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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

#41

Post by CactusOnFire »

dimmuborgir wrote: post #39
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…

AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.

AI is bad at Audio. AI can do MIDI fine.

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

#42

Post by thwayunion »

lupire wrote: post #21
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 mean "generate a Python function that calls a library that does math perfectly, right?

Unlike 99.99% of human programmers, who can and often do implement everything in sympy/numpy from scratch ;-)

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

#43

Post by stephencanon »

dimmuborgir wrote: post #39
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…

AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.

Which is extra funny, because GOFAI models (e.g. David Cope's work) were doing a pretty OK job back in the 1990s!

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

#44

Post by hey_over_here »

CommieBobDole wrote: post #23

Also Excel is terrible at encoding MP3s. It's a language model; why would we expect it do math or try to somehow shoehorn math into the model? Do the language centers of our brain do math? If something approximating AGI is going to happen, it's going to be a lot of models tied together with an executive function to recognize and send things to the area that's good at working with them.

> It's a language model; why would we expect it do math or try to somehow shoehorn math into the model?

Language models can do math, or anyway arithmetic. That's because language models are trained to predict the next token in a sequence and an arithmetic operation can be represented as a sequence of tokens.

For example, see Figure 3.10 on page 22, here:

https://arxiv.org/abs/2005.14165

The only problem is that language models are crap at arithmetic because they can only predict the next token in a sequence. That's enough to guess at the answer of an arithmetic problem some of the time but not enough to solve any arithmetic problem all of the time.

More generally, the answer to your question is in the same Figure 3.10 I've referenced above. OpenAI (and others) have claimed that their large language models can do arithmetic. So then people tested the claim and found it to be a bag of old cobblers.

Hence the article above. Nobody's trying to "shoehorn" anything anywhere. It's just something that language models can do, albeit badly.

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

#45

Post by casey2 »

JacobiX wrote: post #5
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.

I'm not so sure about that. Of course computers can do arithmetic operations, but this is not the same as solving math problems, proving theorems, etc. Even mathematical objects are approximated up to an approximation error in a computer (like a differentiable manifold or a real number).

Counterexample: Shalosh B. Ekhad is a computer who is also a mathematician.

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

#46

Post by zozbot234 »

lupire wrote: post #19
PaulHoule wrote: post #2

Ashby strikes again. Current sequence models don't have the right structures to represent math. Even if they use floating point internally, they can't really float the point because the nonlinearity in the model has a certain scale. A system that processes language can take advantage of the human desire for closure https://www.eurogamer.net/blood-in-the-gutter to fool people into thinking it is more capable than it r…

Floating point isn't relevant here. The problem is that human language is approximate and correct math is not, so pattern matching on prose text is doomed. AI trained on exact math does a lot better. But that's not fully generic so fails the weird GPT goal of modeling all of human intelligence through prose. That's not how people solve math at all. GPT's "Superficially plausible but wrong" math is actually pretty goo…

> GPT's "Superficially plausible but wrong" math is actually pretty good match for non-expert bad-at-math average human behavior.

Relevant blog post: https://www.greaterwrong.com/posts/YhgjmCxcQXixStWMC/artific... "The best experts in the field estimate it will be at least a hundred years before calculators can add as well as a human twelve-year-old."

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

#47

Post by blackbear_ »

burlesona wrote: post #29

I genuinely wonder if we will find there are some inherent tradeoffs to knowledge and understanding such that if we ever have machines that can “think like humans” they would in practice run into human-like cognition limits: ie such machines would be “bad at math” in the same way humans are “bat at math” compared to conventional computers.

That's an interesting thought. However it's not cognitive limits that make humans bad at math, it's just a "hardware" issue: a human with a piece of paper is much better at math.

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

#48

Post by causi »

CactusOnFire wrote: post #41
dimmuborgir wrote: post #39

Earlier quoted context omitted.

AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.

AI is bad at Audio. AI can do MIDI fine.

Which is a real shame. AI-powered restoration of poor-quality audio would be highly useful.

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

#49

Post by ryandvm »

burlesona wrote: post #29

I genuinely wonder if we will find there are some inherent tradeoffs to knowledge and understanding such that if we ever have machines that can “think like humans” they would in practice run into human-like cognition limits: ie such machines would be “bad at math” in the same way humans are “bat at math” compared to conventional computers.

Indeed. I posit that as we get closer and closer to simulating how the human brain works in the pursuit of artificial intelligence, we're going to start seeing more and more of the same "bugs" that humans have (logical fallacies, susceptibility to illusions, mental illness, etc.)

You think your job sucks now, just wait until you're dealing with the general AI over on the UX team that's trying to get your ass fired because it's fostering a 3 year old grudge over that time you said Chappie was stupid.

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

#50

Post by CommieBobDole »

hey_over_here wrote: post #44
CommieBobDole wrote: post #23

Also Excel is terrible at encoding MP3s. It's a language model; why would we expect it do math or try to somehow shoehorn math into the model? Do the language centers of our brain do math? If something approximating AGI is going to happen, it's going to be a lot of models tied together with an executive function to recognize and send things to the area that's good at working with them.

> It's a language model; why would we expect it do math or try to somehow shoehorn math into the model? Language models can do math, or anyway arithmetic. That's because language models are trained to predict the next token in a sequence and an arithmetic operation can be represented as a sequence of tokens. For example, see Figure 3.10 on page 22, here: https://arxiv.org/abs/2005.14165 The only problem is that langu…

Right, but what you're describing is 'not being able to do math'. Like, if I've memorized a multiplication table and can give you any result that's on the table but can't multiply anything that wasn't on the table, I can't do multiplication.
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