DeepMind新研究登上Nature封面，这一数学难题被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":"机器学习第一次发现了人类遗漏的数学联系。"}]},{"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，位於伦敦的人工智能巨头DeepMind的研究人员与数学家合作解决了两个独立的问题——一个是结理论，另一个是对称性研究。在这两种情况下，人工智能技术都帮助研究人员发现了可以使用传统方法进行研究的新模式。"}]},{"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":"在过去，结理论的数学问题一直是未解的难题。机器学习算法以前也曾被用于生成数学中的此类理论思想，但到目前为止，这些算法解决的问题比"},{"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":" 解决的问题小。 "}]},{"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 的机器学习专家、新论文的作者之一Alex Davies说：“利用机器学习在纯数学中做出重大的新发现是前所未有的事。” "}]},{"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":"参与这项研究的数学家之一、英国牛津大学Marc Lackenby也表示，“让我震惊的是，在直觉感知上，机器学习能起到的指导作用真是太大了。”"}]},{"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 年代以来，纽约坎顿的数学家Jeffrey Weeks表示，"},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"绳结的"},{"type":"link","attrs":{"href":"https:\/\/www.infoq.cn\/article\/erV1qQSog0poOYUIXsMV","title":"xxx","type":null},"content":[{"type":"text","text":"计算机模拟"}]},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"和可视化"},{"type":"text","text":"长期以来一直帮助数学家寻找规律并启发他们的直觉。但是，他补充道，“让计算机寻找规律会将研究过程提升到一个完全不同的水平。”"}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"棘手的问题"}]},{"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":"在理解结理论时，数学家依赖于称为不变量的东西，也就是相同的代数、几何或数值量。在这种情况下，他们研究了等效结中相同的不变量；等价可以通过多种方式定义，但是如果可以将一个结扭曲为另一个而不打破结，则可以认为结是等效的。几何不变量本质上是对结整体形状的测量，而代数不变量描述了结如何相互缠绕和打结。"}]},{"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":"“到目前为止，几何和代数不变量这两件事之间还没有经过证实的联系，”Davies说道。但数学家认为这两者之间可能存在某种关系，因此研究人员决定使用 DeepMind 来寻找它。 "}]},{"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":"程序的帮助下，他们能够识别出一种新的几何测量，他们将其称为"},{"type":"text","marks":[{"type":"color","attrs":{"color":"#434343","name":"user"}}],"text":"被称为“天然斜坡”的一个结"},{"type":"text","text":"。这种测量在数学上与称为“signature”的已知代数不变量有关，它描述了结上的某些表面。 "}]},{"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":"研究人员在"},{"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":"杂志上写道，新的猜想——这两种类型的不变量是相关的这一发现将在结的数学中开辟新的理论。 "}]},{"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":"在第二种情况下，DeepMind 采用了 1970 年代后期数学家提出的猜想，并帮助揭示了该猜想为何有效。 "}]},{"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 年来，数学家们一直在猜测，可以查看一种特定类型的非常复杂的多维图形，并找出一种特定类型的方程来表示它。但他们还没有完全弄清楚如何做到这一点。现在，DeepMind 通过将图的特定特征与这些方程的预测联系起来，这些方程被称为 Kazhdan-Lusztig (KL) 多项式，以首次提出这项发现的数学家命名。 "}]},{"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":"“我们能够做的是训练一些机器学习模型，这些模型能够非常准确地从图中预测多项式是什么，”Davies说。该团队还分析了 DeepMind 使用图的哪些特征来进行这些预测，这使他们更接近关于两者如何相互映射的一般规则。"}]},{"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":"这些纯数学猜想没有直接的实际应用，但数学家计划在新发现的基础上进一步揭示这些领域中的更多关系。研究团队还希望他们的成功能够鼓励其他数学家将人工智能作为一种新工具。 "}]},{"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":"“我们想要做的第一件事就是更多地进入数学界，希望能鼓励人们使用这种技术，去那里寻找新的和令人兴奋的东西，”Davies说道。"}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"数学和机器学习 "}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#494949","name":"user"}}],"text":"大部分纯数学都在注意数字中的模式或者规律，然后进行艰苦的数值工作来证明这些直觉预感是否代表了真实的关系。当处理多维的复杂方程时，这会变得非常复杂。 "}]},{"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在接受采访时称，“机器学习非常擅长的事情是发现模式和规律。”"}]},{"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":"事实上，与上述案例类似的数学和机器学习的碰撞还有很多。"}]},{"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曾凭借破解围棋等突破登上头条新闻，但其长期关注点一直是科学应用，例如预测蛋白质如何折叠。"}]},{"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，澳大利亚悉尼大学数学家 Geordie Williamson 与 DeepMind 的首席执行官、神经科学家 Demis Hassabis 之间的一次随意对话引发了数学合作的想法。"}]},{"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，这项工作的重点是识别可以使用 DeepMind 技术进行攻击的数学问题。机器学习使计算机能够利用大型数据集进行猜测，例如将监控摄像头图像与照片数据库中的已知面孔进行匹配。但它的答案本质上是概率性的，数学证明需要确定性。"}]},{"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":"参考链接："}]},{"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"}}]}]}]}