DeepMind新研究登上Nature封面，這一數學難題被AI攻破了

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"機器學習第一次發現了人類遺漏的數學聯繫。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"近日，位於倫敦的人工智能巨頭DeepMind的研究人員與數學家合作解決了兩個獨立的問題——一個是結理論，另一個是對稱性研究。在這兩種情況下，人工智能技術都幫助研究人員發現了可以使用傳統方法進行研究的新模式。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"在過去，結理論的數學問題一直是未解的難題。機器學習算法以前也曾被用於生成數學中的此類理論思想，但到目前爲止，這些算法解決的問題比"},{"type":"link","attrs":{"href":"https:\/\/www.infoq.cn\/article\/cujeeZeWfEjhkxsasX5M","title":"xxx","type":null},"content":[{"type":"text","text":" DeepMind"}]},{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" 解決的問題小。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"DeepMind 的機器學習專家、新論文的作者之一Alex Davies說：“利用機器學習在純數學中做出重大的新發現是前所未有的事。” "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"參與這項研究的數學家之一、英國牛津大學Marc Lackenby也表示，“讓我震驚的是，在直覺感知上，機器學習能起到的指導作用真是太大了。”"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"自 1980 年代以來，紐約坎頓的數學家Jeffrey Weeks表示，"},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"繩結的"},{"type":"link","attrs":{"href":"https:\/\/www.infoq.cn\/article\/erV1qQSog0poOYUIXsMV","title":"xxx","type":null},"content":[{"type":"text","text":"計算機模擬"}]},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"和可視化"},{"type":"text","text":"長期以來一直幫助數學家尋找規律並啓發他們的直覺。但是，他補充道，“讓計算機尋找規律會將研究過程提升到一個完全不同的水平。”"}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"棘手的問題"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"在理解結理論時，數學家依賴於稱爲不變量的東西，也就是相同的代數、幾何或數值量。在這種情況下，他們研究了等效結中相同的不變量；等價可以通過多種方式定義，但是如果可以將一個結扭曲爲另一個而不打破結，則可以認爲結是等效的。幾何不變量本質上是對結整體形狀的測量，而代數不變量描述了結如何相互纏繞和打結。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"“到目前爲止，幾何和代數不變量這兩件事之間還沒有經過證實的聯繫，”Davies說道。但數學家認爲這兩者之間可能存在某種關係，因此研究人員決定使用 DeepMind 來尋找它。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"在"},{"type":"link","attrs":{"href":"https:\/\/www.infoq.cn\/article\/lXpJXp8rA2qeCzGMxzbQ","title":"xxx","type":null},"content":[{"type":"text","text":"人工智能"}]},{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"程序的幫助下，他們能夠識別出一種新的幾何測量，他們將其稱爲"},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"被稱爲“天然斜坡”的一個結"},{"type":"text","text":"。這種測量在數學上與稱爲“signature”的已知代數不變量有關，它描述了結上的某些表面。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"研究人員在"},{"type":"text","text":"《"},{"type":"link","attrs":{"href":"https:\/\/www.nature.com\/articles\/d41586-021-00304-8","title":"xxx","type":null},"content":[{"type":"text","text":"自然"}]},{"type":"text","text":"》"},{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"雜誌上寫道，新的猜想——這兩種類型的不變量是相關的這一發現將在結的數學中開闢新的理論。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"在第二種情況下，DeepMind 採用了 1970 年代後期數學家提出的猜想，並幫助揭示了該猜想爲何有效。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"40 年來，數學家們一直在猜測，可以查看一種特定類型的非常複雜的多維圖形，並找出一種特定類型的方程來表示它。但他們還沒有完全弄清楚如何做到這一點。現在，DeepMind 通過將圖的特定特徵與這些方程的預測聯繫起來，這些方程被稱爲 Kazhdan-Lusztig (KL) 多項式，以首次提出這項發現的數學家命名。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"“我們能夠做的是訓練一些機器學習模型，這些模型能夠非常準確地從圖中預測多項式是什麼，”Davies說。該團隊還分析了 DeepMind 使用圖的哪些特徵來進行這些預測，這使他們更接近關於兩者如何相互映射的一般規則。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"這些純數學猜想沒有直接的實際應用，但數學家計劃在新發現的基礎上進一步揭示這些領域中的更多關係。研究團隊還希望他們的成功能夠鼓勵其他數學家將人工智能作爲一種新工具。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"“我們想要做的第一件事就是更多地進入數學界，希望能鼓勵人們使用這種技術，去那裏尋找新的和令人興奮的東西，”Davies說道。"}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"數學和機器學習 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"大部分純數學都在注意數字中的模式或者規律，然後進行艱苦的數值工作來證明這些直覺預感是否代表了真實的關係。當處理多維的複雜方程時，這會變得非常複雜。 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"然而，Davies在接受採訪時稱，“機器學習非常擅長的事情是發現模式和規律。”"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"事實上，與上述案例類似的數學和機器學習的碰撞還有很多。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"DeepMind曾憑藉破解圍棋等突破登上頭條新聞，但其長期關注點一直是科學應用，例如預測蛋白質如何摺疊。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"2019 年，澳大利亞悉尼大學數學家 Geordie Williamson 與 DeepMind 的首席執行官、神經科學家 Demis Hassabis 之間的一次隨意對話引發了數學合作的想法。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"最初，這項工作的重點是識別可以使用 DeepMind 技術進行攻擊的數學問題。機器學習使計算機能夠利用大型數據集進行猜測，例如將監控攝像頭圖像與照片數據庫中的已知面孔進行匹配。但它的答案本質上是概率性的，數學證明需要確定性。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"參考鏈接："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https:\/\/www.sciencealert.com\/ai-is-discovering-patterns-in-pure-mathematics-that-have-never-been-seen-before","title":null,"type":null},"content":[{"type":"text","text":"https:\/\/www.sciencealert.com\/ai-is-discovering-patterns-in-pure-mathematics-that-have-never-been-seen-before"}],"marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":" "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https:\/\/www.nature.com\/articles\/d41586-021-03593-1","title":null,"type":null},"content":[{"type":"text","text":"https:\/\/www.nature.com\/articles\/d41586-021-03593-1"}],"marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}]}]}]}