So you do agree that an LLM cannot derive math from first principals, or no? If an LLM had only ever seen 1+1=2 and that was the only math they were ever exposed to, along with the numbers 0-10, could an LLM figure out that 2+2=4?

I argue absolutely not. That would be a fascinating experiment.

Hell, train it on every 2-number addition combination of m+n where m and n can be any number between 1-100 (or 0-100 would be better) BUT 2, and have it figure out what 2+2 is.

I would probably change my opinion about “circuits”, which by the way really stretches the idea of a circuit. The “circuit” is just the statistically most likely series of tokens that you’re drawing pretend lines between. Sure, technically connect-the-dots is a circuit, but not in the way you’re implying, or that paper.

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soulofmischief 2 hours ago | parent [-]

> If an LLM had only ever seen 1+1=2 and that was the only math they were ever exposed to, along with the numbers 0-10, could an LLM figure out that 2+2=4?

What? Of course not? Could you? Do you understand just how much work has gone into proving that 1 + 1 = 2? Centuries upon centuries of work, reformulating all of mathematics several times in the process.

> Hell, train it on every 2-number addition combination of m+n where m and n can be any number between 1-100 (or 0-100 would be better) BUT 2, and have it figure out what 2+2 is.

If you read the paper I linked, it shows how a constrained modular addition is grokked by the model. Give it a read.

> The “circuit” is just the statistically most likely series of tokens that you’re drawing pretend lines between.

That is not what ML researchers mean when they say circuit, no. Circuits are features within the weights. It's understandable that you'd be confused if you do not have the right prior knowledge. Your inquiries are good, but they should stop as inquiries.

If you wish to push them to claims, you first need to understand the space better, understand what modern research does and doesn't show, and turn your hypotheses into testable experiments, collect and publish the results. Or wait for someone else to do it. But the scientific community doesn't accept unfounded conjecture, especially from someone who is not caught up with the literature.

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irishcoffee 2 hours ago | parent [-]

My 4-year-old kid was able to figure out 2+2=4 after I taught them 1+1=2. All 3 of them actually, all at 4-5 years old.

Turns out counting 2 sets of two objects (1… 2… 3… 4…) isn’t actually hard to do if you teach the kid how to count to 10 and that 1+1=2

I guess when we get to toddler stage of LLMs I’ll be more interested.

	▲	soulofmischief 2 hours ago \| parent [-]
		That's wonderful, but you are ignoring that your kid comes built in with a massive range of biological priors, built by millions of years of evolution, which make counting natural and easy out of the box. Machine learning models have to learn all of these things from scratch. And does your child's understanding of mathematics scale? I'm sure your 4-year-old would fail at harder arithmetic. Can they also tell me why 1+1=2? Like actually why we believe that? LLMs can do that. Modern LLMs are actually insanely good at not just basic algebra, but abstract, symbolic mathematics. You're comparing apples and oranges, and seem to lack foundational knowledge in mathematics and computer science. It's no wonder this makes no sense to you. I was more patient about it before, but now this conversation is just getting tiresome. I'd rather spend my energy elsewhere. Take care, have a good day.