What is DeepMind AlphaGeometry?

We are in an exciting time for AI. Following the release of ChatGPT in late 2022, the AI industry has embarked on a journey that is rapidly changing how we live and work. Big Tech companies, such as Google, Microsoft, Meta, Apple, and Amazon, are playing a pivotal role in the ongoing AI revolution. Thanks to their enormous budgets, computing resources, and talent, these companies are constantly advancing cutting-edge research in their efforts to lead the AI race.

So far, probably the most significant AI breakthrough in 2024, other than OpenAI’s Sora, is Deepmind’s AlphaGeometry. Designed by DeepMind, Google’s branch responsible for developing general-purpose AI, AlphaGeometry is an innovative AI system that combines a neural language model and a symbolic deduction engine to solve complex geometry problems. The model, portrayed as an Olympiad-level AI system for geometry, represents an important contribution to the long-term goal of creating advanced AI systems that can generalize across mathematical fields.

In this article, we will introduce you to AlphaGeometry. We will analyze the motivations behind AlphaGeometry, how it works, and the most relevant use cases of AlphaGeometry. We will end up with some clues on the implications of AlphaGeometry for the future of AI research.

What is AlphaGeometry?

AlphaGeometry is a next-generation AI system built to solve complex geometry. The system adopts a novel design approach to logical reasoning that allows it to surpass state-of-the-art results in geometry-related tasks.

Thus, as opposed to AI tools, like OpenAI’s ChatGPT and Google’s Gemini, which can be considered general-purpose AI models, AlphaGeometry is a domain-specific AI model.

The code and the model, as well as the methodologies used in synthetic data generation and training (see next section), are released under an open-source license.

To test the performance of AlphaGeometry, Google Deepmind’s researchers prepared a benchmarking set of geometry problems compiled from successive editions of the International Mathematical Olympiads (IMO) between 2000 and 2022.

The IMO is an annual championship that gathers brilliant high-school students from all countries to solve mathematical problems, including in the field of geometry.

AlphaGeometry was able to solve 25 out of 30 selected questions under competition time limits, surpassing state-of-the-art results from previous AI systems and approaching the average score of human gold medallists, as shown in the following image. The design and results of the benchmarking test can be found in a dedicated paper published in Nature.

Source: Google

How Does AlphaGeometry Work?

The key to AlphaGeometry's success lies in its hybrid approach to (geometric) problem-solving. While modern large language models (LLMs), like OpenAI’s ChatGPT and Google’s Gemini, are good at detecting patterns, they cannot often reason precisely.

Google DeepMind tries to overcome this limitation by combining a neural language model with a symbolic deduction engine specialized in algebraic and geometric reasoning. The neural language model helps in providing fast, intuitive ideas and solutions. By contrast, the symbolic model, based on formal logic statements that can be easily explained and verified, provides more deliberate, rational decisions based on the preliminary ideas returned by the first model.

To better know how AlphaGeometry works, we first must understand the nature of IMO geometry problems. These problems are based on diagrams that need new geometric constructs, such as points, lines, and circles, to be added before they can be solved.

When AlphaGeometry encounters one of these problems, it employs its language model in the first place to predict which new constructs would be most useful to add from an infinite number of possibilities. These clues help fill in the gaps and allow the symbolic engine to make further deductions about the diagram and close in on the solution. The whole process is depicted below:

Source: Google

This innovative dual approach allows AlphaGeometry not only to predict useful constructs but also to explain and validate its decisions.

Leveraging synthetic data

One of the most significant challenges during the development of AlphaGeometry was the training process. Translating the properties and relationships within geometric objects (i.e., space, distance, shape, relative positives) to a machine-readable format is a complex undertaking, for geometry-specific programming languages are narrowly defined and struggle to capture human proofs that are derived using tools beyond the scope of geometry, such as complex numbers.

This situation creates a data bottleneck that hinders the use of machine learning techniques for geometry purposes.

To overcome this limitation, Google DeepMind researchers developed a novel method that leverages parallel computing techniques to generate a vast pool of synthetic training data –comprising 100 million unique diagrams of geometric objects. Check out our separate article to discover what synthetic data is.

Such training data was then used by the model to learn all the properties and relationships, as well as the geometric theorem and their associated proofs. All without the need for human demonstrations. The synthetic data generation process is illustrated in the following image:

Source: Nature

The wide availability of synthetic data allows AlphaGeometry’s language model to make good suggestions for new constructs when encountering new geometry problems.

What does AlphaGeometry Mean for the Future of AI Research?

AlphaGeometry is a research model specifically designed for solving abstract geometric problems. Despite its unprecedented performance, AlphaGeometry is solely trained to tackle IMO questions (and only part of it, for IMO tests also comprise problems from other domains of mathematics, such as algebra, number theory, and combinatorics).

AlphaGeometry is not aimed at making contributions in disciplines where geometry plays a fundamental role, such as architecture, engineering, and art. Rather, it’s a promising example of how neural language and symbolic models can be combined to enhance reasoning capabilities in future AI systems.

The development of novel approaches to generate large-scale synthetic data, as demonstrated during the training of AlphaGeometry, is bringing us close to this new frontier of AI research.

The ultimate goal is to build a new generation of AI systems that can surpass the limitations and shortcomings of current large language models. This will be possible by equipping new models with advanced reasoning and problem-solving skills that can help generalize knowledge across mathematical fields and beyond.

Learn More

We hope you enjoyed this article about DeeMind AlphaGeometry. We are just at the beginning of the AI revolution that is rapidly changing our world. The stakes are high, so staying in tune with the latest developments is important.

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