Information in Infinite Ensembles of Infinitely Wide Neural Networks

In order to gain insights into the generalization properties of deep neural networks, in this preliminary work we suggest studying the generalization properties of infinite ensembles of infinitely wide neural networks. Amazingly, this model family admits tractable calculations for many information theoretic quantities. Below we both derive these quantities and report some initial empirical investigations in the search for signals that correlate with generalization on both toy and real datasets.