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Basically, a lot of papers can be rephrased as "we achieved better performance on this specific task by going to great lengths to inject more information about the task in our training setup"
An extreme case of this: working with a synthetically-generated dataset where samples follow a "template" (e.g. bAbI), and manually hard-coding that template into your NN architecture
Fitting parametric models via gradient descent, unsurprisingly, works best when what you are fitting is already a template of the solution. Of course, convnets are an instance of this (but in a good way, since their assumptions generalize to all visual data).
This is often done in Bayesian Machine Learning. Step 1: sample data from the generative model. Step 2: use learning algorithm to see how well it learns from this data. If it works well then you start looking at "real world" datasets.
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