研究大随机矩阵的高秩扰动下特征值渐近行为，为深度神经网络剪枝提供理论支持。
Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
- 基于随机矩阵理论分析高秩扰动下的特征值分布
- 发现随样本量增大，异常特征值数量也持续增长
- 适用于理解深度神经网络权重结构与剪枝机制
本文研究变形的Wigner随机矩阵，这类矩阵与深度神经网络（DNN）密切相关：训练后DNN的权重矩阵可表示为 $R + S$，其中 $R$ 为随机部分，$S$ 具有高度相关性。此类矩阵的谱在基于随机矩阵理论的新剪枝技术中起关键作用。实践中，矩阵 $S$ 的谱结构可能十分复杂。本文对 $S$ 为满秩且异常特征值数量随规模增加的情况进行了渐近分析。
原文摘要 · Abstract (English)
The paper is concerned with deformed Wigner random matrices. These matrices are closely related to Deep Neural Networks (DNNs): weight matrices of trained DNNs could be represented in the form $R + S$, where $R$ is random and $S$ is highly correlated. The spectrum of such matrices plays a key role in rigorous underpinning of the novel pruning technique based on Random Matrix Theory. In practice, the spectrum of the matrix $S$ can be rather complicated. In this paper, we develop an asymptotic analysis for the case of full rank $S$ with increasing number of outlier eigenvalues.
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