They have opened the source code and the dataset https://github.com/facebookresearch/SymbolicMathematics
On Saturday, January 11, 2020 at 2:25:40 AM UTC+9, Aaron Meurer wrote: > > For those who didn't see, the final paper was posted with many updates > https://arxiv.org/abs/1912.01412. The newest version addresses some of > the things that were discussed here, and makes more use of SymPy, > including demonstrating some integrals that SymPy cannot solve, as > well as making it clearer how SymPy was used to check the results of > integration. > > Aaron Meurer > > On Tue, Oct 8, 2019 at 8:16 PM oldk1331 <[email protected] <javascript:>> > wrote: > > > > (This mail is copied from my response at maxima mailing list.) > > > > My opinion on this paper: > > > > First, their dataset (section 4.1) can be greatly improved using > > existing integration theory, Risch algorithm says that every elementary > > function integration can be reduced to 3 cases: transcendental (only > > contains rational functions and exp/log/tan, other trigonometric > > functions can transform to 'tan'), algebraic (only contains rational > > functions and nth-root ^), and mixed-case. > > > > So their method to prepare the dataset concentrates greatly on the > > transcendental cases, extremely lacks algebraic cases. And they uses > > only numbers from -5 to 5. I think it scales badly for wider ranges of > > numbers. > > > > For transcendental cases, I think FriCAS has fully implemented this > > branch of Risch algorithm, so it should always give correct result. For > > algebraic cases, I highly doubt that this ML program can solve > > integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71), x) = > > > log((x^6+15*x^4+(-80)*x^3+27*x^2+(-528)*x+781)*(x^4+10*x^2+(-96)*x+(-71))^(1/2)+(x^8+20*x^6+(-128)*x^5+54*x^4+(-1408)*x^3+3124*x^2+10001))/8 > > > > > > In fact, I doubt that this program can solve some rational function > > integration that requires Lazard-Rioboo-Trager algorithm to get > > simplified result. > > > > So I think this ML program has many flaws, but we can't inspect it. > > > > > 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 totally agree. > > > > - Qian > > > > -- > > 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 [email protected] <javascript:>. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/ca99c7a0-b372-82cb-74e6-2ff978f40d54%40gmail.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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/9d091321-07dd-4ade-9442-795282269627%40googlegroups.com.
