Well then I’ll have to tell you that I have no university background associated with research on LLMs
because I’ve not gone to any university or college as I’m purely self taught.
For your professor I guess she really determined Sawyer 
But since you noted LLMs are error prone and hallucinate that not because they are wrong it’s because of the etiquette they are trained and mainly they are Probabilistic. If you want an LLM that is mathematically proven to be 100% check on:
Source: Axiom Math Axiom
Axiom uses the Lean programming language as a Mathematical prover which makes a model reasoning logic Deterministic instead of Probabilistic.
Has your lecturer experimented in such ?
What do you think but I think this is the way we can make an AI reasoning atmost fit.
Note: I’m not a researcher just an enthusiastic architect who never took the traditional academic path doesn’t feel so bad to be seft taught (highschool grad) I got no limits.
I think if we kinda borrow the logic from Axiom we can halt the error prone dissatisfaction.