Hmm. I guess the trouble in either case is to define what space we’re talking about. Global guarantees in input space are one thing. The thing I was thinking about that led me to local vs asymptotic as the interesting split is something like temporal as the interesting dimension to asymptote along. So that would be a guarantee about future behavior as we asymptote in amount of iteration of development, or so. A model which has no edge cases—which, globally over the space of inputs, displays behavior that is time-locally aligned—would be a big success. But the thing that interests me is whether the behaviors are aligned as you look further and further into their future consequences.
I personally intuitively much prefer a local vs global dichotomy.
Do you think this definition of global alignment makes sense to you and is applicable as another contaxt to local similarly to asymptotic?
Hmm. I guess the trouble in either case is to define what space we’re talking about. Global guarantees in input space are one thing. The thing I was thinking about that led me to local vs asymptotic as the interesting split is something like temporal as the interesting dimension to asymptote along. So that would be a guarantee about future behavior as we asymptote in amount of iteration of development, or so. A model which has no edge cases—which, globally over the space of inputs, displays behavior that is time-locally aligned—would be a big success. But the thing that interests me is whether the behaviors are aligned as you look further and further into their future consequences.