You can take a (calculus) derivative of the mathematical construct that represents the lookup table. And yeah, it is very not obvious how a "lookup/hash table"

You can take a (calculus) derivative of the mathematical construct that represents the lookup table. And yeah, it is very not obvious how a "lookup/hash table" could be differentiable, based on how it's implemented say, in a leetcode exercise. That's part of the genius of the transformer.