In a feedforward network, Transfer Entropy (TE) can be used to measure the
influence that one layer has on another by quantifying the information transfer
between them during training. According to the Information Bottleneck
principle, a neural model's internal representation should compress the input
data as much as possible while still retaining sufficient information about the
output. Information Plane analysis is a visualization technique used to
understand the trade-off between compression and information preservation in
the context of the Information Bottleneck method by plotting the amount of
information in the input data against the compressed representation. The claim
that there is a causal link between information-theoretic compression and
generalization, measured by mutual information, is plausible, but results from
different studies are conflicting. In contrast to mutual information, TE can
capture temporal relationships between variables. To explore such links, in our
novel approach we use TE to quantify information transfer between neural layers
and perform Information Plane analysis. We obtained encouraging experimental
results, opening the possibility for further investigations.

在一个前馈网络中，可以使用传递熵（TE）来衡量一层对另一层的影响，通过在训练期间量化它们之间的信息传递。通过在输入数据中的信息量与压缩表示之间绘制图表来理解信息瓶颈方法中压缩和信息保留之间的权衡，这被称为信息平面分析。我们使用 TE 来量化神经层之间的信息传输，并进行信息平面分析以探索信息理论压缩和泛化之间的因果关系。我们获得了令人鼓舞的实验结果，为进一步研究打开了可能性。

深度学习中的信息平面分析可视化通过传递熵

Information Plane Analysis Visualization in Deep Learning via Transfer  Entropy

We review the current literature concerned with information plane analyses of
neural network classifiers. While the underlying information bottleneck theory
and the claim that information-theoretic compression is causally linked to
generalization are plausible, empirical evidence was found to be both
supporting and conflicting. We review this evidence together with a detailed
analysis of how the respective information quantities were estimated. Our
survey suggests that compression visualized in information planes is not
necessarily information-theoretic, but is rather often compatible with
geometric compression of the latent representations. This insight gives the
information plane a renewed justification.
Aside from this, we shed light on the problem of estimating mutual
information in deterministic neural networks and its consequences.
Specifically, we argue that even in feed-forward neural networks the data
processing inequality need not hold for estimates of mutual information.
Similarly, while a fitting phase, in which the mutual information between the
latent representation and the target increases, is necessary (but not
sufficient) for good classification performance, depending on the specifics of
mutual information estimation such a fitting phase need not be visible in the
information plane.

本文就信息平面分析、神经网络分类器、信息论压缩、潜在表示、互信息估计等方面的问题进行了综述和分析，研究发现信息压缩不一定与信息论有关，而是与潜在表示的几何压缩相容。此外还探讨了神经网络互信息估计的问题及其后果。