
‘Shocking’ unification reduces disparate spin models to just one - croller
http://www.sciencemag.org/news/2016/03/shocking-unification-reduces-lot-tough-physics-problems-just-one?utm_campaign=email-news-latest&et_rid=17042337&et_cid=332196
======
ssivark
TL;DR:

> Crudely their proof works as follows. First, the two scientists note that
> the up-or-down Ising spin resembles the true-or-false character of a logical
> statement such as "the car is white." They then prove that any particular 2D
> Ising model—i.e., with a particular set of coupling and external fields --
> is equivalent to an instance of a logical problem called the satisfiability,
> or SAT, problem, in which the goal is to come up with a set of logical
> statements, A,B,C, … that satisfy a long logical formula such as "A and not
> (B or C) …" The theorists present a way to map the SAT problem onto the 2D
> Ising model.

> Next, they show how any other spin model can also be translated into a SAT
> problem. That SAT problem can then be translated onto the 2D Ising model,
> thus making the two spin models equivalent. There is a price to pay,
> however. The 2D Ising model must have more spins than the original spin
> model. But De las Cuevas says that the computational demands of the Ising
> model are only modestly bigger than those of the original model.

~~~
btilly
Note that SAT is NP-complete. The fact that they reduced from SAT to Ising
spin suggests that Ising spin itself might be hard.

And indeed
[https://www.siam.org/pdf/news/654.pdf](https://www.siam.org/pdf/news/654.pdf)
shows that Ising spin is NP-complete. So this result looks like a case of "all
NP-complete problems in this class can be reduced to another NP-complete
problem". Which sounds pretty unsurprising to me.

I'd therefore need more context to figure out why the result is so shocking.

~~~
raverbashing
I'm thinking now that maybe there could be a magnetic material solving an NP-
problem

~~~
GFK_of_xmaspast
Speaking roughly, spin glasses exist because nature itself can't solve the
minimization problem. Here's a book on the topic:
[http://press.princeton.edu/titles/9917.html](http://press.princeton.edu/titles/9917.html)

------
ivan_ah
Science article is paywalled, but the paper is on the arXiv:
[http://arxiv.org/abs/1406.5955](http://arxiv.org/abs/1406.5955)

------
curuinor
Hopfield was the first to poke at Ising model spin to create memory-having
systems, creating his Hopfield model where memory states are represented as
attractors in the Hamiltonian search space. Add hidden units to that, and you
get the general Boltzmann machine. Restrict the connections, you get a
restricted Boltzmann machine. Layer them up, you get the 2006 Hinton and
Salakhutdinov advance in deep learning.

~~~
curuinor
And if you want to solve SAT with neural networks, you usually go back to a
modified version of the Hopfield network.

Rumelhart was also inspired by poking at MAX-CSP, at least according to
McClelland.

------
Terr_
> It's the sort of physics advance that Sauron might appreciate. [...] That
> "Ising model"

They're taking the models to _Ising_ ard?

~~~
DiabloD3
Goddamnitsomuch.

