(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]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/ca99c7a0-b372-82cb-74e6-2ff978f40d54%40gmail.com.
