建立非线性随机矩阵的集中不等式，用于分析神经网络与非交换多项式。

Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

• 基于非线性随机矩阵构造集中不等式
• 给出神经网络共轭核的线性谱统计估计
• 适用于依赖随机矩阵的非交换多项式分析

我们证明了几类非线性随机矩阵的集中不等式。作为推论，得到了神经网络共轭核的线性谱统计估计，以及在（可能相关的）随机矩阵中非交换多项式的相关结果。该理论为理解深度神经网络的谱特性提供了数学工具，尤其在矩阵间存在依赖关系时具有重要价值。

原文摘要 · Abstract (English)

We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly dependent) random matrices.

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