I feel very comfortable saying, as a mathematician, that the ability to solve grade school maths problems would not be at all a predictor of ability to solve real mathematical problems at a research level. The reason LLMs fail at solving mathematical problems is because: 1) they are terrible at arithmetic, 2) they are terrible at algebra, but most importantly, 3) they are terrible at complex reasoning (more specifica…
If the model then distills that information down to a new feature, and re-examines the original prompt with the new feature embedded in an extra input tensor, then repeats this process ad-infinitum, will the language model's "prime directive" and reasoning ability be sufficient to arrive at new, verifiable and provable conjectures, outside the realm of the dataset it was trained on?
If GPT-4,5,...,n can progress in this direction, then we should all see the writing on the wall. Also, the day will come where we don't need to manually prepare an updated dataset and "kick off a new training". Self-supervised LLMs are going to be so shocking.