What will happen if to train an LLM on taking integrals and solving equations? The process of mathematical education can be absolutely automated by a computer algebra system because the verification is easy.
Is it possible that LLM will gan the ability to take integrals and simplify expressions better than the computer algebra system itself?
If you're interested in research on using LLMs for arithmetic tasks, Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks is a nice recent (May 2023) article.
If you're interested in research on using LLMs for more advanced mathematics, MiniF2F is a common benchmark. Check out the papers linked from the leaderboard.
If you're looking for LLM models or datasets for mathematics, https://huggingface.co/hoskinson-center and https://leandojo.org/ are good starting points.
Depends what you mean by 'better' (in what sense?).
Nevertheless, though it is possible that an LLM can solve algebra, in general it shall not offer any benefit than a computer algebra system (again depends on what is 'better', and assuming a fair comparison).
This is because in doing so an LLM needs to deal with both the language and the math, while computer algebra system only needs to work on the math. It is like a top human runner and a vehicle - in general vehicle moves faster because this is what they are crafted solely for.
And a few words on the comments - finding rhymes is NOT like solving equations, because no rhymes is wrong (even if it sounds terrible, but that's subjective); but there is straight wrong in solving equations.
On the other hand, there are efforts to discover and improve algorithms, most notably Google's AlphaTensor. However it has nothing to do with LLM, but a lot to do with RL.
Is it possible that LLM will gan the ability to take integrals and simplify. expressions better than the computer algebra system itself?
Possibly, but not in one run - i.e., if you instruct it and train it to analyse and simplify step by step, while writing this out, and it fits into the context - it is an experiment.
You may also want to STILL use a GAN approach with multiple LLM working on the problem - one writing, others correcting. Which requires a multi-step approach.
Otherwise: no. Math has specific elements that do not really work well with a "forward only" approach of a neural network.
