Can LLM's compute any computable function? I thought that an LLM can approximate any computable function, if the function is within the distribution that it is are trained on. I think it's jolly interesting to think about different axiomizations in this context.
Also we know that LLM's can't do a few things - arithmetic, inference & planning are in there. They look like they can because they retrieve discussions from the internet that contain the problems, but when they are tested out of distribution then all of a sudden they fail. However, some other nn's can do these things because they have the architecture and infrastructure and training that enables it.
There is a question for some of these as to whether we want to make NN's do these tasks or just provide calculators, like for grade students, but on the other hand something like Alphazero looks like it could find new ways of doing some problems in planning. The challenge is to find architectures that integrate the different capabilities we can implement in a useful and synergistic way. Lots of people have drawn diagrams about how this can be done, then presented them with lots of hand waving at big conferences. What I love is that John Laird has been building this sort of thing for like, forty years, and is roundly ignored by NN people for some reason.
Maybe because he keeps saying it's really hard and then producing lots of reasons to believe him?