Artificial intelligence solves a mathematical problem, but the creators don’t know why

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LLMs are powerful neural networks that learn linguistic patterns, including computer code, from vast amounts of text and other data. Although LLM-based chatbots are very popular, they do not generate new knowledge and are prone to ambiguity, resulting in answers that may be smooth and reliable, but are often incorrect.

DeepMind created FunSearch – a system that uses LLM to create solutions to problems in the form of computer programs. FunSearch is paired with a “rater” that automatically rates programs according to their performance. It uses a large language model called Codey that is fine-tuned to match computer code.

FunSearch connects Codey to other systems that discard invalid or illogical answers and return good answers back. The best programs are then combined and returned to LLM for improvement. In this way, the system constantly develops weak programs into more efficient programs that can discover new knowledge.

The researchers decided to test this system on several mathematical problems. One of them was looking for a set of three dots such that they do not form a straight line.

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FunSearch starts with a diagram of the problem in Python. Cody then fills in the blanks and suggests code that would solve the problem. The following algorithm examines and evaluates what Cody finds. The best suggestions are saved and returned to Codey, who tries to complete the program again. The whole process is repeated several million times, which takes several days

As a result, FunSearch was able to come up with code that yielded a correct and previously unknown solution to the problem of finding the largest size of a set of points whose three elements never form a straight line.

The most important thing in all of this is that the solution to the problem is new, so it cannot even appear in the algorithm’s training data. So we can safely assume that AI itself “invented” a new solution to the problem.

The researchers themselves are also surprised. Hussein Fawzi, a researcher at DeepMind, said in an interview with MIT:

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