I agree that after discussions with a LLM you may be led to novel insights.

However, such novel insights are not novel due to the LLM, but due to you.

The "novel" insights are either novel only to you, because they belong to something that you have not studied before, or they are novel ideas that were generated by yourself as a consequence of your attempts to explain what you want to the LLM.

It is very frequent for someone to be led to novel insights about something that he/she believed to already understand well, only after trying to explain it to another ignorant human, when one may discover that the previous supposed understanding was actually incorrect or incomplete.

The point is that the combined knowledge/process of the LLM and a user (which could be another LLM!) led to it walking the manifold in a way that produced a novel distribution for a given domain.

I talk with LLMs for hours out of the day, every single day. I'm deeply familiar with their strengths and shortcomings on both a technical and intuitive level. I push them to their limits and have definitely witnessed novel output. The question remains, just how novel can this output be? Synthesis is a valid way to produce novel data.

And beyond that, we are teaching these models general problem-solving skills through RL, and it's not absurd to consider the possibility that a good enough training regimen cannot impart deduction/induction skills into a model that are powerful enough to produce novel information even via means other than direct synthesis of existing information. Especially when given affordances such as the ability to take notes and browse the web.

> I push them to their limits and have definitely witnessed novel output.

I’m quite curious what these novel outputs are. I imagine the entire world would like to know of an LLM producing completely, never-before-created outputs which no human has ever thought before.

Here is where I get completely hung up. Take 2+2. An LLM has never had 2 groups of two items and reached the enlightenment of 2+2=4

It only knows that because it was told that. If enough people start putting 2+2=3 on the internet who knows what the LLM will spit out. There was that example a ways back where an LLM would happily suggest all humans should eat 1 rock a day. Amusingly, even _that_ wasn’t a novel idea for the LLM, it simply regurgitated what it scraped from a website about humans eating rocks. Which leads to the crux: how much patently false information have LLMs scraped that is completely incorrect?

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.

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?

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.

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.

> 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.

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.

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.

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?

You compared a LLM blob of numbers to a child.

Everyone else compared them to college interns, I was being generous.

No, you were being arrogant and presumptuous, providing flawed analogies and using them as evidence for unfounded and ill-formed claims about the capabilities of frontier models.

Lack of knowledge is one thing, arrogance is another.