New theory proves SGD convergence in deep linear networks

Researchers have established new theoretical convergence guarantees for stochastic gradient descent (SGD) in the context of deep linear neural networks. This work extends existing gradient descent results to SGD under regularized squared loss, demonstrating almost sure boundedness of SGD iterates. The analysis, utilizing the framework of asymptotic pseudotrajectories from stochastic approximation theory, shows convergence to critical points under mild conditions, without requiring Lipschitz properties or whitened data. This represents a significant step in bridging the gap between theoretical optimization and practical stochastic training for deep learning models. AI

IMPACT Provides theoretical grounding for SGD optimization in simplified deep learning models, potentially informing more complex network training.

RANK_REASON Academic paper detailing theoretical convergence properties of SGD in deep linear networks. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• deep learning
• gradient descent
• Linear Neural Networks
• SGD
• stochastic approximation theory
• stochastic gradient descent
• Ulrich Terstiege

• paper
• other

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