[soulofmischief]

This is not a correct approximation of what happens inside an LLM. They form probabilistic logical circuits which approximate the world they have learned through training. They are not simply recalling stored facts. They are exploiting organically-produced circuitry, walking a manifold, which leads to the ability to predict the next state in a staggering variety of contexts.

As an example: https://arxiv.org/abs/2301.05217

It's not hard to imagine that a sufficiently developed manifold could theoretically allow LLMs to interpolate or even extrapolate information that was missing from the training data, but is logically or experimentally valid.

[irishcoffee]

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.

[soulofmischief]

> 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.

[irishcoffee]

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]

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.

[irishcoffee]

I hope you restore your energy, I had no idea this was so exhausting! Truly, I'll stop afflicting my projected lack of knowledge, sorry I tired you out!

[hrimfaxi]

Ah man, I was curious to read your response about priors.

> 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?

Unless you locked your kid in a room since birth with just this information, it is not the same kind of set up is it?

[baq]

You compared a LLM blob of numbers to a child.

[emp17344]

You could find a pre-print on Arxiv to validate practically any belief. Why should we care about this particular piece of research? Is this established science, or are you cherry-picking low-quality papers?

[soulofmischief]

I don't need to reach far to find preliminary evidence of circuits forming in machine learning models. Here's some research from OpenAI researchers exploring circuits in vision models: https://distill.pub/2020/circuits/ Are these enough to meet your arbitrary quality bar?

Circuits are the basis for features. There is still a ton of open research on this subject. I don't care what you care about, the research is still being done and it's not a new concept.