AlphaGeometry: An Olympiad-level AI system for geometry
research
Our artificial intelligence system exceeds the modern approach to engineering problems, and enhances thinking about artificial intelligence in mathematics
The Olympic spirit of ancient Greece reflects, the International Sports Olympiad is a modern square for the world’s brightest mathematicians in the world. Competition not only shows young talents, but also appeared as a test of testing for advanced artificial intelligence systems in mathematics and thinking.
In a paper published today in natureWe offer alphageometry measurement, a system that solves complex engineering problems at a level that approaches the medal from the Human Olympics – an end in the performance of artificial intelligence. In the measurement test for 30 Olympiad engineering problems, Alphageometry 25 resolved within the time limit of the standard of the Olympics. For comparison, the previous system solved the latest 10 -style of these engineering problems, and the average human gold medal solved 25.9 problems.
In our set of standards of 30 engineering problems from the IMO-AG-30, the Olympics is collected from 2000 to 2022, and the Alphageometry 25 solution is under the time limits of the competition. This is close to the average degree of human gold medals in these same problems. The previous approach was resolved in the latest condition, known as “Wu’a method”, 10.
Artificial intelligence systems often fight with complex problems in engineering and mathematics due to a lack of thinking skills and training data. The alphageometry system combines the predictive power of the nervous language model and a limited grammar engine, which works alongside to find solutions. By developing a way to create a wide range of artificial training data – 100 million unique examples – we can train eternal measurement without any human demonstrations, and the activity of the data bottle.
With alphageometry, we explain AI’s increasing ability to think logically, discover and verify new knowledge. The solution to engineering problems at the level of the Olympics is an important milestone in developing deep sporting thinking on the path towards the most advanced and public artificial intelligence systems. We open the source to the alphageometry code and model, and we hope that it is with tools and other curricula in generating and training artificial data, helps to open new possibilities through mathematics, science and AI.
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It is logical for me now that artificial intelligence researchers try to their hands on IMO engineering problems first because finding solutions to them works a little like chess, meaning that we have a small number of reasonable moves in each step. But I still find it amazing to make them work. It is an impressive achievement.
NGô Bảo Châu, holding the medal and gold medal IMO
Eternal analogy adopts a nervous approach
Alphageometry is a coherent nervous system consisting of a nerve language model and a symbolic discount engine, which works together to find evidence of complex engineering theories. Similar to the idea of ”thinking, fast and slow”, one system provides quick “intuitive” ideas, the other, the most deliberate, and the rational decisions.
Since the language models excel in identifying patterns and public relations in data, they can quickly predict useful constructions, but they often lack the ability to think accurately or explain their decisions. Symbolic discount engines, on the other hand, depend on the official logic and use clear rules to reach the conclusions. It is rational and explained, but it can be “slow” and not flexible – especially when dealing with big and complex problems on their own.
The alphageometry language model directs its symbolic discount engine towards possible solutions to engineering problems. Olympiad engineering problems depend on the graphs that need new engineering structures to add before they are solved, such as points, lines or circles. The alphageometry language model predicts new constructions that will be more useful to add, than an endless number of possibilities. These clues help fill the gaps and allow the symbolic engine to make more discounts on the graph and close the solution.
The alphageometry is a simple problem solution: Given the problem scheme and its theory (left) buildings, alphageometry (middle) first uses its symbolic engine to infer new data about the scheme until the solution is found or new data is exhausted. If a solution is not found, one of the (blue) alphageometry language (blue) that is likely to be useful (blue), adds to the opening of new paths to deduct the symbolic engine. This episode continues until a solution (right) is found. In this example, only one building is needed.
Alphageometry solve the Olympics problem: the problem 3 of the 2015 International Mathematics Olympics (left) and an intense version of alphageometry solution (right). Blue items are added. The alphageometry solution contains 109 logical steps.
Generating 100 million examples of artificial data
Engineering depends on understanding the space, distance, shape and relative positions, which are essential for art, architecture, engineering and many other areas. Humans can learn engineering with pen and paper, study charts and use current knowledge to detect new, more sophisticated engineering properties and relationships. The artificial data data approach simulates this wide -scale building process, allowing us to train the vascular measurement from the zero point, without any human demonstrations.
Using a very parallel computing, the system began to generate a billion random plans from engineering organisms and comprehensively derived all relations between points and lines in each scheme. Alphageometry found all the evidence in each graph, then worked back to see what additional structures, if any, to reach these proofs. We call this process “symbolic discount and tracking”.
The visual representations of the artificial data created by eternal measurement
This gathering the mass data was nominated to exclude similar examples, which led to the final training data set that includes 100 million unique example of various difficulty, including nine million additional structures. With many examples of how these installations established evidence, the alphageometry language model is able to make good suggestions for new structures when submitted with Olympiad engineering problems.
Pioneering mathematical thinking with artificial intelligence
The solution to each Olympics problem is examined by the alphageometry measurement and verified by the computer. We also compared its results with previous artificial intelligence methods, and with human performance in the Olympics. In addition, Ivan Chen, a mathematics coach and a former Olympiad area, evaluated a selection of alphageometry solutions for us.
Chen said: “The Alphageometry product is impressive because it can be verified and clean. Amnesty International solutions to the problems of competition based on proof were sometimes turbulent or Mays (although the products are sometimes correct and need human examination). Driving parasol pages are not.
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Alphageometry is impressive because it can be verified and clean … it uses classic engineering rules with similar corners and triangles as students do.
Ivan Chen, mathematics coach and the Olympics gold medal
Since each Olympiad has six problems, two of which usually do not focus on engineering, eternal measurement can only be applied to a third of the problems in a specific Olympics. However, its engineering ability alone makes it the first Amnesty International model in the world capable of passing the bronze medal threshold in IMO in 2000 and 2015.
In engineering, our system is approaching the golden doctor’s standard at the International Maritime Organization, but we are watching a larger prize: progressing in artificial intelligence systems from the next generation. Given the broader capabilities to train artificial intelligence systems than zero with artificial data on a large scale, this approach can be how artificial intelligence systems in the future discover new knowledge, in mathematics and beyond.
Alphageometry depends on the work of Google DeepMind and Google Research for pioneering mathematical thinking with artificial intelligence – from exploring the beauty of pure mathematics to solving mathematical and scientific problems in language models. Recently, we presented Funsearch, which made the first discoveries in open problems in mathematical sciences using large language models.
Our long -term goal remains to build artificial intelligence systems that can be circulated through sports fields, and developing the solution to advanced problems and logic on which general artificial intelligence systems depend, while expanding the scope of human knowledge.
Thanks and appreciation
This project is a cooperation between the Google DeepMind team and the New York University Science Department. Among the authors of this work are Trieu Trinh, Yuhuai Wu, Quoc LE, HE and Thang Luong. We thank RIF A. Saurous, Denny Zhou, Christian Szenedy, Delesley Hutchins, Thomas Kipf, Hieu PHAM, Petar Veličković, Edward Lockhart, Deebidatta Dwibedi, Kyunghyun Cho, Lerrel Pinto, Alfredo Canziani, to help and support them. We would also like to thank Google DeepMind Leadership for support, especially Ed Chi, Korai Cavoogo, Pushmeet Kohli, and Demis Hassabis.
2024-01-17 16:00:00
