3 ms·

It is not computing the right ones. There is no debate there. These algorithms do not map inputs to outputs reliably.

famouswaffles 3y ago
The point is that this is just blatantly wrong. >Asking a token prediction model to do math is like asking a human to do math without doing the math. What's 9 times 9? I can tell you it's 81 from sheer memorization. I can probably invoke 9 x 9 + 1 = 82 without needing to do any calculation either. But if you ask me 32 * 64, that's very difficult to do without doing calculations. Implicitly doing math is not sensible. It's not about memorization. It's trivial to test on instances that would not appear in training and see GPT-4 be better than a human who would attempt the problem without a tool or pad. The biggest problem with LLM arithmetic is tokenization. https://arxiv.org/abs/2310.02989 https://arxiv.org/abs/2310.02989 Other than that, the algorithms it uses for arithmetic will continue to converge during training until it is correct.
- spywaregorilla 3y ago
  I'm not claiming it's about memorization. I have not memorized 9 x 9 + 1 is 82. I can simply do it without invoking any calculation. That is a close equivalent to trying to do with math token prediction. Humans doing things "without a pad" is not the same thing as doing mental math vs. trying to intuit an answer. Token predictions will not converge on correct arithmetic algorithms.
  - famouswaffles 3y ago
    >I'm not claiming it's about memorization. I have not memorized 9 x 9 + 1 is 82. I can simply do it without invoking any calculation. >What's 9 times 9? I can tell you it's 81 from sheer memorization. I can probably invoke 9 x 9 + 1 = 82 without needing to do any calculation Performing math how you suggest is little more than memorization except you've just memorized a different chain in the process. >That is a close equivalent to trying to do with math token prediction. This isn't going to become true no matter how much you repeat it. You've consistently made assertions that are trivially proven false. >Token predictions will not converge on correct arithmetic algorithms. Yes it will. It literally will. This isn't some debate. This is something that has been researched. https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mechanistic-interpretability-analysis-of-grokking https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec... You think you have an understanding of Language Models and token prediction. Unfortunately you don't.
    - spywaregorilla 3y ago
      > Performing math how you suggest is little more than memorization except you've just memorized a different chain in the process. It's synthesis of memory perhaps, but it's not memorizing specific answers; which is different yet from executing steps of an algorithm you have memorized. > This isn't going to become true no matter how much you repeat it. You've consistently made assertions that are trivially proven false. Then agree to disagree because I think you're full of shit. actually, not even that, I think you just don't even understand what I'm saying. which is agreeing with you 90% of the way. This article is nice. But Memorization -> Generalization -> Cleaning up Noise -> Stability is STILL NOT THE ALGORITHM. It will never be the algorithm. It's always just "generalization-ish". Which is again, a modality that human brains can use to process problems and works pretty well, and can presumably work very well, but is ultimately inferior to established, perfected algorithms. but nah. you chose petty arrogance so yay, we get get to be dicks. fuck off.
      - deleted 3y ago
        [deleted]

The point is that this is just blatantly wrong. >Asking a token prediction model to do math is like asking a human to do math without doing the math. What's 9 times 9? I can tell you it's 81 from sheer memorization. I can probably invoke 9 x 9 + 1 = 82 without needing to do any calculation either. But if you ask me 32 * 64, that's very difficult to do without doing calculations. Implicitly doing math is not sensible. It's not about memorization. It's trivial to test on instances that would not appear in training and see GPT-4 be better than a human who would attempt the problem without a tool or pad. The biggest problem with LLM arithmetic is tokenization. https://arxiv.org/abs/2310.02989 https://arxiv.org/abs/2310.02989 Other than that, the algorithms it uses for arithmetic will continue to converge during training until it is correct.

spywaregorilla 3y ago
I'm not claiming it's about memorization. I have not memorized 9 x 9 + 1 is 82. I can simply do it without invoking any calculation. That is a close equivalent to trying to do with math token prediction. Humans doing things "without a pad" is not the same thing as doing mental math vs. trying to intuit an answer. Token predictions will not converge on correct arithmetic algorithms.
- famouswaffles 3y ago
  >I'm not claiming it's about memorization. I have not memorized 9 x 9 + 1 is 82. I can simply do it without invoking any calculation. >What's 9 times 9? I can tell you it's 81 from sheer memorization. I can probably invoke 9 x 9 + 1 = 82 without needing to do any calculation Performing math how you suggest is little more than memorization except you've just memorized a different chain in the process. >That is a close equivalent to trying to do with math token prediction. This isn't going to become true no matter how much you repeat it. You've consistently made assertions that are trivially proven false. >Token predictions will not converge on correct arithmetic algorithms. Yes it will. It literally will. This isn't some debate. This is something that has been researched. https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mechanistic-interpretability-analysis-of-grokking https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec... You think you have an understanding of Language Models and token prediction. Unfortunately you don't.
  - spywaregorilla 3y ago
    > Performing math how you suggest is little more than memorization except you've just memorized a different chain in the process. It's synthesis of memory perhaps, but it's not memorizing specific answers; which is different yet from executing steps of an algorithm you have memorized. > This isn't going to become true no matter how much you repeat it. You've consistently made assertions that are trivially proven false. Then agree to disagree because I think you're full of shit. actually, not even that, I think you just don't even understand what I'm saying. which is agreeing with you 90% of the way. This article is nice. But Memorization -> Generalization -> Cleaning up Noise -> Stability is STILL NOT THE ALGORITHM. It will never be the algorithm. It's always just "generalization-ish". Which is again, a modality that human brains can use to process problems and works pretty well, and can presumably work very well, but is ultimately inferior to established, perfected algorithms. but nah. you chose petty arrogance so yay, we get get to be dicks. fuck off.
    - deleted 3y ago
      [deleted]