Really gorgeous stuff with philosophically significant and plausibly practical implications. Great work. I assume you’ve also looked at this from a categorial perspective? It would surprise me if treating latents as limits didn’t simplify some of the arguments (or at least the presentation, which is already admirably clear). And I can’t help but wonder whether “bigger” uniqueness/isomorphism/stability results for world-models or other features of agents might result from comparing Bayes net categories. If you haven’t tried categorial abstractions (I dunno the specifics—there are a few categorification choices that I could see being useful here), play around with them.
@Lorxus translated the proofs here into categorical language IIRC (and found these deterministic versions much nicer than the older stochastic versions).
Really gorgeous stuff with philosophically significant and plausibly practical implications. Great work. I assume you’ve also looked at this from a categorial perspective? It would surprise me if treating latents as limits didn’t simplify some of the arguments (or at least the presentation, which is already admirably clear). And I can’t help but wonder whether “bigger” uniqueness/isomorphism/stability results for world-models or other features of agents might result from comparing Bayes net categories. If you haven’t tried categorial abstractions (I dunno the specifics—there are a few categorification choices that I could see being useful here), play around with them.
@Lorxus translated the proofs here into categorical language IIRC (and found these deterministic versions much nicer than the older stochastic versions).
oh good to know, i was thinking about how one might get redund and mediator formally dual to each other. is this written up?