Seems like you can always implement any function f: X → Y as a search process. For any input from the domain X, just make the search objective assign one to f(X) and zero to everything else. Then argmax over this objective.
Yes but my point uses a different approach to the translation, and so it seems like my point allows various standard arguments about argmax to also infect conditioning, whereas your proposed equivalence doesn’t really provide any way for standard argmax arguments to transfer.
(Haven’t double-checked the math or fully grokked the argument behind it, but strongly upvoted for making a case.)
I would be curious to know if it makes sense to anyone or if anyone agrees/disagrees.
Seems like you can always implement any function f: X → Y as a search process. For any input from the domain X, just make the search objective assign one to f(X) and zero to everything else. Then argmax over this objective.
Yes but my point uses a different approach to the translation, and so it seems like my point allows various standard arguments about argmax to also infect conditioning, whereas your proposed equivalence doesn’t really provide any way for standard argmax arguments to transfer.