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Google’s leading AI research lab, an AI system built by Google Dipmind, seems to have surpassed the average gold medal to solve the geometry problem in an international mathematics competition.
The system, known as Alfazometry 2, is an advanced version of a system, alphazometry, That dipmind published last JanuaryThe A Newly published studyDeeply researchers behind Alfiaometry 2 have claimed that the international mathematical Olympiad (IMO) in mathematical competition for their AI high school may solve 84% of all geometry problems in the last 25 years.
Why Dipmind cares about a high school level mathematics competition? Okay, the lab thinks that the key to AI is the key to the challenging geometry problem is to discover new ways to solve – especially Euclidean geometry is the problemThe
Prove mathematical theorem, or logically explaining why a theorem (such as the Pythagorian theorem) is true, because both are the ability to choose from logic and potential steps towards solution. The skills to solve this problem — if the right of the Depmind-if the general public of the future becomes a useful element of the AI models.
In fact, this summer, Dipmind has demo a system that connects Alphymetry 2 to an AI model for formal mathematics to solve four problems of 2024 IMOs. In addition to geometry problems, this type of method can expand in mathematics and other fields of science – for example, to help in complicating complex engineering.
Alfazometry 2 has a number of main elements, including a language model of the Google Jemi family of the AI model and a “symbolic engine”. The Gemini model helps the symbolic engine, which uses mathematical rules to determine the solutions to the problem, reaching potential evidence for the given geometry epitome.
Olympiad geometry problems are created based on the image that needs to be added “Constructs” before solving, such as points, lines or circles. The Gemini Model of Alfazometry 2 predicts which one can be effective in adding an image, which refers to the engine discount.
Basically, the Gemini Model of Alfazometry 2 suggests steps and construction in a formal mathematical language in the engine, which follows specific rules – examine these steps for logical continuity. A search allows algorithm alphazometry 2 to conduct multiple searches in parallelly and allow us to save useful searches probably to a common sense base.
Alfazometry 2 consists of a problem as a “solution” when it comes to a proof that combines the advise of the Gemini model with the familiar principles of the symbolic engine.
Due to the complexity of translating proofs, AI is lacking in the format of the AI, lacking usable geometry training data. Thus, Dipmind has created its own synthetic data for the language model of Alfazometry 2, which creates more than 300 million theorem and various complexities.
The Dipmined Team has selected 45 geometry problems from the IMO competition in the last 25 years (from 2000 to 2024), including linar equations and equations that need to run geometric objects around an aircraft. Then they “translate” to a larger set of 50 problems. (For technical reasons, some problems were to be divided into two)
According to the paper, alphazometry 2 has solved 42 out of 50 problems, the average gold medal score clears 40.9.
Grant, there are restrictions. A technical comedy prevents alphazometry 2 in the variable number points, nonliner equations and discrimination to solve problems. And alphazometry is not 2 Technically The first AI system to reach the gold-plated-level performance in geometry, though it first achieved with the problem set of this size.
Alfazometry 2 worsened in another set of more strict IMO problems. For an additional challenge, the Dipmined Team chose the problems – a total of 29 – which mathematics experts were nominated for the IMO exam, but it has not yet appeared in any competition. Alfazometry 2 can only solve 20 solutions.
Nevertheless, the results of the study can increase the debate on whether the AI systems should be created on symbol manipulates-it is the symbols that represent knowledge using the rules-or obviously neural networks like the brain.
Alfazometry 2 adopts a hybrid method: Its Gemini model has a neural network architecture, while its symbolic engine is rules-based.
The proponents of neural network strategies argue that from the recognition of speech to the image generation, the intelligent behavior can arise from nothing but computing a lot of data and computing. Opposition to the symbolic systems, which define the sets of symbol-manipulating rules dedicated to specific tasks, such as editing a line in the Word Processor software, tries to solve the work through statistical assumptions and try to learn from examples.
Neural networks are the basis of such strong AI systems OpenAI’s OR 1 “Argument” modelThe However, supporters of the symbolic AI have claimed that they are not the end of all time; These supporters have argued that symbolic AI can be in a better position to “explain” the cause of their way to the world, in complex situations and how they reached the answer.
“This type of criterion is interesting to look at the difference between spectacular progress and in the meantime, the language models, including ‘rational’, are fighting some of the most common Communication problems, including ‘rational’,” Specialist University in AI tells Techchen, a specialist university computer science professor. “I don’t think it’s all smoke and mirrors, but it depicts that we still do not know what to expect from the next system. These systems can probably be very effective, so we need to understand them urgently and they make the risks better. “
Alfazometry 2 probably proves that the two methods – symbol manufacturers and neural networks – – Joint Generalizable AI’s commitment to the promised path to proceed. In fact, according to the dipmind paper, the 1, which has a neural network architecture, could not solve any IMO problem that was able to answer Alfazometry 2.
It may not be forever. In the study, the Dipmind team said that it was initial evidence that the model of Alfazometry 2 was able to create a partial solution to the problem without the assistance of the symbolic engine.
“[The] The results that support large -language models may be self -sufficient depending on external equipment [like symbolic engines]”The Dipmind team wrote on paper,” but up to [model] Speed is improved and Hallucination Have been fully resolved, tools for math applications will be necessary ””
