Initially, it has provided a solution for the first problem. I asked it: “please check your answer for any errors”, and then it apologized for the erroneous solution, and made the aforementioned assessment that the problem is still open.
With the second problem, it was a somewhat similar story: it answered with a partial solution involving a Cholesky decomposition, and then clarified that the problem is open.
Seems to be worth talking with GPT-4 on the matter. Perhaps it could give some useful hints.
I don’t think that anyone has ever mentioned problem #2 in the literature and so I would at least consider that answer somewhat misleading.
I strongly suspect that if we put in a similar-sounding but very easy problem GPT-4 would be just as likely to say that it’s an open question.
Initially, it has provided a solution for the first problem. I asked it: “please check your answer for any errors”, and then it apologized for the erroneous solution, and made the aforementioned assessment that the problem is still open.
With the second problem, it was a somewhat similar story: it answered with a partial solution involving a Cholesky decomposition, and then clarified that the problem is open.
Seems to be worth talking with GPT-4 on the matter. Perhaps it could give some useful hints.