I think it applies because lookups can be done by multiplying one-hot vectors (or masks) with matrices; this is roughly analogous to what happens when we multiply Q with K^T in a self-attention head.

Read this: https://e2eml.school/transformers.html#table_lookup

And then read: https://e2eml.school/transformers.html#attention

Also, multiplication is differentiable as you can calculate a partial derivative of this operation, and the ability to do that is what allows gradient descent optimization via the chain rule.

That's exactly the point, though! It's surprising. A hashtable is a map from keys to values. Making it differentiable means that a small change in the key also makes a small change in the value!

differentiable relative to the model parameters. The attention mechanism does store(key(x), value(x)), followed by lookup(query(y)), where key(), value(), lookup(), query() are all designed to be differentiable.