Deep Linear Neural Networks: Error Bound Analysis for Regularized Loss

This paper delves into the optimization principles of deep linear neural networks, a topic of recent significant interest. Researchers analyzed the local geometry of the regularized squared loss around critical points, providing a closed-form characterization. The study establishes an error bound for the regularized loss under specific conditions, quantifying the distance to the critical point set based on the gradient norm. This bound supports the derivation of linear convergence for first-order methods, a finding demonstrated through numerical experiments showing gradient descent's linear convergence to a critical point. AI

IMPACT Provides theoretical insights into the optimization of deep linear neural networks, potentially informing the development of more efficient training algorithms.

RANK_REASON Academic paper on theoretical analysis of neural network optimization. [lever_c_demoted from research: ic=1 ai=1.0]

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• Peng Wang

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