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Deep Linear Neural Networks: Error Bound Analysis for Regularized Loss

By PulseAugur Editorial · [1 sources] ·

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]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Deep Linear Neural Networks: Error Bound Analysis for Regularized Loss

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

  1. arXiv cs.LG TIER_1 English(EN) · Po Chen, Rujun Jiang, Peng Wang ·

    Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks

    arXiv:2502.11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networ…

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