!!!!! What you describe
- is doable, and - is outright academic fraud... I doubt somehow that the authors would be dumb enough to risk that. "Never assign to human ill will what can be explained by human stupidity". (Napoleon Bonaparte, IIRC). However, I agree that using an external problem test set would be more convincing. By the way, translating a standard set to the input language of their integrator would be a good test of their parsing abilities ;-)... Le dimanche 6 octobre 2019 22:22:11 UTC+2, rjf a écrit : > > If they were interested in a fair comparison they would use a test set from > (for example) Rubi or one of the CAS. > My guess is that they did this: > 1. generate a random expression S favoring + and * in the tree. > 2. differentiate S to get S' > 3. "learn" the integral of S'. > > Here's the trick. S' will, with very high probability, be a sum. Say > s1+s2+s3. > A CAS will usually try to compute integrate(s1,x) + integrate(s2,x)+ > integrate(s3,x). > That's the way integral tables work too. > Unfortunately, for many "random" expressions, s1, s2, s3, ... are > NOT integrable in terms of elementary functions. Only their sum. > So a CAS will fail. > > Here's a particular example. exp(-x^3)/x^4. > > Differentiate (I'm copy/pasting from Maxima) to get > > -(3*%e^(-x^3))/x^2- (4*%e^(-x^3))/x^5 > > Neither of these terms is separately integrable in terms of elementary > functions. > So a "real" CAS will fail on even "simple" problems. If you generate > trees with 15 random operators, the probably of failing increases. > > For this particular example, which is the 2nd one I tried, Maxima gives > > gamma_incomplete(-1/3,x^3)+(4*gamma_incomplete(-4/3,x^3))/3 > > Non elementary it seems. But we know this is supposed to be the same as > exp(-x^3)/x^4. > A minute testing numerically suggests it is, indeed, equal. > > So what we have for "ML" here is a made-up test set that is not > reflective of the actual task of computing integrals as needed in > applied math, and as considered in (for example) integral > tables or integration algorithms. > > We are perhaps familiar with the notion of "teaching for the test" > in which students and teachers collude to get excellent grades > on some standardized test. Yet the students may really > not know the material. > This is maybe worse because the "test" is not some > important standardized suite of integration problems. > It is just randomly generated. Maybe it would > be fair to call it noise? The author could post the > test suite, I suppose. > RJF > > RJF > > > > On Tuesday, October 1, 2019 at 11:22:51 PM UTC-7, Emmanuel Charpentier > wrote: >> >> >> >> Le mercredi 2 octobre 2019 01:48:15 UTC+2, rjf a écrit : >>> >>> I think that if you read the paper you would not expect it to compete >>> with a CAS >>> except on its made-up artificial testset. >>> >> >> Could you amplify ? >> >> >>> RJF >>> >>> >>> On Monday, September 30, 2019 at 10:57:44 AM UTC-4, Martin R wrote: >>>> >>>> Actually, I think it would be even more interesting to compare with >>>> FriCAS, because FriCAS has the most complete implementation of the Risch >>>> algorithm and does not at all rely on pattern matching. >>>> >>>> Martin >>>> >>>> Am Sonntag, 29. September 2019 15:00:01 UTC+2 schrieb mmarco: >>>>> >>>>> I would be very interested in comparing their results with RUBI. >>>>> >>>>> El viernes, 27 de septiembre de 2019, 21:53:00 (UTC+2), Eric >>>>> Gourgoulhon escribió: >>>>>> >>>>>> Thanks for sharing! >>>>>> This looks very promising. I hope we have it in Sage some day. >>>>>> >>>>>> Eric. >>>>>> >>>>>> Le vendredi 27 septembre 2019 17:06:31 UTC+2, Dima Pasechnik a écrit : >>>>>>> >>>>>>> https://openreview.net/pdf?id=S1eZYeHFDS >>>>>>> >>>>>>> I wish they had code available... >>>>>>> >>>>>> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/716840d2-65d1-459f-b3cd-1f35e22dc96f%40googlegroups.com.
