I don't think you really answered my question. What's been done by the paper is show experimentally that networks don't have enough information to justify their

I don't think you really answered my question. What's been done by the paper is show experimentally that networks don't have enough information to justify their weight precision, and that's really good and a very important result, but what I was asking was if there's a rigorous way to take an arbitrary network and determine its information content (either by itself, or compared to another network). Possibly that can be relative to its outputs.