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It seems incredibly easy to generate an enormous amount of synthetic data for math. Is that happening? Does it work?

ninetyninenine 2y ago
I don’t think so. The data is biased towards being very general.
Davidzheng 2y ago
In which distribution? Like school math or competition or unsolved problems? FWIW I think one and three and probably easier to generated as synethetically. It's harder to bound the difficulty but I think the recent David silver talk implies it doesn't matter much. Anyway there's some work on this you can find online--they claim to improve gsm8k and MATH a bit but not saturate it. Idk in practice how useful it is
MacsHeadroom 2y ago
Yes, this is how o1 was trained. Math and programming, because they are verifiable. This is also why o1 is not better at English. Math skills transfer to general reasoning but not so much to creative writing.
bentice 2y ago
Data is the wrong approach to develop reasoning. You we don't want LLM's to simply memorize 3x3 = 9 we want them to understand that 3 + 3 + 3 = 9 therefore 3x3 = 9 (obviously a trivial example). If they have developed reasoning very few examples should be needed. The way I see it reasoning is actually the ability of the model to design and train smaller models that can learn with very few examples.
- hackinthebochs 2y ago
  > If they have developed reasoning very few examples should be needed. Yes, once the modules for reasoning have converged, it will take very few examples for it to update to new types of reasoning. But to develop those modules from scratch requires large amounts of examples that overtax its ability to memorize. We see this pattern in the "grokking" papers. Memorization happens first, then "grokking" (god I hate that word). It's not like humans bootstrap reasoning out of nothing. We have a billion years of evolution that encoded the right inductive biases in our developmental pathways to quickly converge on the structures for reasoning. Training an LLM from scratch is like recapitulating the entire history of evolution in a few months.
- dr_dshiv 2y ago
  My understanding is that, if you train these enough, it becomes likely to develop efficient compressions— which “reasoning” would be.
ilaksh 2y ago
They did that for o1 and o1-preview. Which if you read the paper or do your own testing with that SOTA model you will see that the paper is nonsense. With the best models the problems they point out are mostly marginal like one or two percentage points when changing numbers etc. They are taking poor performance of undersized models and claiming that proves some fundamental limitation of large models, even though their own tests show that isn't true.
- foobarqux 2y ago
  You choose to ignore Figure 8 which shows a 18% drop when simply adding an irrelevant detail. In the other test the perturbations aren’t particularly sophisticated and modify the problem according to a template. As the parent comment said this is pretty easy to generate test data for (and for the model to pattern match against) so maybe that is what they did. A better test of “reasoning” would be to isolate the concept/algorithm and generate novel instances that are completely textually different from existing problems to see if the model really isn’t just pattern matching. But we already know the answer to this because it can’t do things like arbitrary length multiplication.
  - ilaksh 2y ago
    This shows there are limitations but it doesn't prove they can't be overcome by changing training data. I don't think that LLMs are the end of AGI research at all, but the extreme skepticism of their current utility is mostly based on failures of small models. It's like 65% for most of the small models they tested and that is what they are really basing their conclusions on
aithrowawaycomm 2y ago
It's easy enough to generate an enormous amount of formal math problems, but utterly quixotic to generate an enormous amount of quantitative reasoning problems, which is the thing LLMs are lacking.

I don’t think so. The data is biased towards being very general.

In which distribution? Like school math or competition or unsolved problems? FWIW I think one and three and probably easier to generated as synethetically. It's harder to bound the difficulty but I think the recent David silver talk implies it doesn't matter much. Anyway there's some work on this you can find online--they claim to improve gsm8k and MATH a bit but not saturate it. Idk in practice how useful it is

MacsHeadroom 2y ago

Yes, this is how o1 was trained. Math and programming, because they are verifiable. This is also why o1 is not better at English. Math skills transfer to general reasoning but not so much to creative writing.

bentice 2y ago

Data is the wrong approach to develop reasoning. You we don't want LLM's to simply memorize 3x3 = 9 we want them to understand that 3 + 3 + 3 = 9 therefore 3x3 = 9 (obviously a trivial example). If they have developed reasoning very few examples should be needed. The way I see it reasoning is actually the ability of the model to design and train smaller models that can learn with very few examples.

hackinthebochs 2y ago
> If they have developed reasoning very few examples should be needed. Yes, once the modules for reasoning have converged, it will take very few examples for it to update to new types of reasoning. But to develop those modules from scratch requires large amounts of examples that overtax its ability to memorize. We see this pattern in the "grokking" papers. Memorization happens first, then "grokking" (god I hate that word). It's not like humans bootstrap reasoning out of nothing. We have a billion years of evolution that encoded the right inductive biases in our developmental pathways to quickly converge on the structures for reasoning. Training an LLM from scratch is like recapitulating the entire history of evolution in a few months.
dr_dshiv 2y ago
My understanding is that, if you train these enough, it becomes likely to develop efficient compressions— which “reasoning” would be.

ilaksh 2y ago

They did that for o1 and o1-preview. Which if you read the paper or do your own testing with that SOTA model you will see that the paper is nonsense. With the best models the problems they point out are mostly marginal like one or two percentage points when changing numbers etc. They are taking poor performance of undersized models and claiming that proves some fundamental limitation of large models, even though their own tests show that isn't true.

foobarqux 2y ago
You choose to ignore Figure 8 which shows a 18% drop when simply adding an irrelevant detail. In the other test the perturbations aren’t particularly sophisticated and modify the problem according to a template. As the parent comment said this is pretty easy to generate test data for (and for the model to pattern match against) so maybe that is what they did. A better test of “reasoning” would be to isolate the concept/algorithm and generate novel instances that are completely textually different from existing problems to see if the model really isn’t just pattern matching. But we already know the answer to this because it can’t do things like arbitrary length multiplication.
- ilaksh 2y ago
  This shows there are limitations but it doesn't prove they can't be overcome by changing training data. I don't think that LLMs are the end of AGI research at all, but the extreme skepticism of their current utility is mostly based on failures of small models. It's like 65% for most of the small models they tested and that is what they are really basing their conclusions on

aithrowawaycomm 2y ago

It's easy enough to generate an enormous amount of formal math problems, but utterly quixotic to generate an enormous amount of quantitative reasoning problems, which is the thing LLMs are lacking.