Audio note: this article contains 36 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Our posts on natural latents have involved two distinct definitions, which we call "stochastic" and "deterministic" natural latents. We conjecture that, whenever there exists a stochastic natural latent (to within some approximation), there also exists a deterministic natural latent (to within a comparable approximation). We are offering a $500 bounty to prove this conjecture.

Some Intuition From The Exact Case

In the exact case, in order for a natural latent to exist over random variables <span>_X_1, X_2_</span>, the distribution has to look roughly like this:

Each value of <span>_X_1_</span> and each value of <span>_X_2_</span> occurs in only one "block", and within the "blocks", <span>_X_1_</span> and <span>_X_2_</span> are independent. In that case, we can take the (exact) natural latent [...]