A type theory has a corresponding geometric interpretation, per topos theory. And this is bidirectional, since there’s an equivalence.
A geometric model of language will correspond to some effective type theory encoded in that language.
So LLMs are essentially learning an implicit “internal language” they’re reasoning in — based on their training data of our language and ways of reasoning.
A type theory has a corresponding geometric interpretation, per topos theory. And this is bidirectional, since there’s an equivalence.
A geometric model of language will correspond to some effective type theory encoded in that language.
So LLMs are essentially learning an implicit “internal language” they’re reasoning in — based on their training data of our language and ways of reasoning.