6 ms·

LLMs are not particularly good at arithmetic, counting syllables, or recognizing haikus, though, because (contrary to the thesis of the article) they don’t magi

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 without doing any addition doesn’t apply to computers (running predictive models). They would start with statistics over lots of similar examples in the training data. It’s still remarkable LLMs do so well on these problems, while at the same time doing somewhat poorly because they can’t do arithmetic!

iliane5 3y ago
> 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.
- rcme 3y ago
  It doesn't have anything to do with tokenization. You can define binary addition using symbols, e.g. a and b, and provide properly tokenized strings to GPT-4. GPT-4 appears to solve the arithmetic puzzles for a few bits, but quickly falls apart on larger examples.
  - iliane5 3y ago
    What I was saying is that because you need to go out of your way to make sure it's tokenized properly, I wouldn't be surprised if there are enough non properly tokenized examples in the dataset. If that was the case, it would make it difficult to generalize these concepts.
- doctor_eval 3y ago
  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.
  - aidenn0 3y ago
    Many humans are also often really bad at doing speech related things when writing. I've known many native English speakers who write things like "an healthy" (because they learned to write "an" before words starting with "h") and write poems that don't rhyme because the words end with the same letters (e.g. "most" and "cost").
    - doctor_eval 3y ago
      Yeah, I find it weird how LLMs make a lot of the kind of mistakes that people do, but somehow this is held up as being a reason why LLMs don’t work similarly to brains. Since discovering LLMs I’ve become convinced that my brain works like them. I really don’t know the next word I’m going to say until it’s nearly out. And since learning about how LLMs work, I really can’t argue it away. It’s a reasonably disturbing feeling.
Ireallyapart 3y ago
> 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 up what they don't understand. I mean you can describe a human brain as simply wetware, a jumble of signals and chemical reactions that twitch muscles and react to pressure waves in the air and light. But obviously there is a higher level description of the human brain that is missing from that description. The same thing could be said about LLMs. I can tell you this, researchers completely understand token prediction that much can be said. What we don't currently understand is the high level description. Perhaps it's not something we can understand as we've never been able to understand human consciousness at a high level either. That's the thing with people. Nobody actually understands the high level description of a fully trained LLM. People are lambasting others because they "think" they understand when they only actually understand the low level primitives. We understand assembly, but you don't understand the Operating system written in assembly. Take this for example: Me: 4320598340958340958340953095809348509348503480958340958304985038530495830 + 1 chatGPT: 4320598340958340958340953095809348509348503480958340958304985038530495830 + 1 equals 4320598340958340958340953095809348509348503480958340958304985038530495831. The chances of chatGPT memorizing or even predicting the next tokens here are in a probability too low to even consider. There are so many possible numbers here even numbers that aren't true but have a "higher probability" of being close to the truth from a token/edit-distance standpoint. It's safe to say, from a scientific standpoint, chatGPT in this scenario understands what it means to add 1. Realize that this calculation results in an overflow. chatGPT needs symbolic understanding to perform the feat it did above. But there are, of course, things it gets wrong. But again we don't truly understand what's going on here. Is it lying to us? Perhaps it can't differentiate between just a generated statistical token or a actual math equation. It's hard to say. But from the example above, by probability, we know that an aspect of true understanding and ability exists.
- hyperliner 3y ago
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pgspaintbrush 3y ago
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 to make that section clearer, so that doesn't come across. Re: "LLMs are not particularly good at arithmetic". There are published results that show that LLMs using certain techniques reach close to 100% accuracy on 8-digit addition: https://arxiv.org/pdf/2206.07682.pdf https://arxiv.org/pdf/2206.07682.pdf. There are also recent results from OpenAI where their model obtained solid results on high school math competition problems, which are harder than arithmetic: https://openai.com/research/improving-mathematical-reasoning-with-process-supervision#fn-2 https://openai.com/research/improving-mathematical-reasoning... I haven't looked into counting syllables or recognizing haikus but I bet that this is a result of tokenization and not an inability of the model to create a representation of the underlying phenomena.
- dgreensp 3y ago
  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.
ipnon 3y ago
Transformers don’t predict next tokens, right? They predict sequences based on their self-attention to some preceding token sequence?
- ludwik 3y ago
  No, what they do is predict a single token that follows the preceding token sequence (which was indeed analyzed using self-attention). Longer output sequences are created by repeating this simple task multiple times, where the previously output tokens become part of the preceding token sequence.
8note 3y ago
I'm surprised they're bad at predicting haikus. I assume because there's little documentation about how many syllables every word has on the internet?
deleted 3y ago
[deleted]
Terr_ 3y ago
> LLMs are not particularly good at arithmetic I'm reminded of "Benny's Rules", where someone sat down with a "self-directed" 6th grader of high IQ who had been doing okay in math classes... but their success so far was actually based on painstakingly constructing somewhat-lexical rules about "math", mumbo-jumbo that had been just good enough to carry them through a lot of graded tests. > Benny believed that the fraction 5/10 = 1.5 and 400/400 = 8.00, because he believed the rule was to add the numerator and denominator and then divide by the number represented by the highest place value. Benny was consistent and confident with this rule and it led him to believe things like 4/11 = 11/4 = 1.5. > Benny converted decimals to fractions with the inverse of his fraction-to-decimal rule. If he needed to write 0.5 as a fraction, "it will be like this ... 3/2 or 2/3 or anything as long as it comes out with the answer 5, because you're adding them" (Erlwanger, 1973, p. 50). [0] https://blog.mathed.net/2011/07/rysk-erlwangers-bennys-conception-of.html https://blog.mathed.net/2011/07/rysk-erlwangers-bennys-conce...

iliane5 3y ago

> 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.

rcme 3y ago
It doesn't have anything to do with tokenization. You can define binary addition using symbols, e.g. a and b, and provide properly tokenized strings to GPT-4. GPT-4 appears to solve the arithmetic puzzles for a few bits, but quickly falls apart on larger examples.
- iliane5 3y ago
  What I was saying is that because you need to go out of your way to make sure it's tokenized properly, I wouldn't be surprised if there are enough non properly tokenized examples in the dataset. If that was the case, it would make it difficult to generalize these concepts.
doctor_eval 3y ago
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.
- aidenn0 3y ago
  Many humans are also often really bad at doing speech related things when writing. I've known many native English speakers who write things like "an healthy" (because they learned to write "an" before words starting with "h") and write poems that don't rhyme because the words end with the same letters (e.g. "most" and "cost").
  - doctor_eval 3y ago
    Yeah, I find it weird how LLMs make a lot of the kind of mistakes that people do, but somehow this is held up as being a reason why LLMs don’t work similarly to brains. Since discovering LLMs I’ve become convinced that my brain works like them. I really don’t know the next word I’m going to say until it’s nearly out. And since learning about how LLMs work, I really can’t argue it away. It’s a reasonably disturbing feeling.

Ireallyapart 3y ago

> 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 up what they don't understand. I mean you can describe a human brain as simply wetware, a jumble of signals and chemical reactions that twitch muscles and react to pressure waves in the air and light. But obviously there is a higher level description of the human brain that is missing from that description. The same thing could be said about LLMs. I can tell you this, researchers completely understand token prediction that much can be said. What we don't currently understand is the high level description. Perhaps it's not something we can understand as we've never been able to understand human consciousness at a high level either. That's the thing with people. Nobody actually understands the high level description of a fully trained LLM. People are lambasting others because they "think" they understand when they only actually understand the low level primitives. We understand assembly, but you don't understand the Operating system written in assembly. Take this for example: Me: 4320598340958340958340953095809348509348503480958340958304985038530495830 + 1 chatGPT: 4320598340958340958340953095809348509348503480958340958304985038530495830 + 1 equals 4320598340958340958340953095809348509348503480958340958304985038530495831. The chances of chatGPT memorizing or even predicting the next tokens here are in a probability too low to even consider. There are so many possible numbers here even numbers that aren't true but have a "higher probability" of being close to the truth from a token/edit-distance standpoint. It's safe to say, from a scientific standpoint, chatGPT in this scenario understands what it means to add 1. Realize that this calculation results in an overflow. chatGPT needs symbolic understanding to perform the feat it did above. But there are, of course, things it gets wrong. But again we don't truly understand what's going on here. Is it lying to us? Perhaps it can't differentiate between just a generated statistical token or a actual math equation. It's hard to say. But from the example above, by probability, we know that an aspect of true understanding and ability exists.

hyperliner 3y ago
[dead]

pgspaintbrush 3y ago

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 to make that section clearer, so that doesn't come across. Re: "LLMs are not particularly good at arithmetic". There are published results that show that LLMs using certain techniques reach close to 100% accuracy on 8-digit addition: https://arxiv.org/pdf/2206.07682.pdf https://arxiv.org/pdf/2206.07682.pdf. There are also recent results from OpenAI where their model obtained solid results on high school math competition problems, which are harder than arithmetic: https://openai.com/research/improving-mathematical-reasoning-with-process-supervision#fn-2 https://openai.com/research/improving-mathematical-reasoning... I haven't looked into counting syllables or recognizing haikus but I bet that this is a result of tokenization and not an inability of the model to create a representation of the underlying phenomena.

dgreensp 3y ago
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.

ipnon 3y ago

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

ludwik 3y ago
No, what they do is predict a single token that follows the preceding token sequence (which was indeed analyzed using self-attention). Longer output sequences are created by repeating this simple task multiple times, where the previously output tokens become part of the preceding token sequence.

8note 3y ago

I'm surprised they're bad at predicting haikus. I assume because there's little documentation about how many syllables every word has on the internet?

deleted 3y ago

[deleted]

Terr_ 3y ago

> LLMs are not particularly good at arithmetic I'm reminded of "Benny's Rules", where someone sat down with a "self-directed" 6th grader of high IQ who had been doing okay in math classes... but their success so far was actually based on painstakingly constructing somewhat-lexical rules about "math", mumbo-jumbo that had been just good enough to carry them through a lot of graded tests. > Benny believed that the fraction 5/10 = 1.5 and 400/400 = 8.00, because he believed the rule was to add the numerator and denominator and then divide by the number represented by the highest place value. Benny was consistent and confident with this rule and it led him to believe things like 4/11 = 11/4 = 1.5. > Benny converted decimals to fractions with the inverse of his fraction-to-decimal rule. If he needed to write 0.5 as a fraction, "it will be like this ... 3/2 or 2/3 or anything as long as it comes out with the answer 5, because you're adding them" (Erlwanger, 1973, p. 50). [0] https://blog.mathed.net/2011/07/rysk-erlwangers-bennys-conception-of.html https://blog.mathed.net/2011/07/rysk-erlwangers-bennys-conce...