addendum to obsidian/lesswrong/archived/The Mind-Market Correspondence.org

I have looked through obsidian/shortform/2023%20Natural%20latents.%20I%20think%20his%20“fundamental%20theorem”%20is%20just%20a%20generalization%20of%20[sufficient%20statistics): a statistic Λ(X) that is sufficient for all X₁, …X_n is also sufficient for any "insensitive" variable Λ′(X), because Λ contains every bit of mutual information, and Λ’ can't depend on any X_i-specific information, so it has to be only determined by mutual information. Furthermore if Λ is both sufficient and insensitive ("a natural latent"), it is a minimal sufficient statistic.

(He doesn't write these as random functions of X, but that's essentially what "resampling latents" does.)

He conjectures that there is a way to naturally construct a natural latent, via "simultaneous resampling", described in [L2], [L3], [L4].