Re: [Maxima-discuss] ML for symbolic math

[oldk1331 <old...@gm...>]

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.

- Qian

On 9/30/19 8:58 AM, Elias Mårtenson wrote:
> Here's a paper titled “Deep learning for symbolic mathematics” that
> might be of interest to the members of this mailing list.
> 
> https://openreview.net/pdf?id=S1eZYeHFDS
> 
> Regards,
> Elias
> 
> 
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