On 12/17/23 10:22, Waldek Hebisch wrote:
IIUC this was version 3.5. Newer version is supposed to be much stronger. Few weeks ago OpenAI people claimed to made "breakthrough" in handling of math problems. Of course, ATM it is not clear what they have. But some things are possible to guess. There were earlier reports that proper "didactics" helps: start training on easy problems and gradually move to harder ones. Supposedly learing "step by step" reasoning is easier than "end to end" approach which was used (and quite sucessful) on other problems. There is also an obvious workaround: since ANN-s seem to have trouble with algorithmically trival math one could couple ANN to a "calculator", that is conventional program for doing calculations. So there are various approaches. In particular
News from 3 days ago: https://deepmind.google/discover/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/ """" FunSearch works by pairing a pre-trained LLM, whose goal is to provide creative solutions in the form of computer code, with an automated “evaluator”, which guards against hallucinations and incorrect ideas. """" """" FunSearch is an iterative procedure; at each iteration, the system selects some programs from the current pool of programs, which are fed to an LLM. The LLM creatively builds upon these, and generates new programs, which are automatically evaluated. The best ones are added back to the pool of existing programs, creating a self-improving loop. """" So similar things can be: Pair an AI integrator with CAS to verify results; Pair an AI theorem generator with theorem prover to verify results. - Qian
neural nets have enough capacity to memorize something like Rubi rules. If "trainig" could teach it to chain rules, than ANN could get to level comparable to Rubi. It would probably get some side conditions wrong, but it could compesate by having more rules and via "beam search" (that is producing many candidate solutions and using external differentiator to remove wrong candidates). Better net could learn to internally discard wrong candidates. I have no idea at what stage is Google offer. Public version is probably weaker than versions available to internal developers and paying customers. Still, progress seem to be rapid and there is something like a year from availability of ChatGPT 3.5.
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