British company DeepMind demonstrated the possibilities of the created system created by it ALPHAGEOMETRY artificial intelligence in solving complex geometric problems used on the prestigious international mathematical Olympiad among secondary school students.
According to the results of testing at 30 tasks from past Olympiads, AlphaGeometry coped with 25 of them as part of the allotted time limit. For comparison, the previous record for AI was 10 solved tasks, and the average result of the winner of the Olympiad was 25.9. Thus, in terms of the level of ownership of the geometry, the neural network actually reached the “golden” result of a person.
Earlier, artificial intelligence systems often suffered failure in solving such problems due to the lack of logical reasoning skills and insufficient amount of training data. At the heart of AlphaGeometry is a neuro-symbol approach that combines the strengths of the neural language model for the quick search for promising solutions and symbolic logical conclusion for formal evidence.
AlphaGeometry system training was carried out on the basis of synthetic data without using ready -made solutions from humans. The process included the generation of random geometric diagrams and the analysis of all possible relationships between the elements in these diagrams. Then the system found all possible evidence in each diagram and determined the necessary additional geometric structures for this. As a result, an extensive set of synthetic training data was created, including more than 100 million unique examples of geometric tasks and their solutions.
Since each Olympiad includes six tasks, of which only two are usually devoted to geometry, AlphaGeometry can be applied to only one third of the tasks at this Olympics. Nevertheless, its capabilities in the field of geometry make it the world’s first model of artificial intelligence, capable of overcoming the threshold of bronze medal at the International Mathematical Olympiad in 2000 and 2015.
Deepmind notes that their ultimate goal is the development of mathematical thinking for the next generation. Successful development of olympiad tasks in geometry is an important milestone along this path, which opens the prospects for the application of similar approaches in mathematics and related areas.