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Can you give an example of the kind of thing you are describing? What is the "prior" knowledge? I think there is a huge gap between the language of architectural structures and typical languages for prior knowledge.
I mentioned the example of bAbI. If you already know how to go from the input data to the answer, you can express the process as a parametric formula and have your network learn the parameters. Most of the work was done by you, not by your network.
Another way to inject prior knowledge is by adding to your network differentiable operations that you have identified as building blocks of the solution (e.g. if you know the solution involves cosines, you can add cos ops to your architecture).
And you say there are 10,000 papers (approx.) doing this?
Are you referring to the original bAbI paper, or a later one?
You can rank every bAbI-solving paper by how closely the solution architecture maps to the data-generation template. It's basically the same as ranking by accuracy. This is true to most tasks outside of perception -- bAbI is just an extreme example.
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