Comment by stego-tech
2 hours ago
As others have pointed out, both can be true:
* LLMs do just interpolate their training data, BUT-
* That can still yield useful "discoveries" in certain fields, absent the discovery of new mechanics that exist outside said training data
In the case of mathematics, LLMs are essentially just brute-forcing the glorified calculators they run on with pseudo-random data regurgitated along probabilities; in that regard, mathematics is a perfect field for them to be wielded against in solving problems!
As for organic chemistry, or biology, or any of the numerous fields where brand new discoveries continue happening and where mathematics alone does not guarantee predicted results (again, because we do not know what we do not know), LLMs are far less useful for new discoveries so much as eliminating potential combinations of existing data or surfacing overlooked ones for study. These aren't "new" discoveries so much as data humans missed for one reason or another - quack scientists, buried papers, or just sheer data volume overwhelming a limited populace of expertise.
For further evidence that math alone (and thus LLMs) don't produce guaranteed results for an experiment, go talk to physicists. They've been mathematically proving stuff for decades that they cannot demonstrably and repeatedly prove physically, and it's a real problem for continued advancement of the field.
> LLMs do just interpolate their training data
"interpolate" has a technical meaning - in this meaning, LLMs almost never interpolate. It also has a very vague everyday meaning - in this meaning, LLMs do interpolate, but so do humans.
An LLM in a harness with any tools (even a calculator) doesn't just interpolate because it can reach states out of its own distribution.
> * That can still yield useful "discoveries" in certain fields, absent the discovery of new mechanics that exist outside said training data
One can argue, new knowledge is just restructured data.
I think the main concerns about LLMs is the inherent "generative" aspects leading to hallucinations as a biproduct, because that's what produces the noi. Joint Embedding approaches are rather an interesting alternative that try to overcome this, but that's still in research phase.