> measure when a deep learning system is making stuff up or hallucinating

That's a great problem to solve! (Maybe biased, because this is my primary research direction). One popular approach is OOD detection, but this always seemed ill-posed to me. My colleagues and I have been approaching this from a more fundamental direction using measures of model misspecification, but this is admittedly niche because it is very computationally expensive. Could still be a while before a breakthrough comes from any direction.