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English(EN) Global Exponential Convergence of Two-Layer Linear Network Training

已证明两层线性网络的全局指数收敛性

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员已证明，使用光滑的Polyak-Lojasiewicz预测损失函数，可以实现宽两层线性网络的全局指数收敛。研究表明，因子中的梯度流可以通过有限维Bures流精确描述，该流受神经元定律协方差的影响。只要初始协方差满足谱支撑间隙条件，均值场守恒定律就能建立隐藏预处理块的谱下界，从而进一步支持了这种收敛速率。这些发现延伸到深度线性ResNets，并通过比较预测速率和观察速率的数值实验进行了说明。 AI

影响 为训练线性神经网络提供了理论保证，可能为未来的优化技术提供参考。

排序理由 关于神经网络训练理论收敛特性的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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已证明两层线性网络的全局指数收敛性

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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Stephen Y Zhang, Gabriel Peyr\'e ·

    Global Exponential Convergence of Two-Layer Linear Network Training

    arXiv:2610.09356v1 Announce Type: new Abstract: We prove global exponential (linear) convergence with an explicit rate in the rich scaling for wide two-layer linear networks trained with smooth Polyak-Lojasiewicz predictor losses. Gradient flow in the factors closes exactly in te…

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