You're thinking along the right track but without formalization it goes nowhere fast. By layering of differential geometry on top of probability and then maybe category theoretic logic on top of that, each layer constraining the one below it, and all layers cohering, you get somewhere... There is work that's been done in this area, and I was recently interviewed by a journalist who published a high level article on it on Forbes (Why LLMs are failing) and it links to the actual technical work (at first to my high level presentation then Prof. L. Thorne McCarty's work): https://www.forbes.com/sites/hessiejones/2025/09/30/llms-are...