  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.
