
Using neural networks to solve advanced mathematics equations - robinhouston
https://ai.facebook.com/blog/using-neural-networks-to-solve-advanced-mathematics-equations/
======
dooglius
Previous discussion:
[https://news.ycombinator.com/item?id=21084748](https://news.ycombinator.com/item?id=21084748)

I think the point in the comments about Mathematica et al just being more
careful about the domain is pretty damning of the claim the neural net beats
them.

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twotwotwo
The potentially interesting thing here, to me, is using networks to short-
circuit searches that could grow explosively with expression size, but then
filter down to answers that can be shown correct. That's also a way to get
some value out of a system that doesn't always produce the correct answer as
its first guess.

In some cases it may be easy to prove the correctness once you have the
proposed answer, but in others the network might need to produce intermediate
steps or some kind of 'argument' to let the CAS check correctness in
reasonable time. Perhaps do that by instrumenting a CAS to output intermediate
steps and train the network on _that_ , not just problem/answer pairs.

Broadly, _humans_ who have seen a lot of problems solved can say "this looks
like a situation where you could try X" and do X without going down all the
blind alleys that a CAS might. So it doesn't seem implausible that _automated_
learned models might _also_ outperform the heuristics CASes have hard-coded in
for making those kinds of guesses.

(You can imagine closer coupling, e.g. a CAS that calls out to an NN to
propose solutions to certain hard-to-solve-but-easy-to-check subproblems, or
uses learned models to try to guess the right branch to go down in a solution
process that already looks like searching a tree of possibilities. But the
more you have to crack open the CAS, the less appealing the whole thing
becomes.)

~~~
7373737373
I wonder how much of this intuition can be formalized, if, say, the number of
deduction steps from a theorem to another can be _provably_ reliably
approximated before attempting its proof.

[https://math.stackexchange.com/questions/3299096/resource-
me...](https://math.stackexchange.com/questions/3299096/resource-metalogic-
proving-that-a-theorem-can-not-be-deduced-from-given-axiom)

[https://math.stackexchange.com/questions/3477810/estimating-...](https://math.stackexchange.com/questions/3477810/estimating-
meta-mathematical-properties-of-conjectures)

------
xvilka
There is CoqHammer[1] and ProverBot[2] for going even further - proving the
theorems.

[1]
[https://github.com/lukaszcz/coqhammer](https://github.com/lukaszcz/coqhammer)

[2] [https://github.com/UCSD-PL/proverbot9001](https://github.com/UCSD-
PL/proverbot9001)

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gambler
This paper makes so many convoluted and arbitrary decisions about what they
are doing with the domain (i.e. how they're generating and measuring
performance on their dataset), I don't think it should be considered
legitimate publishable research until the model is checked in some sane
manner.

At this point in time AI research is so saturated with hype and BS, it needs
some sort of adversarial process to be taken seriously.

------
haskellandchill
> Facebook AI has built the first AI system that can solve advanced
> mathematics equations using symbolic reasoning

Uh, this isn't true. Even their paper cites previous work. I guess it's PR
speak.

A little disappointing that it just guesses solutions and doesn't offer
proofs.

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lvh
It seems bananas to me that Mathematica and other existing CASes can't solve
that first sample equation: it reads like a straightforward integration,
taking just a parameter substitution and an inverse trig derivative (which I
feel like everyone doing calculus knows by heart?). Maybe I should go do it on
paper and I'm missing the hard part?

~~~
nimish
The risch algorithm is not trivial to implement.

~~~
lvh
Sure, but this is Mathematica, the self-proclaimed leading mathematics
package!

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mdswanson
"First, we developed a process that effectively unpacks equations, laying them
out in a branching, treelike structure..." Umm...like an expression tree,
perhaps? [https://www.geeksforgeeks.org/expression-
tree/](https://www.geeksforgeeks.org/expression-tree/)

~~~
laxd
They call it an expression-tree syntax two paragraphs down.

~~~
mdswanson
Congratulations! They re-invented it: "...our expression-tree syntax..."

------
sarosh
Actual paper is at
[https://arxiv.org/pdf/1912.01412.pdf](https://arxiv.org/pdf/1912.01412.pdf)

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carapace
See also "Deep Algebra" (sorry no link handy at the moment) where they are
trying to train networks to extract or generate new math from old; input is
arxiv algebra papers (LaTeX, PDF) IIRC.

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whatshisface
Solving "advanced mathematics equations," as opposed to advanced English
literature equations?

~~~
dragonwriter
More likely as opposed to advanced chemical or logic or ... equations.

“Mathematical” is a meaningful modifier, not a frivolous one, for “equation”.

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m3kw9
Would this be more like calculus where you plug in a range of numbers to get
to a target?

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thanatropism
I wonder if there is research on using deep learning for stuff like SAT
solvers.

~~~
brtanymore
SAT may be a game with rules too simple for DL approaches to outperform state-
of-the-art traditional solvers right now, but SMT (Satisfiability modulo
theories) is another story:

[https://papers.nips.cc/paper/8233-learning-to-solve-smt-
form...](https://papers.nips.cc/paper/8233-learning-to-solve-smt-formulas.pdf)

------
boyadjian
Now, we can really talk about AI.

