arXiv:2502.05074cond-mat.dis-nncs.LG2025-02被引 7
提出随机梯度动力学的确定性等价，统一分析高维线性模型性能
Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models
- 基于随机矩阵理论推导两点半定等价公式
- 首次统一解释高维线性回归、核回归等模型的渐近表现
- 适用于研究深度学习优化机制的学者
我们推导出随机矩阵谱函数的两点关联函数的新确定性等价。利用这一结果，对多种高维线性模型在随机梯度下降训练下的性能给出了统一的推导。涵盖高维线性回归、核回归以及线性随机特征模型。结果包含已有渐近结论及新的发现。
原文摘要 · Abstract (English)
We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with stochastic gradient descent. This includes high-dimensional linear regression, kernel regression, and linear random feature models. Our results include previously known asymptotics as well as novel ones.
随机梯度线性模型确定性等价统计学习
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