The idea of singularity--that AI will improve itself--is that it assumes intelligence is an important part of improving AI.

The AIs improve by gradient descent, still the same as ever. It's all basic math and a little calculus, and then making tiny tweaks to improve the model over and over and over.

There's not a lot of room for intelligence to improve upon this. Nobody sits down and thinks really hard, and the result of their intelligent thinking is a better model; no, the models improve because a computer continues doing basic loops over and over and over trillions of times.

That's my impression anyway. Would love to hear contrary views. In what ways can an AI actually improve itself?