Is there active research being done in which large neural networks are trained on hard mathematical problems which are easy to generate and verify (like finding prime numbers, etc.)? I’d be curious at what point, if ever, such networks can solve problems with less compute than our best-known “hand-coded” algorithms (which would imply the network has discovered an even faster algorithm than what we know of). Is there any chance of this (or something similar) helping to advance mathematics in the near-term future?
It seems like the sort of thing that might be possible in principle, but unlikely much before AGI. Neural networks that iterate over their own output can in principle execute arbitrary algorithms, but so far none of the systems involved with automated programming do that yet. They don’t appear to “understand” much about the code they emit either. We’re barely at the “hello world” stage of automated programming.
For plenty of problems we know there are faster ways to solve them than we’ve yet discovered (I know this was true of multiplication as of a few years ago at least), so this seems like a plausible thing that can be done. If I’m wrong, I’m curious how my reasoning fails.
Is there active research being done in which large neural networks are trained on hard mathematical problems which are easy to generate and verify (like finding prime numbers, etc.)? I’d be curious at what point, if ever, such networks can solve problems with less compute than our best-known “hand-coded” algorithms (which would imply the network has discovered an even faster algorithm than what we know of). Is there any chance of this (or something similar) helping to advance mathematics in the near-term future?
It seems like the sort of thing that might be possible in principle, but unlikely much before AGI. Neural networks that iterate over their own output can in principle execute arbitrary algorithms, but so far none of the systems involved with automated programming do that yet. They don’t appear to “understand” much about the code they emit either. We’re barely at the “hello world” stage of automated programming.
For plenty of problems we know there are faster ways to solve them than we’ve yet discovered (I know this was true of multiplication as of a few years ago at least), so this seems like a plausible thing that can be done. If I’m wrong, I’m curious how my reasoning fails.