Google DeepMind has created an AI system that may solve complex geometry problems. It’s a big step towards machines with more human-like reasoning skills, experts say. 

Geometry, and arithmetic more broadly, have challenged AI researchers for a while. Compared with text-based AI models, there may be significantly less training data for mathematics since it is symbol driven and domain specific, says Thang Wang, a coauthor of the research, which is published in today.

Solving mathematics problems requires logical reasoning, something that the majority current AI models aren’t great at. This demand for reasoning is why mathematics serves as a crucial benchmark to gauge progress in AI intelligence, says Wang.

DeepMind’s program, named AlphaGeometry, combines a language model with a variety 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. Nevertheless, their reasoning lacks the rigor required for mathematical problem-solving. The symbolic engine, however, is predicated purely on formal logic and strict rules, which allows it to guide the language model toward rational decisions. 

These two approaches, accountable for creative considering and logical reasoning respectively, work together to resolve difficult mathematical problems. This closely mimics how humans work through geometry problems, combining their existing understanding with explorative experimentation. 

DeepMind says it tested AlphaGeometry on 30 geometry problems at the identical level of difficulty found on the International Mathematical Olympiad, a contest for top highschool mathematics students. It accomplished 25 inside the deadline. The previous state-of-the-art system, developed by the Chinese mathematician Wen-Tsün Wu in 1978, accomplished only 10.

“This can be a really impressive result,” says Floris van Doorn, a mathematics professor on the University of Bonn, who was not involved within the research. “I expected this to still be multiple years away.”

DeepMind says this technique demonstrates AI’s ability to reason and discover latest mathematical knowledge.

“That is one other example that reinforces how AI may help us advance science and higher understand the underlying processes that determine how the world works,” said Quoc V. Le, a scientist at Google DeepMind and one among the authors of the research, at a press conference.

When presented with a geometry problem, AlphaGeometry first attempts to generate a proof using its symbolic engine, driven by logic. If it cannot achieve this using the symbolic engine alone, the language model adds a brand new point or line to the diagram. This opens up additional possibilities for the symbolic engine to proceed trying to find a proof. This cycle continues, with the language model adding helpful elements and the symbolic engine testing latest proof strategies, until a verifiable solution is found.

To coach AlphaGeometry’s language model, the researchers needed to create their very 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 their properties. These statements were organized into 100 million synthetic proofs to coach the language model.

Roman Yampolskiy, an associate professor of computer science and engineering on the University of Louisville who was not involved within the research, says that AlphaGeometry’s ability shows a big advancement toward more “sophisticated, human-like problem-solving skills in machines.” 

“Beyond mathematics, its implications span across fields that depend on geometric problem-solving, equivalent to computer vision, architecture, and even theoretical physics,” said Yampoliskiy in an email.

Nevertheless, there may be room for improvement. While AlphaGeometry can solve problems present in  “elementary” mathematics, it stays unable to grapple with the kinds of advanced, abstract problems taught at university.

“Mathematicians can be really interested if AI can solve problems which are posed in research mathematics, perhaps by having latest mathematical insights,” said van Doorn.

Wang says the goal is to use the same approach to broader math fields. “Geometry is just an example for us to reveal that we’re on the verge of AI having the ability to do deep reasoning,” he says.