The concept of the ‘kissing number’ encompasses the maximum number of spheres that can simultaneously contact a single sphere of similar size without overlapping. In one dimension, the kissing number is two, increasing to six in two dimensions. As dimensions increase, pinpointing the kissing number becomes increasingly intricate, with known limits for most dimensions beyond four. Recently, Google’s DeepMind introduced an AI agent, AlphaEvolve, which has raised the lower bound of the kissing number in eleven dimensions from 592 to 593.
Although this correction may appear minimal when compared to an upper limit of 868, it represents a significant advancement in mathematics by an AI model, challenging the perception that large language models lack originality in scientific contributions. AlphaEvolve has also tackled various mathematical problems, mirroring known optimal solutions in 75 percent of cases and discovering new optimal solutions in 20 percent. Such discoveries are noteworthy, even as the model’s efficiency diminished in 5 percent of instances.
Moreover, AlphaEvolve has devised a new algorithm for matrix multiplication essential for many machine learning applications, building upon earlier advances made by AlphaTensor. The development team has also applied their model to enhance Google’s practical operations, achieving incremental improvements in data center efficiencies, and optimizations related to the tensor processing unit. Alexander Novikov, a senior research scientist, noted the impressive versatility of a single system managing such varied tasks.
The adaptability of AlphaEvolve arises from its ability to solve nearly any problem expressed as code, tested by a verification segment. With an initial, albeit suboptimal, solution proposed, Gemini, a large language model, offers alternative programs for examination. The approach utilizes a genetic algorithm to evolve the best solutions through successive iterations, and demonstrates the capacity of large language models to develop genuinely innovative algorithms. While such advancements raise concerns over the rapid enhancement of AI systems, the DeepMind team asserts their commitment to utilizing AI for the betterment of humanity.
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