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.

翻译：本文研究变形Wigner随机矩阵。这类矩阵与深度神经网络（DNNs）密切相关：训练后的DNNs权重矩阵可表示为$R + S$的形式，其中$R$为随机矩阵，$S$为高度相关矩阵。此类矩阵的谱性质在基于随机矩阵理论的新型剪枝技术的严格论证中起着关键作用。实践中，矩阵$S$的谱结构可能相当复杂。本文针对满秩矩阵$S$中离群特征值个数递增情形，建立了相应渐近分析框架。