Mm, this one’s shaky. Cross-hypothesis abstractions don’t seem to be a good idea, see here.
yea so I think the final theory of abstraction will have a weaker notion of equivalence espeically when we incorporate ontology shifts. E.g. we want to say that water is the same concept before and after we discover water is H2O, but the discovery obviously breaks predictive agreement (Indeed, the solomonoff version of natural latent is more robust to the agreement condition)
Also, you can totally add new information/abstraction that is not shared between your current and new hypothesis, & that seems consistent with the picture you described here (you can have separate ontologies but you try to capture the overlap as much as possible)
My guess is that there’s something like a hierarchy of hypotheses, with specific high-level hypotheses corresponding to several lower-level more-detailed hypotheses, and what you’re pointing at by “redundant information across a wide variety of hypotheses” is just an abstraction in a (single) high-level hypothesis which is then copied over into lower-level hypotheses. (E. g., the high-level hypothesis is the concept of a tree, the lower-level hypotheses are about how many trees are in this forest.)
yes I think that’s the right picture
But we don’t derive it by generating a bunch of low-level hypotheses and then abstracting over them, that’d lead to broken ontologies.
I agree that we don’t do that practically as it’d be slower (instead we simply generate an abstraction & use future feedback to determine whether it’s a robust one), but I think if you did generate a bunch of low-level hypotheses and look for redundant computation among them, then an adequate version of it would just recover the “high-level low-level hypotheses” picture you’ve described?
In particular, with cross-hypothesis abstraction we don’t have to separately define what the variables are, so we can sidestep dataset-assembly entirely & perhaps simplify the shifting structures problem
yea so I think the final theory of abstraction will have a weaker notion of equivalence espeically when we incorporate ontology shifts. E.g. we want to say that water is the same concept before and after we discover water is H2O, but the discovery obviously breaks predictive agreement (Indeed, the solomonoff version of natural latent is more robust to the agreement condition)
Also, you can totally add new information/abstraction that is not shared between your current and new hypothesis, & that seems consistent with the picture you described here (you can have separate ontologies but you try to capture the overlap as much as possible)
yes I think that’s the right picture
I agree that we don’t do that practically as it’d be slower (instead we simply generate an abstraction & use future feedback to determine whether it’s a robust one), but I think if you did generate a bunch of low-level hypotheses and look for redundant computation among them, then an adequate version of it would just recover the “high-level low-level hypotheses” picture you’ve described?
In particular, with cross-hypothesis abstraction we don’t have to separately define what the variables are, so we can sidestep dataset-assembly entirely & perhaps simplify the shifting structures problem