谷歌DeepMind的科研团队近日推出了一项重大创新——AlphaGeometry人工智能系统，该系统在解决复杂的几何问题上展现了强大的能力，甚至可以应对奥林匹克级别的数学挑战。AlphaGeometry的独特之处在于，它结合了先进的语言模型与一种称为符号引擎的AI技术，该引擎能够运用符号和逻辑规则进行推理。
根据MIT Technology Review的报道，AlphaGeometry在一项包含30个最新奥林匹克级别几何问题的测试中，成功解开了25道难题，这一成绩超越了此前最佳方法的10道问题，显示出其在几何问题解决上的显著优势。这一成就距离国际数学奥林匹克（IMO）金牌得主的平均表现仅一步之遥，预示着AI在解决高难度数学问题上的潜力正在不断攀升。
AlphaGeometry的诞生，不仅在AI领域开辟了新的研究方向，也为教育和数学问题解决提供了革命性的工具。未来，这样的技术有望帮助学生和教育工作者在理解和解决几何问题上找到新的路径，同时也为AI在更广泛的知识领域应用打开了新的可能。
报道原文如下：
Google DeepMind has created an AI system that can solve complex geometry problems. It’s a significant step toward machines with more human-like reasoning skills, experts say.
Google DeepMind 创建了一个可以解决复杂几何问题的 AI 系统。专家表示，这是朝着具有更像人类推理技能的机器迈出的重要一步。
Geometry, and mathematics more broadly, have challenged AI researchers for some time. Compared with text-based AI models, there is significantly less training data for mathematics because it is symbol driven and domain specific, says Thang Luong, a coauthor of the research, which is published in Nature today.
几何学和更广泛的数学问题对 AI 研究人员提出了一段时间的挑战。与基于文本的 AI 模型相比，数学的训练数据要少得多，因为它是符号驱动且特定于领域的，该研究的合著者 Thang Luong 说，该研究今天发表在《自然》杂志上。
Solving mathematics problems requires logical reasoning, something that most current AI models aren’t great at. This demand for reasoning is why mathematics serves as an important benchmark to gauge progress in AI intelligence, says Luong.
解决数学问题需要逻辑推理，而目前的大多数 AI 模型并不擅长这一点。Luong 说，这种对推理的需求就是数学成为衡量 AI 智能进展的重要基准的原因。
DeepMind’s program, named AlphaGeometry, combines a language model with a type of AI called a symbolic engine, which uses symbols and logical rules to make deductions. Language models excel at recognizing patterns and predicting subsequent steps in a process. However, their reasoning lacks the rigor required for mathematical problem-solving. The symbolic engine, on the other hand, is based purely on formal logic and strict rules, which allows it to guide the language model toward rational decisions.
DeepMind 的程序名为 AlphaGeometry，它将一种语言模型与一种称为符号引擎的 AI 相结合，该引擎使用符号和逻辑规则进行推论。语言模型擅长识别模式和预测流程中的后续步骤。然而，他们的推理缺乏解决数学问题所需的严谨性。另一方面，符号引擎纯粹基于形式逻辑和严格的规则，这使得它能够引导语言模型做出理性的决策。
These two approaches, responsible for creative thinking and logical reasoning respectively, work together to solve difficult mathematical problems. This closely mimics how humans work through geometry problems, combining their existing understanding with explorative experimentation.
这两种方法分别负责创造性思维和逻辑推理，共同解决困难的数学问题。这与人类解决几何问题的方式非常相似，将他们现有的理解与探索性实验相结合。
DeepMind says it tested AlphaGeometry on 30 geometry problems at the same level of difficulty found at the International Mathematical Olympiad, a competition for top high school mathematics students. It completed 25 within the time limit. The previous state-of-the-art system, developed by the Chinese mathematician Wen-Tsün Wu in 1978, completed only 10.
DeepMind 表示，它在 30 道几何问题上测试了 AlphaGeometry，其难度与国际数学奥林匹克竞赛（International Mathematical Olympiad）上的难度相同，该竞赛是面向顶尖高中数学生的比赛。它在时限内完成了 25 次。以前最先进的系统由中国数学家 温-Tsün Wu 于 1978 年开发，只完成了 10 个。
“This is a really impressive result,” says Floris van Doorn, a mathematics professor at the University of Bonn, who was not involved in the research. “I expected this to still be multiple years away.”
“这是一个非常令人印象深刻的结果，”波恩大学数学教授弗洛里斯·范·多恩 （Floris van Doorn） 说，他没有参与这项研究。“我预计这还需要很多年的时间。”
DeepMind says this system demonstrates AI’s ability to reason and discover new mathematical knowledge.
DeepMind 表示，该系统展示了 AI 推理和发现新数学知识的能力。
“This is another example that reinforces how AI can help us advance science and better understand the underlying processes that determine how the world works,” said Quoc V. Le, a scientist at Google DeepMind and one of the authors of the research, at a press conference.
“这是另一个例子，它强调了人工智能如何帮助我们推进科学并更好地了解决定世界如何运作的潜在过程，”谷歌 DeepMind 的科学家、该研究的作者之一 Quoc V. Le 在新闻发布会上说。
When presented with a geometry problem, AlphaGeometry first attempts to generate a proof using its symbolic engine, driven by logic. If it cannot do so using the symbolic engine alone, the language model adds a new point or line to the diagram. This opens up additional possibilities for the symbolic engine to continue searching for a proof. This cycle continues, with the language model adding helpful elements and the symbolic engine testing new proof strategies, until a verifiable solution is found.
当遇到几何问题时，AlphaGeometry 首先尝试使用其符号引擎生成证明，由逻辑驱动。如果仅使用符号引擎无法执行此操作，则语言模型将向图中添加新的点或线。这为符号引擎继续搜索证明提供了更多可能性。这个循环继续，语言模型添加有用的元素，符号引擎测试新的证明策略，直到找到可验证的解决方案。
To train AlphaGeometry’s language model, the researchers had to create their own training data to compensate for the scarcity of existing geometric data. They generated nearly half a billion random geometric diagrams and fed them to the symbolic engine. This engine analyzed each diagram and produced statements about its properties. These statements were organized into 100 million synthetic proofs to train the language model.
为了训练 AlphaGeometry 的语言模型，研究人员必须创建自己的训练数据，以弥补现有几何数据的稀缺性。他们生成了近五亿个随机几何图，并将它们提供给符号引擎。该引擎分析每个图表并生成有关其属性的语句。这些语句被组织成 1 亿个合成证明来训练语言模型。
Roman Yampolskiy, an associate professor of computer science and engineering at the University of Louisville who was not involved in the research, says that AlphaGeometry’s ability shows a significant advancement toward more “sophisticated, human-like problem-solving skills in machines.”
路易斯维尔大学计算机科学与工程副教授 Roman Yampolskiy 没有参与这项研究，他说，AlphaGeometry 的能力表明，它朝着更“复杂、类似人类的机器问题解决技能”迈进了一大进步。
“Beyond mathematics, its implications span across fields that rely on geometric problem-solving, such as computer vision, architecture, and even theoretical physics,” said Yampoliskiy in an email.
“除了数学之外，它的影响还跨越了依赖几何问题解决的领域，例如计算机视觉、建筑学，甚至理论物理学，”Yampoliskiy 在一封电子邮件中说。
However, there is room for improvement. While AlphaGeometry can solve problems found in “elementary” mathematics, it remains unable to grapple with the sorts of advanced, abstract problems taught at university.
但是，仍有改进的余地。虽然 AlphaGeometry 可以解决“初等”数学中发现的问题，但它仍然无法解决大学教授的各种高级抽象问题。
“Mathematicians would be really interested if AI can solve problems that are posed in research mathematics, perhaps by having new mathematical insights,” said van Doorn.
“如果人工智能能够解决研究数学中提出的问题，也许通过获得新的数学见解，数学家们会非常感兴趣，”van Doorn 说。
Luong says the goal is to apply a similar approach to broader math fields. “Geometry is just an example for us to demonstrate that we are on the verge of AI being able to do deep reasoning,” he says.
Luong 说，目标是将类似的方法应用于更广泛的数学领域。“几何学只是一个例子，让我们证明我们正处于 AI 能够进行深度推理的边缘，”他说。
英语如下：
News Title: “Google DeepMind’s New Breakthrough: AlphaGeometry AI System Solves Complex Geometry Puzzles at IMO Gold Medal Level”
Keywords: AlphaGeometry, AI in Geometry, Olympic-Level Challenges
News Content:
Google DeepMind’s research team has recently unveiled a major innovation with the AlphaGeometry artificial intelligence system, demonstrating exceptional prowess in tackling intricate geometry problems, including those at an Olympic level. The uniqueness of AlphaGeometry lies in its integration of advanced language models with a symbol engine AI technology, which enables reasoning using symbols and logical rules.
As reported by MIT Technology Review, AlphaGeometry successfully solved 25 out of 30 recent Olympic-level geometry problems in a test, outperforming the previous best method by 15 problems. This accomplishment puts it on par with the average performance of International Mathematical Olympiad (IMO) gold medalists, indicating a significant step forward in AI’s potential for tackling complex mathematical issues.
The emergence of AlphaGeometry not only opens new avenues for research in the AI field but also presents a revolutionary tool for education and geometry problem-solving. In the future, such technology has the potential to assist students and educators in finding novel approaches to understanding and resolving geometric challenges, while also paving the way for AI applications in a broader spectrum of knowledge domains.
【来源】https://www.technologyreview.com/2024/01/17/1086722/google-deepmind-alphageometry/
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