Neural nets are trained for a particular statistical distribution of inputs and in the paper they describe their method for generating a particular ensemble of possibilities. There might be something inherent about the examples they give that means they are all solved using a particular approach. From their description I could imagine writing a pattern-matching integrator that would explicitly try to reverse the way the examples are generated.
Perhaps the examples from e.g. the SymPy test suite would in some ways represent a more "natural" distribution since they are written by humans and show the kinds of problems that humans wanted to solve. It would be interesting to see how the accuracy of the net looks on that distribution of inputs (although any comparison with SymPy on that data would be unfair). Oscar On Sat, 28 Sep 2019 at 07:30, Aaron Meurer <asmeu...@gmail.com> wrote: > > On Fri, Sep 27, 2019 at 11:56 PM Ondřej Čertík <ond...@certik.us> wrote: > > > > 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. > > It actually isn't clear to me yet that they've shown it. I want to see > what their test suite of functions looks like. > > Aaron Meurer > > > > > 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. > > -- > 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/CAKgW%3D6JExav6cUscxJbv%2B9QhY_S2AP52L9ycNzA%2Be2jtgdGSQQ%40mail.gmail.com. -- 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/CAHVvXxTMoxh6fG8Yb%2B3%3Dgmr1bqt9tQXf_rWMTkLAAThRnW-wyw%40mail.gmail.com.
