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The systems artificial intelligence (AI) often have difficulty with complex math approaches due to a lack of reasoning and training data. Google now presents a new model capable of solving geometry problems at the same level as the winners of a mathematical olympiad.
The system of Google DeepMind is called AlphaGeometry and its description is published this Wednesday in the journal Nature. Those responsible assure that the new model represents a “great advance” in AI performance.
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“With AlphaGeometry we demonstrate the growing AI’s ability to reason logically and discover and verify new knowledge. Solving Olympic-level geometry problems is a milestone in the development of a deep mathematical reasoningon the path towards more advanced and general AI systems”, summarize those responsible.
The system is capable of solving complex geometry problems at a level similar to that of a human gold medalist at the International Mathematics Olympiad. In a benchmark test of 30 geometry problems from this competition, AlphaGeometry solved 25 within the standard time limit set.
According to DeepMind, the most advanced previous system solved 10 of these geometry problems and an average gold medal human solved 25.9 problems.
Trieu Trinh and his team present in this article an alternative method of theorem proving that avoids the need for human proofs.
Their system uses a neural language model that is trained by synthesizing millions of theorems and proofs of different levels of complexity. This approach, combined with a symbolic deduction engine (which can search through a large number of branch points in difficult problems), allows AlphaGeometry learn and solve complex problems without direct human intervention.
Trieu Trinh and Thang Luong, both from DeepMind, recall in a note that the International Mathematics Olympiad not only serves as a showcase for young talents, but has also become a testing ground for advanced artificial intelligence systems in mathematics and reasoning. .
Geometry is based on the understanding of space, distance, shape and relative positions; and humans can learn it with pencil and paper, examining diagrams and using existing knowledge to discover new and more sophisticated geometric properties and relationships.
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“Our synthetic data generation method emulates this process of knowledge construction at scale, allowing AlphaGeometry to be trained from scratch,” the researchers say.
The system began by generating 500 million random diagrams of geometric objects and exhaustively deduced all the relationships between the points and lines in each diagram.
That huge data set was filtered to exclude similar examples, resulting in a final training data set of 100 million unique examples of varying difficulty.
AlphaGeometry’s code is open and researchers hope that, along with other tools and approaches in synthetic data generation and training, it will help open up new possibilities in mathematics, science and AI.
Evan Chen, a mathematical Olympiad gold medalist who evaluated a series of theorems for DeepMind, concludes that the AlphaGeometry results “They are impressive because they are verifiable and clean”.
Currently, AlphaGeometry is limited to specific forms of geometry, but the authors suggest that the method can be applied to other mathematical fields.
Source: Elcomercio
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