The matrix-based Renyi's \alpha-entropy functional and its multivariate
extension were recently developed in terms of the normalized eigenspectrum of a
Hermitian matrix of the projected data in a reproducing kernel Hilbert space
(RKHS). However, the utility and possible applications of these new estimators
are rather new and mostly unknown to practitioners. In this paper, we first
show that our estimators enable straightforward measurement of information flow
in realistic convolutional neural networks (CNN) without any approximation.
Then, we introduce the partial information decomposition (PID) framework and
develop three quantities to analyze the synergy and redundancy in convolutional
layer representations. Our results validate two fundamental data processing
inequalities and reveal some fundamental properties concerning the training of
CNN.

本文介绍了基于重现核希尔伯特空间中投影数据的 Hermitian 矩阵的归一化特征谱而发展起来的基于矩阵的 Renyi's alpha-entropy functional 及其多元扩展方法，拓展其使用价值并应用于卷积神经网络（CNN）中，通过发展三个量来分析卷积层表示中的协同作用和冗余，验证了两个基本的数据处理不等式，揭示了训练 CNN 的一些基本特性。