Measuring Information Transfer in Neural Networks

Quantifying the information content in a neural network model is essentially estimating the model's Kolmogorov complexity. Recent success of prequential coding on neural networks points to a promising path of deriving an efficient description length of a model. We propose a practical measure of the generalizable information in a neural network model based on prequential coding, which we term Information Transfer ($L_{IT}$). Theoretically, $L_{IT}$ is an estimation of the generalizable part of a model's information content. In experiments, we show that $L_{IT}$ is consistently correlated with generalizable information and can be used as a measure of patterns or "knowledge" in a model or a dataset. Consequently, $L_{IT}$ can serve as a useful analysis tool in deep learning. In this paper, we apply $L_{IT}$ to compare and dissect information in datasets, evaluate representation models in transfer learning, and analyze catastrophic forgetting and continual learning algorithms. $L_{IT}$ provides an information perspective which helps us discover new insights into neural network learning.