It takes 3 minutes to train the Shakespeare model with gradient descent. The black-box methods I tested so far likely take 30+ hours to train (I haven't tried to take them to the end yet). I've hit a wall where progress is very slow. The text generated at that stage has punctuation and words are split with spaces but the words themselves are mostly nonsense. Almost feels like it learned that English is letters separated by spaces, and that you put exclamation marks or periods at the end but not that much more.
There's some larger scale CMA-ES variants I still want to test that don't have quality implementations. I've tried to stare at pictures of gradients and weights from half-trained models and trying to come up with ideas how to get there with black-box optimization. Also trying some original ideas where you compute a gradient, but you would not compute it against a loss function. The gradient would be more for discovering hidden structure in weights, that you would then put on some black-box optimizer as a guide (which I guess makes it not entirely black box. Gray box?)
Possible? I mean, I guess technically. Practical? No way, unless some major breakthrough happens.
My current goal is to just produce a model, even if training takes laughably long so I can say I've trained a language model using nothing but getting a fitness score from a black box function.
Edit: if you are reading this and are aware of any other serious attempts at training a non-trivial sized language model without gradient descent I would want to know. So I can try their methods. I know there's some large scale stuff used in reinforcement learning like in one Uber paper but not in LLMs specifically.