我們（Alfred 與 Jeremy）啟動了一個關於「自然潛在變量」（Natural Latents）的 Dovetail 專案，目的是為了獲得一些證明方面的經驗。最初我們打算挑戰這項懸賞，但就在我們開始之前，John 和 David 發表了一個證明，結束了該懸賞。這個證明涉及一系列轉換，可以將任何隨機潛在變量（stochastic latent）轉換為確定性潛在變量（deterministic latent），且每一步轉換增加的誤差僅限於一個小的倍數。我們決定深入研究這個證明並理解每個步驟，並嘗試改進其誤差界限。在花費大約 20 小時研究後，我們在證明的一個步驟中發現了一個致命缺陷，並在接下來的幾天裡進行了理解與驗證。在 David 的幫助下，我們發現的反例得到了強化，顯示出該轉換步驟在某些情況下具有無窮大的誤差。我們開始使用 sympy 進行反例的任意精度評估，過程中發現了 sympy 的一個錯誤，偶爾會給我們帶來困擾。於是我們切換到了 Mathematica。

從那時起，我們一直以兼職的方式嘗試自己證明該懸賞猜想（或證明該猜想是錯誤的）。最終到目前為止我們還沒有成功，但仍感覺目標近在咫尺。或許自動定理證明器會在未來一兩年內攻克它。這是一個很好的測試案例。

經驗證據表明該猜想是正確的

我們仍然認為整體的懸賞猜想［(存在隨機自然潛在變量) 隱含 (存在確定性自然潛在變量)］是正確的。事實上，我們在經驗上能找到的最大誤差差異約為 1.82。（即：最優確定性誤差總和 < 1.82 * 最優隨機誤差總和）。

在我們的探索過程中，我們製作了許多像上面那樣的圖表。橘色和藍色曲線上的每個點都是經過數值優化的潛在分佈 P[Λ|X,Y] 的評分。mjx-chtml {display: inline-block; line-height: 0; text-indent: 0; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0; min-height: 0; border: 0; margin: 0; padding: 1px 0}
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