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. > 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.
