> Doesn’t that imply that there is some topological structure to the hallucinations? What does that topology look like? Maybe! I'm not an AI researcher or math

> Doesn’t that imply that there is some topological structure to the hallucinations? What does that topology look like? Maybe! I'm not an AI researcher or mathematician, so I don't know if anyone has pursued this idea. The problem might be that any such structure is intractably complicated to describe within the limits of human understanding. > How do you know that there are no discontinuous regions or that you are not stuck in a local minima? Are you talking about f() getting stuck in some kind of bad region while generating text, or about the optimization process itself? The answer is the same in both cases: we don't. Regarding text generation, we've seen plenty of examples where specific prompts result in pathological output. Although I'm not sure if newer models have that problem. Regarding optimization, there is absolutely no guarantee that we have found a global minimum. Some interesting research has been done on the "loss landscape" of these giant neural network models, and my understanding is that they are messy and complicated. Keep in mind that the training data is part of the loss function! Finding a local minimum on the training data might just result in overfitting.