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I’m a bit skeptical. Without instructional materials from textbooks, programming language reference manuals and guides, as well as general knowledge about logic and discrete mathematics, I doubt a model could work very well.
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Yes. Model would be limited in its performance, but it would perform well in the limited domain because LLM interpolate from training data. They don't think like humans.

We might think that knowledge from logc and discrete math would spill over to coding. Unfortunately, it doesn't seem to work like that. Even 1T parameter LLM fail on tasks if there are no variants of it in the training data.

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I'm skeptical that the "logical ability" is much more then the elided data. Obviously some things get fully memorized and other things don't, but I don't think there's anything like functional circuits.
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