Why do formal research papers keep statements that should be interpreted informally?
In the two examples you give, I don't agree the statements need to be &quot;interpreted informally&quot;. Rather I would say that the meaning is clear within the context of the problem. For example, suppose you have a function f(a,b,c,d) or an expectation E_{a~p, b~q}[ f(a, b)]. Often authors will just write f or E[f] respectively. There is no mistake, it's just the notation is being left out. It's basically the same thing in the examples you point out. &quot;our generative model learned pdata&quot; is just a shorthand for &quot;we learn a model f(z) which maps a latent space z to an output S so that we can approximate drawing samples from pdata by drawing a sample z&quot;. And that's not unclear or &quot;informal&quot;, because the latter is just a definition of what generative model means in that context.
Specific problems can have their own language or jargon, and it can be confusing to read papers without knowing it. Part of becoming an expert in a specific problem is learning how people think about that problem.