新的梯度下降方法在过参数模型上展现指数级收敛性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-08-12 04:00

研究人员提出了一种用于优化过参数模型的新方法——双空间预条件梯度下降（Dual Space Preconditioned Gradient Descent）。该方法包含归一化梯度下降（Normalized Gradient Descent）和梯度裁剪（Gradient Clipping）等变体，已被证明在线性模型上可以指数级收敛到完美拟合数据的解。研究还探讨了这些方法的隐式偏差，表明收敛点可能取决于步长，并提供了一种近似偏差性质，将预条件方法与标准梯度下降的收敛性联系起来。 AI

影响引入了一种新颖的优化技术，有望提高大型、过参数化机器学习模型的训练效率。

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arXiv stat.ML TIER_1 English(EN) · Reza Ghane, Danil Akhtiamov, Babak Hassibi · 2026-08-12 04:00

过参数化条件下梯度下降的双空间预处理

arXiv:2603.10485v3 Announce Type: replace Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping. We consider preconditioners of the form $\na…

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过参数化条件下梯度下降的双空间预处理

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