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Researchers at Google have created a mathematical system based on artificial intelligence (AI) that can outperform gold medalists in international geometry competitions.
The system, called AlphaGeometry2 (AG2), is an advanced AI framework that can solve 84% of the geometry problems presented at the International Mathematical Olympiad (IMO). On average, IMO gold medalists solve 81.8% of the Olympiad problems.
Developed by Google DeepMind, it not only performs image matching but also solves problems in creative ways, say the scientists. They outlined their findings in a study uploaded to the arXiv preprint database on February 7.
The company’s announcement comes a month after Microsoft unveiled its rStar-Math AI-powered mathematical reasoning system, which uses small language models (SML) to solve complex equations. Both companies are seeking to become leaders in the field of mathematical AI, as researchers argue that highly advanced systems that can solve math problems can largely mimic other forms of human reasoning. AG2 differs from Microsoft’s rStar-Math in that it focuses on solving complex problems using a hybrid reasoning model, while rStar uses smaller language models to solve a broader range of problems.
Google released the first version of AlphaGeometry in January 2024, and the latest version shows a 30% performance boost over previous versions, the researchers said. The improvements in AG2 focus on mastering geometry, which, unlike calculus and algebra, requires a combination of visual perception and logical thinking to solve difficult problems.
However, experts caution that this stage should not be seen as achieving artificial general intelligence (AGI), where an AI system becomes smarter than a human in multiple areas, not just one, regardless of the training data.
“AlphaGeometry2 is a form of intelligence, but human intelligence goes far beyond that — we invent, not just apply knowledge or create the illusion of thinking,” John Bates, CEO of artificial intelligence company SER Group and a computer science PhD from the University of Cambridge, told Live Science.
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DeepMind’s breakthrough is the successful combination of neural language models and symbolic engines (logic-based systems designed to solve problems using symbols and parameters). The language model suggests geometric constructions, while the symbolic engine verifies them. This combination allows the system to translate the everyday language that a person sees in a geometric problem and transform it into “helper constructions” that the symbolic engine can understand and verify.
The system then works in concert, suggesting new designs if previous ones do not fit. This search for solutions is carried out in parallel, passing information from one side of the system to the other until a solution is found.
AG2 improves on its first version with a neural language model trained on a larger and more diverse dataset, as well as a faster symbolic engine prepared to test a larger number of geometric constructions. The system also has a unique algorithm for searching and finding geometric proofs.
DeepMind researchers noted that AG2's weaknesses include longer processing times and an inability to handle IMO's most complex geometric problems in 3D geometry, nonlinear equations, or problems with variable points (points that change position in a geometric problem) and/or infinite points (problems with an infinite sequence of points and having an infinite number of solutions). Finally, the system cannot explain how it arrived at its solutions in any human-readable language.
DeepMind's research focus for its AG2 system remains on improving mathematical reasoning. However, advances in this area can be applied to a variety of disciplines, including engineering design, automated systems testing, robotics, pharmaceuticals, and more.
Sourse: www.livescience.com
