On Fri, Sep 27, 2019, at 12:48 PM, Aaron Meurer wrote: > There's a review paper for ICLR 2020 on training a neural network to > do symbolic integration. They claim that it outperforms Mathematica by > a large margin. Machine learning papers can sometimes make overzealous > claims, so scepticism is in order. > > https://openreview.net/pdf?id=S1eZYeHFDS > > The don't seem to post any code. The paper is in double blind review, > so maybe it will be available later. Or maybe it is available now and > I don't see it. If someone knows, please post a link here. > > They do cite the SymPy paper, but it's not clear if they actually use SymPy.
They wrote: "The validity of a solution itself is not provided by the model, but by an external symbolic framework (Meurer et al., 2017). " So that seems to suggest they used SymPy to check the results. > > I think it's an interesting concept. They claim that they generate > random functions and differentiate them to train the network. But I > wonder if one could instead take a large pattern matching integration > table like RUBI and train it on that, and produce something that works > better than RUBI. The nice thing about indefinite integration is it's > trivial to check if an answer is correct (just check if > diff(integral(f)) - f == 0), so heuristic approaches that can > sometimes give nonsense are tenable, because you can just throw out > wrong answers. > > I'm also curious (and sceptical) on just how well a neural network can > "learn" symbolic mathematics and specifically an integration > algorithm. Another interesting thing to do would be to try to train a > network to integrate rational functions, to see if it can effectively > recreate the algorithm (for those who don't know, there is a complete > algorithm which can integrate any rational function). My guess is that > this sort of thing is still beyond the capabilities of a neural > network. I saw this paper too today. My main question is whether their approach is better than Rubi (say in Mathematica, as it doesn't yet work 100% in SymPy yet). They show that their approach is much better than Mathematica, but so is Rubi. The ML approach seems like a brute force. So is Rubi. So it's fair to compare ML with Rubi. On the other hand, I feel it's unfair to compare brute force with an actual algorithm, such as Risch. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/db41cf67-acc9-4a84-8267-2742b748de4d%40www.fastmail.com.
