On this particular example you can achieve deterministic error ≈2.5ϵ with latent A∧B, but it seems easy to find other examples with ratio > 5 (including over latents A∧B,A∨B) in the space of distributions over (X,Y,Z) with a random-restart hill-climb. Anyway, my takeaway is that if you think you can derandomize latents in general you should probably try to derandomize the latent Λ:=Y for variables A:=X⊕Y, B:=Z⊕Y for distributions over boolean variables X,Y,Z.
My impression is that prior discussion focused on discretizing Λ. Λ is already boolean here, so if the hypothesis is true then it’s for a different reason.
On this particular example you can achieve deterministic error ≈2.5ϵ with latent A∧B, but it seems easy to find other examples with ratio > 5 (including over latents A∧B,A∨B) in the space of distributions over (X,Y,Z) with a random-restart hill-climb. Anyway, my takeaway is that if you think you can derandomize latents in general you should probably try to derandomize the latent Λ:=Y for variables A:=X⊕Y, B:=Z⊕Y for distributions over boolean variables X,Y,Z.
(edited to fix typo in definition of B)
My impression is that prior discussion focused on discretizing Λ. Λ is already boolean here, so if the hypothesis is true then it’s for a different reason.