“Small Steps Towards Proving Stochastic → Deterministic Natural Latent” by Alfred Harwood, Jeremy Gillen

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Recorded08 Jan 2026

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Audio note: this article contains 116 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description. The story so far We (Alfred and Jeremy) started a Dovetail project on Natural Latents in order to get some experience with the proofs. Originally we were going to take a crack at this bounty, but just before we got started John and David published a proof, closing the bounty. This proof involves a series of transformations that can take any stochastic latent, and transform it into a deterministic latent, where each step can only increase the error by a small multiple. We decided to work through the proof and understand each step, and attempt to improve the bound. After 20 hours or so working through it, we found a fatal flaw in one step of the proof, and spent the next several days understanding and verifying it. With David's help, the counterexamples we found were strengthened to show that this transformation step had unbounded error on some cases. We started using sympy for arbitrary precision evaluation of counterexamples, and along the way found a bug in sympy [...] ---Outline:(00:26) The story so far(01:51) Empirical evidence suggests the conjecture is true(03:20) Larger N(04:28) The Problem(06:11) Upper bounds on deterministic errors(06:37) Constant Latents(07:29) Copy Latents(08:35) Deterministic Functions of X,Y(09:19) General Upper Bound(12:10) Lower Bounding the Stochastic Latent error(13:08) Mixing Latents and Reverse Jensen inequalities(16:14) Characterizing the optimal stochastic latent(20:50) Summary The original text contained 1 footnote which was omitted from this narration. --- First published: January 8th, 2026 Source: https://www.lesswrong.com/posts/4q3kMfJHB4rxr3Z8m/small-steps-towards-proving-stochastic-deterministic-natural --- Narrated by TYPE III AUDIO. ---Images from the article:Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.

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