Artificial intelligence surpasses humans again

Pushmeet Kohli, head of AI for Science at Google DeepMind, said in an interview with the Guardian, “When we started the project, there was really no indication that the AI would produce something new,” and added: “As far as we know, this is the first time a major scientific discovery has been made with a large language model.”

According to engineers in Google’s AI department, a chatbot now appears to be one of the leading minds in the field of combinatorics, which can be a grueling and frustrating area of mathematics. While it was initially intended to be just a proof of concept, the real breakthrough was a new algorithm the team called FunSearch. However, the AI did not settle for being a proof of concept and continued on, finding solutions to unsolved problems that were far better than any previously found.

Alhussein Fawzi and Bernardino Romera Paredes wrote in a blog post for DeepMind, “FunSearch has discovered new solutions for the cap set problem, a long-standing open problem in mathematics,” and continued: “The problem consisted of finding the largest set of points (called a cap set) in a high-dimensional grid that does not contain three points on a line.”

At this point, an example might be helpful. In the game Set, 12 cards are dealt, each marked with a unique combination of shape, color, shading, and number. Players then aim to find a set of three cards where each of these features is either completely different or the same as the others. For example, a group consisting of one card with a red diamond, a second card with two blue striped diamonds, and a third with three green empty diamonds forms a set because they all have diamonds. However, other than being diamonds, the colors, shadings, and numbers on each are different.

If no one can find one of these sets with the 12 cards on the table, which is certainly possible, then more cards are laid out until a set is found. Mathematicians decided to ask how many cards could be dealt before a set appears, or in mathematical terms, what the maximum size of a set in Z34 is.

In fact, this specific problem was solved in 1971, and the answer was 20. However, things get much more difficult when larger sets are involved. As is depressingly common in combinatorics, the number of potential solutions increases incredibly fast, and just by going up to eight features, you have to deal with combinations like 31,600 potential “cards.”

Unsurprisingly, humans have not yet been able to solve this problem. Perhaps even more important than the question of why we would try such a thing is that it is not even clear how we would try. Mathematicians have not even been able to reach a consensus on the best way to attempt the cap set problem for n = 8, let alone find the answer.

Therefore, it becomes a very remarkable achievement that Google’s AI appears to have solved this problem with a cap set of 512 dimensions, which was previously unknown.

“This is the first time that a system based on large language models has shown it can go beyond what is known by mathematicians and computer scientists,” Kohli said in an interview with Nature, adding: “This is not only new, but also more effective than anything that exists today.”

Although the results of DeepMind’s discoveries are incredible, mathematicians probably do not need to worry about their job security just yet. For now, FunSearch is limited to problems that meet a specific set of criteria. For it to be able to solve problems, they must be able to be evaluated and scored easily and efficiently, and it must follow the same “fill-in-the-missing-code” trick that the team used for the cap set and bin packing problems. Researchers note, for example, that generating proofs would currently be too difficult for AI because you cannot grade such things in a way that makes sense to a computer.

Nevertheless, the fact that a puzzle that has long been without an answer has been solved is another example of the power and capabilities of artificial intelligence.

The study was published in the journal Nature.

News Source: 12punto