Maxime Bergeron

@ch402 There is probably a way to construct a universal disentangled model. The projections from this disentangled model onto observed ones are then analogous to covering space maps from a universal cover. Isomorphism of models should correspond to isomorphisms of covering spaces.

But as we push in this direction, we'll want to think carefully about what makes a "good" isomorphism. I suspect there's some important notion of "mechanistic faithfulness" to be pinned down.

Early days, but I'm pretty excited about crosscoders (transformer-circuits.pub/2024/crosscode…) as a way to start to create a more universal language of features, less tied to a specific embedding in a specific layer of a specific model... Model diffing is a striking consequence.

@neilchriss There’s a sneaky fourth possibility: the observations are implicitly conditioned on an event C that causes the correlation between A and B but does not actually cause either of them.

@complainerstore This could be along the lines of what you’re looking for jvns.ca/blog/2017/06/0…

@convexcocompact @_nilradical You might like parts of Harer’s notes on the moduli space of curves: link.springer.com/content/pdf/10…