AlphaGeometry: Google’s Geometry Genius

AlphaGeometry

Google’s DeepMind team published a new approach to solving complex geometry problems called AlphaGeometry.

This new approach performs really closely to the average level of International Mathematical Olympiad (IMO) gold medalists. IMO gold medalists on average solve ~26 problems within the standard time limit, while AlphaGeometry can solve 25.

How it works

AlphaGeometry uses two major components in its system, a Language Model and a Symbolic Engine.

1. Language models, like ChatGPT or Gemini (Bard), are indeed powerful for generating stuff, but they lack the precision and accuracy in order to produce a working answer that will solve a complex geometry problem.
2. Symbolic engines on the other hand, are more logical and precise, and are able to solve complex geometry problems, but they are too slow as they try to find every fact and process that can solve the problem.

AlphaGeometry combines the best of both worlds.

AlphaGeometry’s approach uses the pros of both components. The symbolic engine solves the problem logically, and instead of directly searching for all possible facts and steps, the language model provides the facts instead.

This significantly reduces the time needed by the symbolic engine to solve the problem. After attempting to solve it, the symbolic engine will send feedback to the language model. The cycle goes on until the problem is solved.

Training

In order to train AlphaGeometry, Google — with their vast resources, generated a billion diagrams and derived all the properties and relationships within them. Then they used a method they call “symbolic deduction and traceback” in order to train AlphaGeometry.

What’s next?

Based on their post, it feels like DeepMind team is looking to develop more advancements in the field of mathematical reasoning and reasoning even beyond math. I guess, we’ll just have to wait and see then?

Open Source Access

If you’re excited to try it out, then great news — Google open-sourced AlphaGeometry! If you want to try it out, the code and the model weights can be accessed from here:

GitHub - google-deepmind/alphageometry

Contribute to google-deepmind/alphageometry development by creating an account on GitHub.

github.com

My Thoughts

This is a pretty interesting approach that works around the limitations of two different things by combining them.

In my brain, I’ll call this a Generator + Solver pattern.

It makes me think about how to apply this kind of approach to other things, like maybe:

1. Software verification by using an LLM with TLA+, or
2. Logical problem solving using LLM + Prolog

I’m sure there are a lot of other fields we can use these on!

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