The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works also demonstrate the potential for neural networks to go beyond NTK regime and perform feature learning. Recently, a line of work highlighted the feature learning capabilities of the early stages of gradient-based training. In this paper we consider another mechanism for feature learning via gradient descent through a local convergence analysis. We show that once the loss is below a certain threshold, gradient descent with a carefully regularized objective will capture ground-truth directions. We further strengthen this local convergence analysis by incorporating early-stage feature learning analysis. Our results demonstrate that feature learning not only happens at the initial gradient steps, but can also occur towards the end of training.

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