I appreciate the author showing some of the math that drives the optimization. As a reader, I'd suggest introducing SGD ahead of the PD calculations, because it would give a clearer motivation for the PDs.
The typical operation applied to sets of functions is composition, so idempotency of a function f is the condition that f(f(x)) = f(x) for all x in the domain of f. I don't think that applies meaningfully to GET.
Nothing about names like StopIteration and AttributeError indicate to me that I should use them for control flow. Python just instructs me to use them that way...
The birthday paradox arises because the probability that two candidates do not match is small compared to the number of candidates. In this case, the candidates are photos and a match in fact requires a match on multiple variables (e.g. angle, timing) that are effectively continuous. A match between 2 arbitrary photos must then have zero-ish probability and a non-match must have one-ish. So it still seems inestimably improbable that something like this would happen.