  Understanding the informative behaviour of deep neural networks is challenged
by misused estimators and the complexity of network structure, which leads to
inconsistent observations and diversified interpretation. Here we propose the
LogDet estimator -- a reliable matrix-based entropy estimator that approximates
Shannon differential entropy. We construct informative measurements based on
LogDet estimator, verify our method with comparable experiments and utilize it
to analyse neural network behaviour. Our results demonstrate the LogDet
estimator overcomes the drawbacks that emerge from highly diverse and
degenerated distribution thus is reliable to estimate entropy in neural
networks. The Network analysis results also find a functional distinction
between shallow and deeper layers, which can help understand the compression
phenomenon in the Information bottleneck theory of neural networks.
