there might be no canonical topology for the original computation
This sounds right to me, and overall I mostly think of treeification as just a kind of extensional rewrite (plus adding more inputs).
these hypotheses can’t be understood as making precise claims about the original computation anymore
I think of the underlying graph as providing some combination of 1) causal relationships, and 2) smaller pieces to help with search/reasoning, rather than being an object we inherently care about. (It’s possibly useful to think of hypotheses more as making predictions about the behaviorbut idk.)
I do agree that in some applications you might want to restrict which rewrites (including treeification!) are allowed. e.g., in MAD for ELK we might want to make use of the fact that there is a single “diamond” (which may be ~distributed, but not ~duplicated) upstream of all the sensors.
Not sure if I’m fully responding to your q but...
This sounds right to me, and overall I mostly think of treeification as just a kind of extensional rewrite (plus adding more inputs).
I think of the underlying graph as providing some combination of 1) causal relationships, and 2) smaller pieces to help with search/reasoning, rather than being an object we inherently care about. (It’s possibly useful to think of hypotheses more as making predictions about the behavior but idk.)
I do agree that in some applications you might want to restrict which rewrites (including treeification!) are allowed. e.g., in MAD for ELK we might want to make use of the fact that there is a single “diamond” (which may be ~distributed, but not ~duplicated) upstream of all the sensors.