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I'm not sure how this is germane? I'm talking about specific tasks: saying if 10000 or 10050 is larger. GPT is demonstrably bad at that. The ByT5 paper doesn't

I'm not sure how this is germane? I'm talking about specific tasks: saying if 10000 or 10050 is larger. GPT is demonstrably bad at that. The ByT5 paper doesn't mention arithmetic tasks or show benchmark results for the specific task I mention. Your linked comment says: >This is a common myth but in practice no one (as far as I know) has shown that byte level predictions result in superior overall performance. Stating if BPE or character tokenization is better for everything is a much broader claim, one I didn't make! One could easily imagine a toolformer that calls out to calc.exe for anything involving numbers which would get much better numeric performance while still using BPEs.

sillysaurusx 4y ago
> GPT is bad at math because BPE input compression obfuscates individual digits. https://bbot.org/etc/gpt-math.png https://bbot.org/etc/gpt-math.png You'd be bad at math too if every number was scrambled. This is the myth I was referring to. BPE compression may slow down training, but it doesn't follow that slower training is the reason for being bad at math. If you trained GPT specifically on arithmetic tasks, you'd get superior performance to GPT-3, regardless of which tokenization scheme you'd use. But you'd destroy most of its knowledge about everything not-arithmetic.
- f_devd 4y ago
  > If you trained GPT specifically on arithmetic tasks Sure but you'd have a lot of overlapping tokens with BPE, which doesn't help with convergence. GP is claiming it's specifically worse at arithmetic because of BPE which is true.
- sbierwagen 4y ago
  >BPE compression may slow down training, but it doesn't follow that slower training is the reason for being bad at math. It's not so much that it slows down training, is that it completely destroys the relationship between digits and results. Every number is assigned a random token ID, so GPT-3 had to memorize every operation separately. It couldn't generalize at all, which is why it got worse at larger numbers, which showed up less often in the training set-- no examples to remember. You can try the tokenizer online here: https://platform.openai.com/tokenizer https://platform.openai.com/tokenizer It assigns the input text `10 11 12 13 14 15 16` token IDs `940, 1367, 1105, 1511, 1478, 1315, 1467`. How is it supposed to figure out incrementing numbers from that? Well, it can't, so it memorizes them. "Neural nets want to work"! I used the past tense above, because while writing this comment I asked ChatGPT Mar 14 Version a bunch of manydigit addition and substraction questions and it got them all right. Then I asked it if one of those large numbers contained an 8 and it... hallucinated a completely wrong answer, oops: https://bbot.org/etc/gpt-math2.png https://bbot.org/etc/gpt-math2.png It's also still spotty at multiplication: "The product of 82368 and 33333 is 2745504384." Well, you got the first five digits right...
  - sillysaurusx 4y ago
    Again, repeating the myth that BPE is the reason for GPT being bad at math doesn't make it true. (Nor does labeling it a myth make it false.) It hasn't been demonstrated that this is the reason. And it's not merely a pedantic point – this is an interesting look into why models behave the way they do. To get us both on the same page, let's restate the arguments. - Your position is that in a hypothetical world where a GPT-3 was trained without BPE, yet somehow still managed to maintain the same context window as BPE (i.e. around three to five pages of text), it would be superior at math, because it can see the individual digits. - My position is that it can still see the same context window, and the context window is all that matters. Regardless of whether you tokenize it using OpenAI BPE or LLaMA BPE or digit level, model performance isn't tied to it. What matters is parameter count, training time, and dataset. If you were to pit the two models against each other, given the same dataset and same amount of training, the BPE model would likely perform significantly better at math. The larger the model, the more it can do, and the better the performance at any individual task. And the BPE model would perform better because the compression allows it to learn at a faster rate -- i.e. the same amount of training computation spent on the BPE'd model gives you much more impact than computation spent on the byte level model. In other words, the larger context window is the whole point. You get 2048 tokens. If you make it 2048 bytes, then you get a very limited view of the input text, which harms overall performance. But if you train it on specifically math problems, then of course it'll achieve superior performance, and not simply because it has an unscrambled view of the digits. As I said before, this is like saying that JPG compression is harmful to our understanding of an image. But it's clearly not. The JPG may be composed of wavelets, but what matters is the overall signal -- and that signal is what GPT is being trained on (the understanding of language), not the individual characters. This also explains why tokenization doesn't seem to affect performance across languages that much. Russian tokenizes into many more characters than English, yet GPT can still achieve pretty good performance on it. This isn't because the characters are scrambled, but rather because it's seen many more examples of English than Russian.
    - wongarsu 4y ago
      What about a tokenizer where the digits 0-9 just get the tokens 0-9, all other tokens are derived in the usual BPE manner (except that no token other than 0-9 is allowed to contain digits). Such a model wouldn't have a notable reduction in context size and should behave largely the same in terms of training speed and language tasks, but if sbierwagen is right it might be significantly better at math (and at least on an intuitive level this seems to make sense).
stormfather 4y ago
Are you referring to how BPE is permutation invariant? (ignoring positional encoding)
forgotusername6 4y ago
Complete tangent here. The current usage of the word germane apparently comes from a line in Hamlet. Try asking chatGPT to quote the line and explain it to you. When I tried it failed utterly, not in the explanation but in returning to the actual quote.

sillysaurusx 4y ago

> GPT is bad at math because BPE input compression obfuscates individual digits. https://bbot.org/etc/gpt-math.png https://bbot.org/etc/gpt-math.png You'd be bad at math too if every number was scrambled. This is the myth I was referring to. BPE compression may slow down training, but it doesn't follow that slower training is the reason for being bad at math. If you trained GPT specifically on arithmetic tasks, you'd get superior performance to GPT-3, regardless of which tokenization scheme you'd use. But you'd destroy most of its knowledge about everything not-arithmetic.

f_devd 4y ago
> If you trained GPT specifically on arithmetic tasks Sure but you'd have a lot of overlapping tokens with BPE, which doesn't help with convergence. GP is claiming it's specifically worse at arithmetic because of BPE which is true.
sbierwagen 4y ago
>BPE compression may slow down training, but it doesn't follow that slower training is the reason for being bad at math. It's not so much that it slows down training, is that it completely destroys the relationship between digits and results. Every number is assigned a random token ID, so GPT-3 had to memorize every operation separately. It couldn't generalize at all, which is why it got worse at larger numbers, which showed up less often in the training set-- no examples to remember. You can try the tokenizer online here: https://platform.openai.com/tokenizer https://platform.openai.com/tokenizer It assigns the input text `10 11 12 13 14 15 16` token IDs `940, 1367, 1105, 1511, 1478, 1315, 1467`. How is it supposed to figure out incrementing numbers from that? Well, it can't, so it memorizes them. "Neural nets want to work"! I used the past tense above, because while writing this comment I asked ChatGPT Mar 14 Version a bunch of manydigit addition and substraction questions and it got them all right. Then I asked it if one of those large numbers contained an 8 and it... hallucinated a completely wrong answer, oops: https://bbot.org/etc/gpt-math2.png https://bbot.org/etc/gpt-math2.png It's also still spotty at multiplication: "The product of 82368 and 33333 is 2745504384." Well, you got the first five digits right...
- sillysaurusx 4y ago
  Again, repeating the myth that BPE is the reason for GPT being bad at math doesn't make it true. (Nor does labeling it a myth make it false.) It hasn't been demonstrated that this is the reason. And it's not merely a pedantic point – this is an interesting look into why models behave the way they do. To get us both on the same page, let's restate the arguments. - Your position is that in a hypothetical world where a GPT-3 was trained without BPE, yet somehow still managed to maintain the same context window as BPE (i.e. around three to five pages of text), it would be superior at math, because it can see the individual digits. - My position is that it can still see the same context window, and the context window is all that matters. Regardless of whether you tokenize it using OpenAI BPE or LLaMA BPE or digit level, model performance isn't tied to it. What matters is parameter count, training time, and dataset. If you were to pit the two models against each other, given the same dataset and same amount of training, the BPE model would likely perform significantly better at math. The larger the model, the more it can do, and the better the performance at any individual task. And the BPE model would perform better because the compression allows it to learn at a faster rate -- i.e. the same amount of training computation spent on the BPE'd model gives you much more impact than computation spent on the byte level model. In other words, the larger context window is the whole point. You get 2048 tokens. If you make it 2048 bytes, then you get a very limited view of the input text, which harms overall performance. But if you train it on specifically math problems, then of course it'll achieve superior performance, and not simply because it has an unscrambled view of the digits. As I said before, this is like saying that JPG compression is harmful to our understanding of an image. But it's clearly not. The JPG may be composed of wavelets, but what matters is the overall signal -- and that signal is what GPT is being trained on (the understanding of language), not the individual characters. This also explains why tokenization doesn't seem to affect performance across languages that much. Russian tokenizes into many more characters than English, yet GPT can still achieve pretty good performance on it. This isn't because the characters are scrambled, but rather because it's seen many more examples of English than Russian.
  - wongarsu 4y ago
    What about a tokenizer where the digits 0-9 just get the tokens 0-9, all other tokens are derived in the usual BPE manner (except that no token other than 0-9 is allowed to contain digits). Such a model wouldn't have a notable reduction in context size and should behave largely the same in terms of training speed and language tasks, but if sbierwagen is right it might be significantly better at math (and at least on an intuitive level this seems to make sense).

stormfather 4y ago

Are you referring to how BPE is permutation invariant? (ignoring positional encoding)

forgotusername6 4y ago

Complete tangent here. The current usage of the word germane apparently comes from a line in Hamlet. Try asking chatGPT to quote the line and explain it to you. When I tried it failed utterly, not in the explanation but in returning to the actual quote.