On Wed, Dec 18, 2019 at 6:05 PM E. Madison Bray <erik.m.b...@gmail.com> wrote: > > On Wed, Dec 18, 2019 at 6:39 AM rjf <fate...@gmail.com> wrote: > > > > I was trying to come up with a simple example of how this integration > > program claim > > was bogus. Here it is. > > > > Take one of your favorite prime-testing programs and generate > > a list of 10,000 Largish Primes. I don't know how large, but > > say 50 decimal digits or more. > > > > Make 10^8 factorization problems by multiplying them together > > in pairs, a*b=c. In a table with 10^8 entries of all the values of c, > > remember the a, b that are the factors of that c. > > Now write a "machine learning factoring program" "trained" on > > exactly those entries in the table. (It can be done in about 3 lines, that > > program). That's going to be a factoring program that is much faster > > than (say) Mathematica. And if you want to make it much much much > > faster than Mathematica, just use numbers with 500 or 5000 digits. > > > > Now, is this a breakthrough that demonstrates that machine learning > > can be used to factor integers fast? > > > > Indeed, outside of the 10^8 preset problems, it can't factor anything. > > > > What do you think? Is this a fair comparison to the integration program? > > I think so, based on my limited read. More to the point, if you throw > a bunch of tables of integrals at a machine learning program it will > know how to integrate exactly those integrals, and *maybe* some simple > compound expressions like sums and products; maybe... > > But if you throw at it, say, some special function that it's never > seen before of course it won't know what to do with it.
Yes, I agree - perhaps even more to the point would be integration of rational functions, where one does not merely seek an expansion into sums over roots of irreducible polynomials, but also building radical experessions for the roots of solvalbe polynomials. (so that for solvable polynomials these sums over roots may be made fully explicit). I'd be very, very surprised if an ML system would be able to build enough Galois theory to be able to solve any problem from such a class... :-) > > > > On Tuesday, December 17, 2019 at 5:03:59 PM UTC-8, Richard_L wrote: > >> > >> I was unclear. Davis disagrees with Lample and Charton in their claim of > >> neural nets being somehow superior to established CAS. > >> (And yes, the review is by Davis, not Lample.) > >> > >> On Tuesday, December 17, 2019 at 4:21:07 PM UTC-8, rjf wrote: > >>> > >>> disagrees with me? or Emmanuel? > >>> Lample's abstract (of the review) concluded with > >>> > >>> The claim that this outperforms Mathematica on symbolic integration needs > >>> to be very much qualified. > >>> > >>> I glanced at the full review and I don't see that I disagree with it. > >>> Generating 80 million randomly generated expressions, storing them and > >>> claiming > >>> that you can integrate their derivatives does not become a method for > >>> doing integrals. > >>> It is a method for looking up expressions in a table. Since most of > >>> those expressions > >>> will be sums, and the one of the main methods for actually computing > >>> integrals > >>> is to observe that the integral of a sum is the sum of the integrals, > >>> there is > >>> very little use for such a table. > >>> > >>> > >>> On Monday, December 16, 2019 at 7:14:02 AM UTC-8, Richard_L wrote: > >>>> > >>>> Apparently, someone disagrees. See Ernest Lample's posting to the arXiv: > >>>> https://arxiv.org/abs/1912.05752 > >>>> > >>>> On Friday, September 27, 2019 at 8:06:31 AM UTC-7, Dima Pasechnik wrote: > >>>>> > >>>>> 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/636e16e5-668f-4946-94b3-fab04c7ba265%40googlegroups.com. > > -- > 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/CAOTD34Zpkz22xhp1pwwsNpDP_FwYJOMO86RFm5BeUdk-%3DoFTsA%40mail.gmail.com. -- 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/CAAWYfq0TFMbb_ZdydBvdCSu09gE2k1aVaseAsV1gB_UnnWD%2BcA%40mail.gmail.com.
