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This research aims to analyze the convergence rates of gradient descent in overparameterized neural networks.

Convergence rates for gradient descent in the training of overparameterized artificial neural networks with piecewise affine activation

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This research aims to analyze the convergence rates of gradient descent in overparameterized neural networks.
Considered fully connected shallow artificial neural networks with piecewise affine activation.
Analyzed gradient descent optimization in the overparameterized regime.
Examined the relationship between network width, learning rate, and convergence rate.
Batch gradient descent can achieve zero training loss with high probability.
Convergence occurs at a linear rate when certain conditions on network width and learning rate are met.

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Analysis shows optimized artificial neural networks can achieve zero training loss, indicating effective learning in supervised tasks.

Jentzen et al. (2026) studied this question.

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