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AI language models are struggling to “get” math

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Re: AI language models are struggling to “get” math

#131

Post by mirker »

saghm wrote: post #117
mjburgess wrote: post #27

How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell . It's all just passable garbled nonesense that the reader (goes to lengths) to interept based on their prior knowledge, which is not expressed in the syntax of what these systems output. In the case of mathematics, we're far less willing to "BS away" the interpretive failures. But if we were equally deman…

> How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell Honestly, even as someone generally pretty dismissive of the AI hype, I'm not sure you can go that far. The whole reason we have specific mathematical notation is that human languages often are not super great at dealing with it, and English in particular is pretty abysmal for being both unambiguous and…

Because there is an algorithm for it. Convert the strings into floating point numbers, add them, convert them back to strings. It’s a leetcode medium question. It should be learnable.

The article talks about abstract math questions, but even arithmetic is hard for language models.

Re: AI language models are struggling to “get” math

#132

Post by visarga »

spywaregorilla wrote: post #123
visarga wrote: post #113

Earlier quoted context omitted.

It's not that they were not built for math, but more like verification is hard. But it's hard for humans as well. A large generative model + a fast verifier could do wonders. AlphaGo was built on that - the model can propose moves, but you can verify who won in the end. There are some code generation models that write their own tests as well, or use externally provided tests to verify their solutions. The DeepMind ma…

I disagree. It is that they were not built for math. While brain analogies are shittier than most people assume, this is like trying to do math in your head without being allowed to think through calculations.

Brains weren't built for math either, just for surviving. And the "trying to do math in your head" is true if you use naive question answering, but if you ask "step by step" or "chain of thought", or "supporting questions", any of them will allow for flexible time steps. There are some solutions called "Language Model Cascades" that compose language models calls to simulate arbitrary complex reasoning chains including recursion. There is no reason to think language models are unfit for math, they are fit for generating possible solutions that need to be verified somehow.

Re: AI language models are struggling to “get” math

#133

Post by nl »

the_af wrote: post #75
sharemywin wrote: post #3

Earlier quoted context omitted.

computers already do math. language models just need to translate problems into code of some kind that can be run to get the answer. executive function/planning is probably the biggest problem at this point for ai.

> language models just need to translate problems into code of some kind that can be run to get the answer A huge "just"! Isn't this the magic step? Translating ambiguous symbols to meaning and combining them in meaningful ways is a big deal which, apparently, these AI models cannot do. They can just parrot things.

> Translating ambiguous symbols to meaning and combining them in meaningful ways is a big deal which, apparently, these AI models cannot do.

Plenty of AI models do exactly this. Very clear examples include question answering models and code generation. In both cases novel, meaningful responses are generated.

> They can just parrot things.

That isn't true. While language models can parrot things it is generally special conditions that make them do it. Specifically, the conditional probability of the next character (or BPE or word depending on the model) has to be much higher than anything else which happens when the thing being parroted is unique text.

If you ask most Americans or a language model what word comes next in this: fourscore and seven year.. they'll give the same answer, for the same reason.

Re: AI language models are struggling to “get” math

#134

Post by ricopags »

enord wrote: post #54
sharemywin wrote: post #10

Earlier quoted context omitted.

The point I'm trying to make is LLMs don't need to do everything just be the glue to other systems.

Wait what? Glue as in extract high level semantic representations from _syntatic probabilities_ and pass on to appropriate domain specific tools? This is the glaring hole in LLMs, a paradoxical semantic incoherence despite impressive sentenial and gramatical coherence. As glue it is so thin as to be potable.

Quoting this tweet[0]:

"Here's a brief glimpse of our INCREDIBLE near future.

GPT-3 armed with a Python interpreter can · do exact math · make API requests · answer in unprecedented ways"

[0]https://twitter.com/sergeykarayev/status/1569377881440276481

Re: AI language models are struggling to “get” math

#135

Post by nl »

swyx wrote: post #36
yshrestha wrote: post #9

Language models can generate a Python function that does the math perfectly. I bet you would get better results if you tweaked the prompt to say "Generate a Python program that solves X math problem" and then just ran the resulting Python script. It does not need to be AGI to be useful.

you can also tell the model that it doesnt know how to do math, and it respects that https://twitter.com/goodside/status/1568448128495534081

This is pretty cool, although the "don't use outside the security sandbox" made me laugh: https://twitter.com/goodside/status/1568704302813700096/phot...

Re: AI language models are struggling to “get” math

#136

Post by nl »

mavu wrote: post #114

Talking about this stuff would be so much easier if we stopped calling those software "AI". It is a machine learning algorithm. It is an electronic Parrot. thats it. And suddenly no one will wonder "OH MY WHY CANN IT NOT DO MATH< IT SMART?!?!"

> It is a machine learning algorithm.

True

> It is an electronic Parrot.

This is incorrect, and unclear why people think this.

The whole point of a good ML system is that it doesn't parrot training data. A good system can extrapolate novel answers from things it has seen. That is very far from "parroting".

Re: AI language models are struggling to “get” math

#137

Post by edouard-harris »

mjburgess wrote: post #27

How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell . It's all just passable garbled nonesense that the reader (goes to lengths) to interept based on their prior knowledge, which is not expressed in the syntax of what these systems output. In the case of mathematics, we're far less willing to "BS away" the interpretive failures. But if we were equally deman…

This might make sense as a response solely to the title of the article, but I have to admit I find it puzzling as a reaction to its content. Notwithstanding the title, the article mentions a model called Minerva that scored fully 50% on the MATH dataset of high-school/undergrad mathematical problems. For comparison, a human computer science PhD student scored 40%. [1]

For context, Minerva came out this July. When it was tested on a national math exam, it scored higher than that year's class of graduating high school seniors. [2] A mere eight months (!) earlier, OpenAI had announced [3] they'd trained a language model that solved math word problems almost as well as an average middle-schooler. So even if you believe — rightly or wrongly — that current capabilities aren't very impressive, it's worth remembering that your understanding of current capabilities might not be entirely accurate, even if it's only a few months out of date.

Incidentally, it may be worth looking at some examples of these models' outputs before deciding what they can or can't do. Here's Minerva solving some math problems, for example:

https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7...

https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d1...

https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015...

https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14...

https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b...

I'll admit I find it challenging to interpret these results as "passable garbled nonesense [sic]", though perhaps I'm not being demanding enough. At any rate, when these models go from beating 10-year olds at math to beating 18-year olds at math in the span of 8 months, one does start to wonder how much of the hype is really due to over-interpretation — and what the next 8 months have in store.

========================

[1] https://arxiv.org/pdf/1709.04326.pdf (For comparison, a 3-time Mathematics Olympiad gold-medalist scored 90%.)

[2] This was Poland's National Math Exam. Minvera scored 65%; the 2021 national average was 57%. See https://www.aitracker.org/ and Section 3 of the Minerva paper at https://arxiv.org/pdf/2206.14858.pdf

[3] https://openai.com/blog/grade-school-math/

Re: AI language models are struggling to “get” math

#138

Post by vladf »

p1esk wrote: post #100
vladf wrote: post #96

Earlier quoted context omitted.

Isn’t that as good as it gets? The whole point of the continuations is that given a short leading prompt from a real piece that it should continue it realistically. It didn’t get to train on the test set, if that’s what you’re implying, and I find it hard to believe the assertion that continuations are copies of the train set (if that’s your claim).

It definitely copied a piece of Moonlight sonata in the last 7 seconds of the first continuation sample: https://youtu.be/4Tr0otuiQuU?t=516

Wow, good find! They definitely sound similar but it’s not a facsimile. I wonder if this holds for the other samples.

I guess in retrospect we asked it to continue the music in a likely way, not be novel. And it definitely convinced me enough to be impressive. An NN that composes completely fresh music, whatever that means (I’m sure most modern human music has a hefty dose of cross song sampling), would certainly be a good next goal post.

Re: AI language models are struggling to “get” math

#139

Post by spywaregorilla »

visarga wrote: post #132
spywaregorilla wrote: post #123

Earlier quoted context omitted.

I disagree. It is that they were not built for math. While brain analogies are shittier than most people assume, this is like trying to do math in your head without being allowed to think through calculations.

Brains weren't built for math either, just for surviving. And the "trying to do math in your head" is true if you use naive question answering, but if you ask "step by step" or "chain of thought", or "supporting questions", any of them will allow for flexible time steps. There are some solutions called "Language Model Cascades" that compose language models calls to simulate arbitrary complex reasoning chains includin…

> Brains weren't built for math either, just for surviving.

Brains were, however, built for language processing, in addition to many other tasks.

> There is no reason to think language models are unfit for math, they are fit for generating possible solutions that need to be verified somehow.

This is just a dumb idea though. Guess and check based on semantically well positioned answers in the ambiguity that is the embedding space until you find something that's not wrong is not the same thing as defining an algorithm and then executing it, which is how people do math.

Sure, you could probably get it to a pretty good working state, but it seems pretty dumb to me.

> There are some solutions called "Language Model Cascades" that compose language models calls to simulate arbitrary complex reasoning chains including recursion.

If you're creating the reasoning chains yourself, you're arguably doing the hard part for the model and giving credit to the language part. If you're able to do get the model to define the chains, then you've already solved the hard part of the problem and could likely use something very different from language models altogether to greater effect.

Re: AI language models are struggling to “get” math

#140

Post by pessimizer »

mgraczyk wrote: post #98
pessimizer wrote: post #95

Earlier quoted context omitted.

> I'm disagreeing with the language you are using to characterize models. "copying from memory" implies that there is something being copied, and a memory that you are copying it from. I am pointing out that LLMs do not do this. It's not how they work. Then we're arguing about the semantics of the word "copy." That is not an interesting argument when you know exactly what I mean and can express it clearly. edit: If i…

It is semantics, but that was your whole point no? > That's because they're not modelling anything If we agree on "how LLMs work", then how can you claim that they aren't modeling anything? They are modeling language, and while it's unlikely current paradigms will be proving new mathematical truths, it's completely plausible to me that bigger models will be able to handle simple math word problems like those in the a…

I disagree that they are modeling language.* I think that not only bigger models but same-sized or much smaller models will be able to handle arbitrarily complicated word problems if they're eventually supplemented with some explicit model-building process.

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* ...and that would be a completely semantic argument to have. I don't care whether it's called modeling, other than the fact that when I'm talking about modeling, I'm not talking about language probability, I'm talking about categories. But discussing what current AI is (a language model, copying?) is a waste of time, because I absolutely agree with your description of how it works, so we're talking about exactly the same thing.

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