Will a prompt that enables GPT-4 to solve easy Sudoku puzzles be found?

https://manifold.markets/Mira/will-a-prompt-that-enables-gpt4-to

by kilobit • 3 years ago

37 66 3 years ago

manifold.markets

brucethemoose2• 3 years ago

A relevant PR:

https://github.com/ggerganov/llama.cpp/pull/1773

version_five• 3 years ago

Easy-rated Sudoku puzzle means a puzzle classified as easy by any reputable Sudoku site or puzzle generator. This market plans to use the LA Times(Sudoku - Free daily Sudoku games from the Los Angeles Times (latimes.com)) for judging, but I maintain the option to use a different Sudoku generator.

Is there any theoretical reason why an attention based llm could or couldn't generate an answer to an NP hard problem? As I understand, attention is N^2, but it's not obvious if that's relevant to the complexity of problems that can be solved. It's obviously not relevant to answers that are regurgitated, which may be all answers?

It would be better if "easy" had a mathematical definition.

MichaelBurge• 3 years ago

A single forward pass shouldn't be able to, but remember the format allows it to be iterated. So it should be Turing Complete, if the error rate is low enough and enough iterations are allowed.

AdieuToLogic3• 3 years ago

Is there any theoretical reason why an attention based llm could or couldn't generate an answer to an NP hard problem?

Putting aside for the moment that a Large Language Model (LLM) is a predictive statistical model based on and producing from what consisted its training set, answering whether or not any algorithm can solve an NP hard problem first requires a clarification; is a brute force exhaustive search allowed?

If it is, I am unsure if an arbitrary LLM could find a solution due to the dependence on training. If not, I am confident in saying an LLM could not solve arbitrary NP hard problems in P time as that has yet to be proven possible AFAIK.

epylar• 3 years ago

LLM's aren't statistical in the sense of memorizing percentages of words that come after other words. They are modeling a very high dimensional function using a neural net. I suppose they're statistical in the sense of learning how to mimic what they've seen, but this includes some very surprising emergent abilities as well.

shawntan3• 3 years ago

I recommend reading the theoretical work on the computational capabilities of Transformers: https://twitter.com/lambdaviking/status/1630581475425828864 References to other work can probably be found in that article.

Shameless plug to my own blogpost about this: https://blog.wtf.sg/posts/2023-02-03-the-new-xor-problem/

TL;DR: The theoretical class of problems that Transformers can solve (without Chain-of-Thought style responses) is fairly limited. Generally, universal approximation proofs rely on infinite precision assumptions, which are not practical in reality. Empirical results also show very limited capabilities when tested on certain formal languages.

In the Sudoku case, the problem-length is limited, so one could conceptually make a large enough model that could memorise all solutions to all possible combinations of permissible sudoku boards, which could then just access and read out the solutions.

gwern2• 3 years ago

The theoretical class of problems that Transformers can solve (without Chain-of-Thought style responses) is fairly limited.

Which is irrelevant because how would a Transformer emit a complete Sudoku solution in a single forward-pass/token in the first place?

charcircuit• 3 years ago

Only allowing 50 generations makes this very hard.

heliophobicdude• 3 years ago

The title is funny to me. We should consider a new computation complexity class for LLMs. Let's call the ones that can be solved with a prompt, Promptable. For the problems that we cannot reliably solve with a single prompt yet, let's call them non-deterministic promptable, or NP.

Question is, for most of these hard problems, is there a prompt that can solve them? Better yet, is there a prompt good enough that we collapse all of the hardest problems in NP with a single prompt?

Will we ever know if NP can be reduced to P???

AdieuToLogic3• 3 years ago

Will we ever know if NP can be reduced to P???

My opinion is that it cannot, due to the unbounded nature of NP problems[0]. Regarding sudoku specifically, the question is a bit more nuanced (as described here[1]).

As for the NP nature of sudoko in its general form, a short but very informative description can be found here[2].

HTH

0 - https://en.wikipedia.org/wiki/NP_(complexity)

1 - https://stackoverflow.com/questions/50703174/is-sudoku-np-co...

2 - http://www.cs.ox.ac.uk/people/paul.goldberg/FCS/sudoku.html

janalsncm2• 3 years ago

Are large language models even Turing complete? Or more specifically, is there something we can say about LLMs as a class with respect to this question?

For any architecture like Vaswani’s GPT or a bigger iteration of it, eventually you run out of attention heads and layers.

If the answer is categorically no, then any sufficiently sophisticated code is not “promotable”. However, I don’t think there’s anything in principle which prevents LLMs from being Turing complete.

dragonwriter2• 3 years ago

Are large language models even Turing complete?

Idealized deterministic computing systems are the only thing that can be Turing complete, actual systems cannot be (because Turing completeness requires infinite space), LLMs are actual systems, and also are not limited-space approximation of idealized deterministic systems (they are, I suppose, deterministic if you know all the relevant parameters, including potentially some that are hardware-dependent, but they generally are a deterministic approximation of a nondeterministic system.) You can, of course, prompt an LLM to predict the output of a deterministic system and to do direct computation, but, absent an interface to external tools that actually do the computation, the results for that are notoriously unreliable.

bippihippi1• 3 years ago

attention is turing complete https://news.ycombinator.com/item?id=36332033

I'd guess it's not as efficient as a native algorithm i many cases though

famouswaffles4• 3 years ago

With memory they are. https://arxiv.org/abs/2301.04589

solomatov6• 3 years ago

Are large language models even Turing complete?

If you want to see where they have problem ask them to do something about deep hierarchical objects. For example, consider this prompt: "Draw me a complete binary tree with numbers from 1 to 128 using pseudographics"

In my experience, the deeper the structure, the more problematic it is for the current generation of LLMs.

ComplexSystems• 3 years ago

From what I can tell, experts currently project the problem "TURN HUMANS TO PAPERCLIPS" is in complexity class "Promptable," but that the Boolean Satisfiability problem is not in "Promptable."

ineedasername• 3 years ago

Or prompt(n) time, where n = the known minimum # of prompts required to solve a given class of problems.

From there we can define various classes of problems:

1) those with an absolute floor minimum # of required prompts

2) those with a known ceiling

Etc.

This should be combined with traditional Big-O notation to provide a more specific classification, e.g. a constant-time complexity task with a known ceiling of two prompts would be prompt(2)-O(1)

A problem known to, in some specific cases but not all, be solvable with some minimum number of prompts with no ceiling known might be Prompt(n(np)) where n = minimum prompts known to solve at least some problems in that class.

Classifications would be applied to specific systems but the best performing system would set the general classification for a problem. So the general classification for a problem might be prompt(1(5)) to denote a min 1 max 5 prompts required based on the best performance seen to date, a specific system might only rate a prompt(3(np)) classification.

I’m overthink this but I think I like it.

itsdrewmiller• 3 years ago

I honestly can't tell if any of the other replies to this comment got the joke.

throwawaylinux2• 3 years ago

The title is funny to me. We should consider a new computation complexity class for LLMs. Let's call the ones that can be solved with a prompt, Promptable. For the problems that we cannot reliably solve with a single prompt yet, let's call them non-deterministic promptable, or NP.

Promptable is old hat now. I propose an entirely new class of problems which is whether you can prompt GPT to construct a prompt for GPT that can solve a problem. I call it Deep-Promptability™ (patent pending). The "order" is defined by how many levels of prompting can you solve the problem in, so if a problem is order-3 deep-promptable then you can prompt GPT to construct a prompt for GPT that will construct a prompt that allows GPT to solve it.

earthboundkid2• 3 years ago

An LLM is a tool. It is a very versatile tool. It can be used in many situations. It does not therefore follow that it should be used in all situations. Even if you wanted to use an AI to solve sudoku, there is no particular reason to begin with a model trained for language modeling instead of a model better suited to the task.

thumbuddy5• 3 years ago

I don't get it there are so many ways to solve sudokus why does anyone care about this anyways?

jyap• 3 years ago

It’s just a well known problem case that has a straightforward answer that is easily verifiable.

Eg. Can a model play tic-tac-toe or solve chess puzzles

coldtea2• 3 years ago

Well, it's not really about finding a way to solve sudokus.

Nobody involved in this cares for that as a goal in itself.

It's about the mystery of why an LLM can't do it well.

It's about the challenge of finding a way (prompt) to get it to.

It's about what this reveals about the inner workings and limitations of an LLM.

joe_the_user• 3 years ago

I would, uh, bet that you're right.

But given that there has been a lot of discussion of the possibility that an LLM has "general intelligence", it seems worthwhile to figure out whether the solving of a random problem is possible.

sfn42• 3 years ago

They don't possess general intelligence, end of discussion. Thanks for attending my TED talk.

akrolsmir• 3 years ago

Austin from Manifold here - cool to see this trending! I thought the structure of this prediction market was especially cool, as it forms a collaborative, crowdsourced puzzle challenge to generate the perfect prompt.

(I've personally bet yes, but not sure if that prediction is holding up...)

andythemoron• 3 years ago

Seeing this thread makes me want to bust out some Prolog.

SomewhatLikely• 3 years ago

I haven't seen prediction contacts that can be resolved at 50% before. It seems like that throws off the interpretation of the probability.

swayvil2• 3 years ago

Can we use this technology to find a recognizable pattern in any complex blob of data? Is that how this works?

How about, "Given 100000 readings from a person's body/brain, determine whether they are lying". Can we do that?

eschaton• 3 years ago

I don’t understand how so many people on Hacker News engage in this line of questioning.

If by “this technology” you mean “large neural networks” the answer is yes, and we’ve been doing so for several decades now. That’s very specifically what they’re good at.

If you mean “LLMs like ChatGPT” specifically, then no, they’re extremely large neural networks trained on very specific data sets. To perform a different recognition task, you train with different data sets.

Where does this idea that ChatGPT and friends are general-purpose come from?

famouswaffles4• 3 years ago

Where does this idea that ChatGPT and friends are general-purpose come from?

Maybe reality?

https://general-pattern-machines.github.io/

Large Language Models are as general purpose as they come especially for Machine Learning. They generalize to any kind of pattern, linguistic or not.

famouswaffles4• 3 years ago

Can we use this technology to find a recognizable pattern in any complex blob of data? Is that how this works?

Possibly in general. https://general-pattern-machines.github.io/

As for your example, I don't think so.

supersat2• 3 years ago

Unlikely, for reasons explained in this video: https://youtu.be/bEovhfxJsM4?t=2339

However, it apparently can write a program using the Z3 SAT solver to find a solution.

throwawaylinux2• 3 years ago

However, it apparently can write a program using the Z3 SAT solver to find a solution.

Not that it's unimpressive in general that a LLM can write a program from a prompt like that, but for this particular juxtaposition it doesn't seem like it's especially interesting or impressive that it can write such a program. A SAT program is basically just re-stating the the rules in a particular form. It doesn't even have to be able to apply those rules. The solver does the hard work.

kaba04• 3 years ago

Also, if it has enough training data to know how to write such a SAT solver problem, it has surely seen sudoku exercises as part of that data set..

supersat2• 3 years ago

Unlikely, for reasons explained in this video: https://youtu.be/bEovhfxJsM4?t=2339

However, apparently it can write a program using the Z3 SAT solver to find a solution.

zacmps• 3 years ago

It seems like it might be possible to get around this by letting the model emit moves like ` discard last 5` which would also let it keep a history of it's previous branches.

marmakoide• 3 years ago

Will a prompt that enables a prompt that enables GPT-4 to solve easy Sudoku puzzles be found ?

I don't know how much meta-prompting have been explored. Maybe it's where The Singularity is at ?

dave333• 3 years ago

For most sudoku puzzles solving each cell is a logic puzzle that can be expressed in words just as current solvers have it in code. It can try to solve each vacant cell in turn using each of its rules until it finds a solution for that cell. And then it can be told to keep trying to solve another cell until it finishes the puzzle. Brute force with a core of logic.

Will a prompt that enables GPT-4 to solve easy Sudoku puzzles be found?

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