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AlphaEvolve Tackles Kissing Problem & More

There is a sports concept called “Kissing number“Somewhat disappointing, has nothing to do with the actual kissing; There are a number of areas that can touch (or “kiss” one field of equal size without crossing it. In one dimension, kissing number is two. In two dimensions, 6 (Think of me New York TimesCertainly composition of the spelling bee). With the growth of the number of dimensions, the answer becomes less clear: for most dimensions that exceed 4, the upper and lower boundaries are known only on the kissing number. Now, the Google DeepMind developed agent called Alphavolve called his contribution to the problem, which increased the minimum kissing number in 11 dimensions from 592 to 593.

This may seem to serve as a gradual improvement in the problem, especially since the upper limit for kissing in 11 dimensions is 868, so the unknown range is still very large. But it represents a new mathematical discovery by artificial intelligence agent, and challenges the idea that large language models are not capable of original scientific contributions.

This is just one example of what alphavolve has accomplished. “We have applied alphavolve through a set of open problems in research mathematics, and we have deliberately selected problems of different parts of mathematics: analysis, collusion, engineering,” says Matej Balog, the DeepMind research world who worked on the project. They found that for 75 percent of the problems, the artificial intelligence model repeated the optimal solution already known. In 20 percent of cases, I found that the new optimum exceeded any known solution. “Every case of this is a new discovery,” says Balge. (In 5 percent of cases, artificial intelligence is close to a solution that was worse than optimal cases known.)

The model also developed a new algorithm to hit the matrix – a process that lies behind a lot of machine learning. There was a previous release of the DeepMind’s Ai, called Alphatensor, who had already overcome the best previously known algorithm, discovered in 1969, to hit 4 of 4 matrices. Alphaevolve found a more general version of that improved algorithm.

DeepMind has made improvements to many practical problems in Google. Google DeepMind

In addition to abstract mathematics, the team also applied its model to the practical problems facing Google every day. Artificial intelligence has also been used to improve the data center coincidence for a 1 percent improvement, to improve the next Google Tensor processing unit design, and to discover improvement in Kernel used in Gemini training, leading to a 1 percent decrease in training time.

“It is very surprising that you can do many different things with one system,” says Alexander Novkov, the chief research scientist in Dibind, who also worked on Alfifel.

How to work alphavolve

The alphavolve can be very general because it can be applied to almost any problem that can be expressed as a symbol, which can be examined by another symbol. The user provides a preliminary stab in the problem – a program that solves the offered problem, whatever optimal level – and the verification program that checks the extent of part of the code with the required standards.

After that, the Great Language Model comes in this case Gemini, with other filters programs to solve the same problem, and each one is tested by verification. From there, Alphaevolve uses a genetic algorithm so that the “most appropriate” solution remains for the proposed solutions and develops to the next generation. This process is repeated until solutions stop improvement.

Plan with four components indicating the codeAlphavolve uses a group of large Gemini models (LLMS) in conjunction with the evaluation code, all of which are a genetic algorithm to improve a symbol. Google DeepMind

“The great language models came, and we started asking ourselves, is it the situation that will only add what is in training data, or can we actually use them to discover something completely new, new algorithms or new knowledge?” Balt says. This research claims, as Balog claims, “If you use large language models in the right way, you can, in a very accurate sense, have something new and correctly new in the form of an algorithm.”

Alphavolve comes from long proportions of DeepMind models, and return to Alphazero, which amazed the world by learning to play Chess, Go, and other games better than any human player without using any human knowledge – only by playing the game and using reinforcement learning to master it. Amnesty International for Solving Other Mathematics Constituent Learning, Alphabab, at the Silver Medical level on the International Mathematics Olympics 2024.

For alphavolve, the team exploded from the tradition of reinforcement learning in favor of the genetic algorithm. “The system is much simpler.” “This actually has consequences, it is much easier to prepare a wide range of problems.”

The future (not completely scary)

The team hopes behind Alphavolve to develop its system in two ways.

First, they want to apply it to a wide range of problems, including those in natural sciences. To follow this goal, they are planning to open an early access program for academics interested in using alphavolve in their research. It may be difficult to adapt the system to the natural sciences, because checking the proposed solutions may be less clear. However, Balge says, “We know that in the natural sciences, there are a lot of simulation devices for different types of problems, after which they can be used in Alphavolve as well. We, in the future, are very interested in expanding a range in this direction.”

Second, they want to improve the system itself, perhaps by associating it with another Deepmind project: the co -teacher of Amnesty International. This artificial intelligence also uses LLM and a genetic algorithm, but it focuses on generating hypotheses in the natural language. “They are developing these ideas and assumptions with a higher level,” says Balge. “Integating this component into alphavolve systems, I think, will allow us to go to higher levels of abstraction.”

These possibilities are exciting, but for some it may also seem threat-for example, the improvement of alphavolve training to train Gemini can be considered as a start from artificial intelligence, which will lead some concern to a fugitive intelligence explosion referred to as uniqueness. Deepmind asserts that this is not their goal, of course. “We are excited to contribute to the progress of artificial intelligence that benefits humanity,” Novikov says.

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2025-05-14 21:33:00

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