In a lot of academic fields it's assumed that a researcher really understands their stuff to first principles. I think being able to derive back prop is a really straightforward exercise and definitely you should expect a researcher in the area to be able to do it off the cuff. I think it's akin to fizz buzz; it'll weed out people who really don't know what they're doing but it won't tell you too much about those who do it without trouble.
I thought so too, until my friend told me that CIT PhD and an applied research scientist in a FANNG company derived an incremental Gaussian mixture model without using the property of GMM at all, and another CIT PhD in the same team defended the algorithm by saying something like "but the intuition is correct". I couldn't believe my ears.
but most researchers don't use first principles day to day, like others in this thread -have said - if you don't use it you lose it. researchers don't utilize the details of back prop in there day to day work, so expecting an off the cuff derivation isn't a fair assessment of what makes a good researcher
Researchers specialize and as such even in a "single field" they work at very different levels of abstraction; one subfield will care about building up some novel construction from first principles and then another subfield will want to use that construction as a basic axiomatic building block and abstracting from the details. E.g. execution performance optimization of a known formula is orthogonal to developing a better formula, we want people working on both these aspects, these are going to be different people who each build on their own subfields first principles that don't overlap much with the first principles of the other researcher.
