Just struck me that an important AI problem, formal logic reasoning, is actually defined at the wrong level. The problem is not to get a computer to do logic, but to get it to conclude logic is in fact a thing to do, and invent/discover the *idea* of logic via ML
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Logic is easy. Discovering that logic is a thing you can do, uncovering its rules, and deciding when to use them, is the hard part.
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There is like zero line of sight to how to do this in current leading edge ML research.
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Doesn't this depend on whether scaling holds? My impression has been that the scaling argument as applied to prosaic LMs extends to the idea of learnable logic.
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what do you mean 'scaling argument'? I am not sure what you're referring to.
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Roughly, as AI models are scaled up (data + compute + model params) they develop deeper, more general and abstract reasoning capabilities.
The view among proponents of the scaling hypothesis is that these capabilities may (will) eventually include principles of logic.
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Ah, okay. Yeah, I've heard that argument, but I think it's kinda a leap of faith at this point. There's no clear reason to believe it other than that biological brains seem to be an existence proof if you squint enough.
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hmm I've tended to take it more seriously, given that it seems to explain the history of language modelling quite well.
As model size, data, compute ↑, models went from writing words → phrases → sentences → paragraphs, to now being able to write blogs & do math (GPT+)
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The math thing might be at the core of the question: GPT-3 can add small numbers (~3 digits) together pretty well but fails for larger ones
So an interesting question (currently debated) is whether it's "learned math" or is just babbling really well
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Yeah, it hasn't learned math. But it's not babbling either. It's just learned math-words as part of a probabilistic language model.
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Yes, but the key question for scaling is whether "it just learned math words as part of a language model" is any different from "it understands math words", or "it understands math".
Pro-scalers would argue that the answer converges to "no" in the high-scale limit.
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I'd call that a problem of insufficient introspection. It simply does not map to how humans seem to do math.
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