Understanding Neural Networks with Logarithm Determinant Entropy Estimator
This work addresses the challenge of interpreting neural network behavior for researchers, though it appears incremental as it builds on existing entropy estimation methods.
The authors tackled the problem of understanding neural network behavior by proposing the LogDet estimator, a reliable matrix-based entropy estimator that approximates Shannon differential entropy, and demonstrated its effectiveness in analyzing neural networks, finding a functional distinction between shallow and deeper layers.
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.