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Why are LLMs general learners?

intuitiveai.substack.com

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Re: Why are LLMs general learners?

#23

Earlier quoted context omitted.

LLMs are bad at math because they don't actually understand the rules of math. They can write code to do math, but without code they can only estimate how likely a series of numbers are to be seen together. They're very likely to get things like 2+2=4 correct because that's probably unique and common in their training data. They're unlikely to get two random numbers correct because it doesn't actually know what those…

What would an LLM have to do to convince you it was good at math? Check out this recent post by OpenAI where one of their models is solving 60%+ of problems from a high school math competition dataset: https://openai.com/research/improving-mathematical-reasoning...

It’s actually better at math than it is at arithmetic, and I think this discussion has been about arithmetic. I could make up something about how math is more like language than arithmetic is. I suspect the hypothesis that math tests tend to have a lot of stereotypical problem structures from a shared curriculum is also relevant. But who knows at this point?

Anyway, to convince me it’s good at arithmetic is not complicated…just be good at arithmetic! That is do it correctly, every time, for any size number.

Re: Why are LLMs general learners?

#24
post #10
post #3

Earlier quoted context omitted.

A lot of universal approximators are piss poor at general learning. It's taken a lot of hard work and clever people to get LLM's to where they are. It's not as simple as neural network and done.

Current LLM’s are also piss poor general learners, they are however really good at learning specific things which people value highly.

Some 15 years ago, textbooks taught that multi level perceptrons (fully connected feed forward network) with one hidden layer were sufficient because they were universal approximators. That thought kinda held back the field for a long time. Going against that dogma was so revolutionary that new paradigm was given its own name: deep learning.

Just because you can find some gotcha counterexample LLM's struggle with doesn't invalidate that we've come a very long way.

Re: Why are LLMs general learners?

#25
post #5
post #4

LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus, though, because (contrary to the thesis of the article) they don’t magically acquire whatever ability would “simplify” predicting the next token. I don’t feel like the points made here align with any insight about the workings of LLMs. The fact that, as a human, I “wouldn’t know where to start” when asked to add two numbers witho…

> LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus I suspect most of this is due to tokenization making it difficult to generalize these concepts. There are some weird edge cases though, for example GPT-4 will almost always be able to add two 40 digits number but it is also almost always wrong when adding a 40 digit and 35 digit number.

Could it also be that syllables are intrinsically mechanical? They are strongly related to how our mouths work. While it may be possible to extract syllables from written text - following the consonants and vowels - I'm not sure that many humans could easily count syllables without using their mouths.

Re: Why are LLMs general learners?

#26
post #15

Earlier quoted context omitted.

> LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus, though, because (contrary to the thesis of the article) they don’t magically acquire whatever ability would “simplify” predicting the next token. LLMs understand it to a certain extent. It's more then "predicting" the next token. When people ascribe "predicting the next token" it's a niave and unintelligent description to cover…

I do think that LLMs have emergent properties that do some interesting things, however I would like to point out simple next token prediction would work on your example quite well. 0 + 1 -> 1 Even simple attention mechanisms would handle that quite well with enough examples of

I agree with you, but it also works for

    4320598340958340958340953095809348509348503480958340958304985038530999999 + 1 ?

    The sum of 4320598340958340958340953095809348509348503480958340958304985038530999999 and 1 is 4320598340958340958340953095809348509348503480958340958304985038531000000.
which is more complex.

I'm too lazy to get it to add two large numbers together.

Also, I've never been convinced that "ability to do arithmetic" has any relationship to intelligence. We don't expect regular humans to be able to add two large numbers together reliably, either.

Re: Why are LLMs general learners?

#27
post #4

LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus, though, because (contrary to the thesis of the article) they don’t magically acquire whatever ability would “simplify” predicting the next token. I don’t feel like the points made here align with any insight about the workings of LLMs. The fact that, as a human, I “wouldn’t know where to start” when asked to add two numbers witho…

Author here. First off, thank you for reading and for your thoughts. I provided examples that I thought would be intuitive for humans to help folks understand that an understanding of the underlying phenomena is useful for next token prediction (I've added this as a note). Could you share what part of the article came across as suggesting that LLMs "magically" acquire whatever ability helps them to predict? I'd like…

Thanks for responding to my comment.

I'm not an expert in the field, but, there are lots of previous algorithms for predicting the next token in a series (Markov chains, autocomplete). None of them felt so much pressure to make an accurate prediction that they had no alternative but to teach themselves arithmetic! It seems what is different about LLMs (as far as the post goes) is that we can anthropomorphize them.

More seriously, I guess I just feel like a meaningful sketch of an explanation for why algorithm X (where X is LLMs in this case) for continuing a piece of text is good at problem A should involve something about X and A. Because it is clearly highly dependent on the exact values of X and A, not just whether A can be posed as a text completion problem and humans would prefer the computer learn to solve the underlying problem to produce better text. For example, it could help to imagine a mechanism by which algorithm X could solve problem A. The closest thing to a mechanism (something algorithm X, i.e. LLMs, might be doing that's special) in the post is the talk of necessity being the mother of invention and "a deeper understanding of reality simplifies next-token prediction tasks," and the suggestion that if you were an LLM you might want to use "the rules of addition."

It's true that modeling arithmetic in some way could help a LLM account for known arithmetic problems in the training data, which could help it on unseen arithmetic problems, but what problems an LLM can solve is a function of what it can model. Anything an LLM can't model or can't do, it just doesn't. LLMs are really bad at chess, for example. The patterns of digits in addition may be similar enough to the hierarchical patterns in language the LLM is modeling. But it's not clear if the LLM is using the "rules of addition" or not. As far as I know, we don't actually understand why LLMs are able to store so much factual information, produce such coherent stories, and do the specific things they can do.

Re: Why are LLMs general learners?

#28
post #23

Earlier quoted context omitted.

What would an LLM have to do to convince you it was good at math? Check out this recent post by OpenAI where one of their models is solving 60%+ of problems from a high school math competition dataset: https://openai.com/research/improving-mathematical-reasoning...

It’s actually better at math than it is at arithmetic, and I think this discussion has been about arithmetic. I could make up something about how math is more like language than arithmetic is. I suspect the hypothesis that math tests tend to have a lot of stereotypical problem structures from a shared curriculum is also relevant. But who knows at this point? Anyway, to convince me it’s good at arithmetic is not compl…

>That is do it correctly, every time, for any size number.

Then no human is good at arithmetic.

Re: Why are LLMs general learners?

#29
post #23

Earlier quoted context omitted.

It’s actually better at math than it is at arithmetic, and I think this discussion has been about arithmetic. I could make up something about how math is more like language than arithmetic is. I suspect the hypothesis that math tests tend to have a lot of stereotypical problem structures from a shared curriculum is also relevant. But who knows at this point? Anyway, to convince me it’s good at arithmetic is not compl…

>That is do it correctly, every time, for any size number. Then no human is good at arithmetic.

I suspect most people on this forum can do arithmetic for any "reasonable" size number. It might take weeks to complete, but most people on this forum can calculate large numbers by hand.

Re: Why are LLMs general learners?

#30
post #4

LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus, though, because (contrary to the thesis of the article) they don’t magically acquire whatever ability would “simplify” predicting the next token. I don’t feel like the points made here align with any insight about the workings of LLMs. The fact that, as a human, I “wouldn’t know where to start” when asked to add two numbers witho…

Transformers don’t predict next tokens, right? They predict sequences based on their self-attention to some preceding token sequence?
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