11–20 of 201 posts
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.
But it's also quite interesting to see how the model would do "by itself". All kinds of interesting lessons to be learned!
Are there any general purpose models that are good at learning math? I mainly know basic feed-forward neural nets, but I don't think they do well outside their training region. Math, of course, has an infinite training region.
From my (limited) experience with the advanced ML models, they can "do basic math", but they make amateur mistakes with basic things - which indicates they don't actually know addition , but they are good at looking at patterns in existing language. I would assume that state-of-the-art ML models could "convert a word problem into an equation", then feed that equation into a 30 year-old graphing calculator to "do the…
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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).
https://en.wikipedia.org/wiki/Automated_theorem_proving
you just don't hear about it much because the technology is not so fashionable today. Also it is more clear what the limits are, I mean, Turing, Godel, Tarski and all of those apply to neural networks as well any other formal system but people mostly forget it.
Knuth wrote a really fun volume of The Art of Computer Programming about advances in SAT solvers which are the foundation for theorem provers
https://www.amazon.com/Art-Computer-Programming-Fascicle-Sat...
Everybody is aware that neural network techniques have improved drastically in performance, it's much more obscure that the toolbox of symbolic A.I. has improved greatly. Back in the 1980s production rules engines struggled to handle 10,000 rules, now Drools can handle 1,000,000+ rules with no problems.
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.
That is also a very valid and interesting thing to do. But it's also quite interesting to see how the model would do "by itself". All kinds of interesting lessons to be learned!
Earlier quoted context omitted.
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).
Online Integral Calculator Solve integrals with Wolfram|Alpha https://www.wolframalpha.com/calculators/integral-calculator...
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).
Computers can solve math problems and prove theorems; this remains a significant subfield of Computer Science with lots of industrial use cases. However, pure machine learning based approaches toward these problems remain subpar.
> Even mathematical objects are approximated up to an approximation error in a computer (like a differentiable manifold or a real number).
Only because it caught on (and in the case of non-computationally-intensive applications, for purely historical reasons). For example, Mathematica has Reals and even functionality for Reals that is literally impossible to implement for integers [1,2]. There are also precise characterizations of objects in differential geometry [3]. You could imagine applying LLMs to these types of programs a la Copilot, but when you do this you will find yourself agreeing with Paul Houle's observation that math is harder to fake than eg art, language, or even glue code for web apps.
[1] https://reference.wolfram.com/language/ref/Reduce.html
[2] https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
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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).
There has been big progress in automated theorem proving lately https://en.wikipedia.org/wiki/Automated_theorem_proving you just don't hear about it much because the technology is not so fashionable today. Also it is more clear what the limits are, I mean, Turing, Godel, Tarski and all of those apply to neural networks as well any other formal system but people mostly forget it. Knuth wrote a really fun volume of The…
It doesn't seem like there has been much progress for anything but FOL?
Earlier quoted context omitted.
From my (limited) experience with the advanced ML models, they can "do basic math", but they make amateur mistakes with basic things - which indicates they don't actually know addition , but they are good at looking at patterns in existing language. I would assume that state-of-the-art ML models could "convert a word problem into an equation", then feed that equation into a 30 year-old graphing calculator to "do the…
This seems so much like humans that it makes me think lots of people are learning math with an ML-like approach instead of… whatever the heck people like engineers and mathematicians are doing.
If the teachers don't love math, how can we expect students to?
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…
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 good match for non-expert bad-at-math average human behavior.
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Online Integral Calculator Solve integrals with Wolfram|Alpha https://www.wolframalpha.com/calculators/integral-calculator...
Now try to make a computer prove that there are no natural numbers a,b,c; so that a^n + b^n = c^n for any n > 2.