Seems related to recent results about compression and generalization in neural networks (https://arxiv.org/abs/1804.05862). Also to Bayesian Occam's razor arguments about univeral priors etc. All of these seem to be converging on the same point about how information content of a representation relates to generalization. Glad this paper points out that measures like BIC ignore information, instead substituting a weak heuristic such as number of parameters.