This week’s AI tip is about: the amazing achievements of AlphaProof and AlphaGeometry
Today, we’ll analyze how AI is revolutionizing the field of mathematics. On July 25, 2024, DeepMind unveiled a groundbreaking achievement in artificial intelligence (AI) with its models, AlphaProof and AlphaGeometry 2. These systems have reached an unprecedented milestone by solving complex mathematical problems at a level equivalent to a silver medal in the International Mathematical Olympiad (IMO) – a prestigious competition for young mathematicians worldwide.
DeepMind's AlphaProof and AlphaGeometry 2 managed to solve four out of six challenging problems from this year's IMO. This performance earned them a total of 28 points, which is on par with the silver-medal threshold – nearly reaching the gold-medal standard of 29 points. This is the first time an AI solution has achieved such a high standard in the IMO and showcases its potential in advanced mathematical reasoning.
AlphaProof: Revolutionizing Formal Math Reasoning
AlphaProof is a reinforcement-learning based system designed for formal mathematical reasoning. It combines a pre-trained language model with the AlphaZero algorithm, known for mastering complex games like chess and Go. AlphaProof translates informal math problems into the formal language Lean, enabling it to generate and verify solutions through rigorous proof steps. This system, trained on millions of problems across various mathematical topics, proves its capability to tackle challenging problems effectively.
AlphaProof starts by learning from a vast database of existing mathematical theorems, proofs, and problem-solving techniques. This is similar to how a student might study textbooks and attempt problems to understand mathematical concepts.
The system then practices solving mathematical problems on its own, generating millions of its own problems and solutions. AlphaProof uses a technique called reinforcement learning, where it learns from its successes and failures. When it solves a problem correctly, it reinforces that approach. When it fails, it learns to avoid that method in similar situations.
The system incorporates a large language model, which enables AlphaProof to understand and work with mathematical concepts expressed in natural language.
When faced with a new mathematical problem, AlphaProof breaks it down into smaller parts and applies its learned strategies to solve each component. It can generate multiple potential solutions and evaluate which one is most likely to be correct.
As AlphaProof solves more problems, it continues to learn and improve its capabilities, becoming more efficient and tackling increasingly complex mathematical challenges.
AlphaGeometry 2: A Leap in Geometry Problem-Solving
AlphaGeometry 2, an enhanced version of its predecessor, leverages a neuro-symbolic hybrid system. It was trained on significantly more synthetic data, thereby improving its ability to solve intricate geometry problems. The model's symbolic engine is two orders of magnitude faster, allowing it to solve problems with remarkable efficiency. In this year's IMO, AlphaGeometry 2 successfully solved one geometry problem in just 19 seconds.
AlphaGeometry 2 is built on top of Google's Gemini language model. This allows it to understand and interpret geometry problems written in natural language, much like how a human would read and comprehend a math question.
It combines two parts:
a) Neural Language Model: This part quickly generates ideas and suggestions for solving a problem, similar to how a student might brainstorm initial approaches.
b) Symbolic Engine: This part applies strict logical reasoning to work through the problem step-by-step, like a meticulous math teacher checking each stage of a solution.
The system was trained on a vast amount of synthetic data – about 100 million unique geometry problems and solutions.
Unlike some AI systems that produce hard-to-understand outputs, AlphaGeometry 2 generates solutions that humans can read and follow, using classical geometry rules and concepts. As it solves more problems, AlphaGeometry 2 improves its skills, much like how a student gets better with practice.
The success of AlphaProof and AlphaGeometry 2 marks a new frontier in AI-driven mathematical research. These advancements promise to assist mathematicians in exploring new hypotheses, solving long-standing problems, and automating time-consuming proof processes. DeepMind's ongoing research aims to further enhance AI's problem-solving capabilities by integrating natural language reasoning systems for broader applications.
Read more about this topic: https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
