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Comment by xyzzy123

3 days ago

Using this reasoning, would you argue that a new proof of a theorem adds no new information that was not present in the axioms, rules of inference and so on?

If so, I'm not sure it's a useful framing.

For novel writing, sure, I would not expect much truly interesting progress from LLMs without human input because fundamentally they are unable to have human experiences, and novels are a shadow or projection of that.

But in math – and a lot of programming – the "world" is chiefly symbolic. The whole game is searching the space for new and useful arrangements. You don’t need to create new information in an information-theoretic sense for that. Even for the non-symbolic side (say diagnosing a network issue) of computing, AIs can interact with things almost as directly as we can by running commands so they are not fundamentally disadvantaged in terms of "closing the loop" with reality or conducting experiments.

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xyzzy123

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measurablefunc  3 days ago

Sound deductive rules of logic can not create novelty that exceeds the inherent limits of their foundational axiomatic assumptions. You can not expect novel results from neural networks that exceed the inherent information capacity of their training corpus & the inherent biases of the neural network (encoded by its architecture). So if the training corpus is semantically unsound & inconsistent then there is no reason to expect that it will produce logically sound & semantically coherent outputs (i.e. garbage inputs → garbage outputs).

  • xyzzy123  2 days ago

    Maybe? But it also seems like you are that you are not accounting for new information at inference time. Let's pretend I agree the LLM is a plagiarism machine that can produce no novelty in and of itself that didn't come from what it was trained on, and produces mostly garbage (I only half agree lol, and I think "novelty" is under-specified here).

    When I apply that machine (with its giant pool of pirated knowledge) _to my inputs and context_ I can get results applicable to my modestly novel situation which is not in the training data. Perhaps the output is garbage. Naturally if my situation is way out of distribution I cannot expect very good results.

    But I often don't care if the results are garbage some (or even most!) of the time if I have a way to ground-truth whether they are useful to me. This might be via running a compile, a test suite, a theorem prover or mk1 eyeball. Of course the name of the game is to get agents to do this themselves and this is now fairly standard practice.