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You've actually shown your poor understanding of LLMs. I just asked Llama-2 7b the same question and it answered perfectly fine. It did not need to use an exter

You've actually shown your poor understanding of LLMs. I just asked Llama-2 7b the same question and it answered perfectly fine. It did not need to use an external python interpreter or a function call, or need to be prompted with chain of thought reasoning. You're correct, LLMs are not (usually) explicitly trained to solve math calculations, this does not mean they cannot solve basic math equations (they can!).

viraptor 3y ago
LLMs don't solve basic math equations. They can pattern match on some aspects, but it's not calculation. Try random numbers for the sum and you'll find examples where it fails. Especially with longer numbers with repeating digits.
- jackblemming 3y ago
  I chose a simple math equation that should almost assuredly be in a dataset of 1 trillion tokens exactly to check its basic pattern matching skills. The token "10" and "20" are even in its hardcoded vocabulary set. I think GPT-4 might be exceeding HN discourse on ML at this point.
  - viraptor 3y ago
    I guess we have a disagreement about what "solve basic math equations" actually means.
- famouswaffles 3y ago
  >They can pattern match on some aspects, but it's not calculation Oh ? So what is it then ? Magic ? When you give GPT-4 random multidigit arithmetic that would not have appeared in it's dataset and it's more accurate than you can manage without a calculator, what is that ? "Pattern matching" has really lost all meaning.
  - viraptor 3y ago
    Sums can be solved at a character level (you can only carry 10, so that's doable). Anything more complicated solved at a generic level would require the network to either model the operation itself, or work recursively. So you either get an imprecise floating point math with noise from the model itself, or a recursion limit that works mostly on integers. Basically, if you can write the list of operations and base it on digits, the network can learn to replicate that. Actual calculation on values - not really. You can tell which mode is used by using large random numbers and seeing what kind of error happens. Missed digits - it's not actually doing the calculation. Also, we don't know how much gpt4 cheats at math. OpenAI may be replacing those bits with external calculation.
    - famouswaffles 3y ago
      >Actual calculation on values - not really. Uh yes really. https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mechanistic-interpretability-analysis-of-grokking https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec... >You can tell which mode is used by using large random numbers and seeing what kind of error happens. Missed digits - it's not actually doing the calculation. Missed digits doesn't mean anything other than the wrong calculation. The assertion that it isn't doing calculation is absurd. >Also, we don't know how much gpt4 cheats at math. OpenAI may be replacing those bits with external calculation Pick one. Either it's so bad it's obviously not doing any calculations at all or it's so good you suspect Open AI are passing numbers through a calculator behind the scenes. Not only is the latter baseless speculation, the 2 options are mutually exclusive.
      - viraptor 3y ago
        > Uh yes really. This is based on integer addition up to 113 with a data set that only trains that. Yes, you can achieve that in a special case. No, LLMs don't achieve that. Conclusion from the post you linked: "Epistemic status: I feel confident in the empirical results, but the generalisation to non-toy settings is more speculative" > Pick one. Either it's so bad it's obviously not doing any calculations at all or it's so good you suspect Open AI are passing numbers through a calculator behind the scenes. That's not the claim. I'm saying LLMs don't do real, precise calculation, but can do digit level operation and some implementations of systems around an LLM could pass the problem through a calculator. LLMs can rewrite the problem into a function, but the execution of it doesn't happen inside LLMs. If you squint it's like the json output - LLMs can kind of do it most of the time, but you can implement a system around the LLM which ensures that any json output will be valid.

viraptor 3y ago

LLMs don't solve basic math equations. They can pattern match on some aspects, but it's not calculation. Try random numbers for the sum and you'll find examples where it fails. Especially with longer numbers with repeating digits.

jackblemming 3y ago
I chose a simple math equation that should almost assuredly be in a dataset of 1 trillion tokens exactly to check its basic pattern matching skills. The token "10" and "20" are even in its hardcoded vocabulary set. I think GPT-4 might be exceeding HN discourse on ML at this point.
- viraptor 3y ago
  I guess we have a disagreement about what "solve basic math equations" actually means.
famouswaffles 3y ago
>They can pattern match on some aspects, but it's not calculation Oh ? So what is it then ? Magic ? When you give GPT-4 random multidigit arithmetic that would not have appeared in it's dataset and it's more accurate than you can manage without a calculator, what is that ? "Pattern matching" has really lost all meaning.
- viraptor 3y ago
  Sums can be solved at a character level (you can only carry 10, so that's doable). Anything more complicated solved at a generic level would require the network to either model the operation itself, or work recursively. So you either get an imprecise floating point math with noise from the model itself, or a recursion limit that works mostly on integers. Basically, if you can write the list of operations and base it on digits, the network can learn to replicate that. Actual calculation on values - not really. You can tell which mode is used by using large random numbers and seeing what kind of error happens. Missed digits - it's not actually doing the calculation. Also, we don't know how much gpt4 cheats at math. OpenAI may be replacing those bits with external calculation.
  - famouswaffles 3y ago
    >Actual calculation on values - not really. Uh yes really. https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mechanistic-interpretability-analysis-of-grokking https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec... >You can tell which mode is used by using large random numbers and seeing what kind of error happens. Missed digits - it's not actually doing the calculation. Missed digits doesn't mean anything other than the wrong calculation. The assertion that it isn't doing calculation is absurd. >Also, we don't know how much gpt4 cheats at math. OpenAI may be replacing those bits with external calculation Pick one. Either it's so bad it's obviously not doing any calculations at all or it's so good you suspect Open AI are passing numbers through a calculator behind the scenes. Not only is the latter baseless speculation, the 2 options are mutually exclusive.
    - viraptor 3y ago
      > Uh yes really. This is based on integer addition up to 113 with a data set that only trains that. Yes, you can achieve that in a special case. No, LLMs don't achieve that. Conclusion from the post you linked: "Epistemic status: I feel confident in the empirical results, but the generalisation to non-toy settings is more speculative" > Pick one. Either it's so bad it's obviously not doing any calculations at all or it's so good you suspect Open AI are passing numbers through a calculator behind the scenes. That's not the claim. I'm saying LLMs don't do real, precise calculation, but can do digit level operation and some implementations of systems around an LLM could pass the problem through a calculator. LLMs can rewrite the problem into a function, but the execution of it doesn't happen inside LLMs. If you squint it's like the json output - LLMs can kind of do it most of the time, but you can implement a system around the LLM which ensures that any json output will be valid.