They need to be high-dimensional for the linear models themselves to do anything interesting, but I think adding a large number of low-dimensional linear models might, despite being boring, still change the dynamics of the graphs to be marginally more realistic for settings involving optimization. X turns into an estimate of Y, and tries to control this estimate towards zero; that’s a pattern that I assume would be rare in your graph, but common in reality, and it could lead to real graphs exhibiting certain “conspiracies” that the model graphs might lack (especially if there are many (X, Y) pairs, or many (individually unidimensional) Xs that all try to control a single common Y).
But there’s probably a lot of things that can be investigated about this. I should probably be working on getting my system for this working, or something. Gonna be exciting to see what else you figure out re natural abstractions.
They need to be high-dimensional for the linear models themselves to do anything interesting, but I think adding a large number of low-dimensional linear models might, despite being boring, still change the dynamics of the graphs to be marginally more realistic for settings involving optimization. X turns into an estimate of Y, and tries to control this estimate towards zero; that’s a pattern that I assume would be rare in your graph, but common in reality, and it could lead to real graphs exhibiting certain “conspiracies” that the model graphs might lack (especially if there are many (X, Y) pairs, or many (individually unidimensional) Xs that all try to control a single common Y).
But there’s probably a lot of things that can be investigated about this. I should probably be working on getting my system for this working, or something. Gonna be exciting to see what else you figure out re natural abstractions.