This study evaluates thresholds for removing singular values from singular value decomposition-based low-rank approximations of deep neural network weight matrices. Each weight matrix is modeled as the sum of signal and noise matrices. The low-rank approximation is obtained by removing noise-related singular values using a threshold based on random matrix theory. To assess the adequacy of this threshold, we propose an evaluation metric based on the cosine similarity between the singular vectors of the signal and original weight matrices. The proposed metric is used in numerical experiments to compare two threshold estimation methods.

翻译：本研究评估了基于奇异值分解的深度神经网络权重矩阵低秩近似中去除奇异值的阈值。每个权重矩阵被建模为信号矩阵和噪声矩阵之和。通过使用基于随机矩阵理论的阈值去除与噪声相关的奇异值，获得低秩近似。为评估该阈值的充分性，我们提出了一种基于信号矩阵与原始权重矩阵奇异向量之间余弦相似度的评估指标。该指标被用于数值实验，以比较两种阈值估计方法。