Google DeepMind has harnessed the power of a groundbreaking large language model to crack a renowned unsolved problem in the realm of pure mathematics. This groundbreaking achievement signifies the inaugural instance where such a sophisticated language model has been employed to unravel a perplexing scientific enigma, resulting in the creation of verifiable and invaluable new information that was previously undiscovered. Pushmeet Kohli, the coauthor and vice president of research at Google DeepMind, emphasizes that the breakthrough goes beyond the model’s training data, representing a significant leap in computational discovery.
The innovative tool introduced by Google DeepMind, known as FunSearch, challenges the prevailing notion that large language models are predisposed to fabricate content rather than generating new facts. FunSearch dispels this skepticism, showcasing that these models can indeed make discoveries under precise conditions, provided the majority of their output is judiciously filtered out.
In contrast to DeepMind’s earlier tools, such as AlphaTensor and AlphaDev, which achieved milestones in fundamental math and computer science without leveraging large language models, FunSearch adopts a distinctive approach. It combines a large language model named Codey—a variant of Google’s PaLM 2 fine-tuned on computer code—with supplementary systems designed to eliminate incorrect or nonsensical answers. This multi-step process involves Codey suggesting code to solve a given problem, subject to subsequent scrutiny and scoring by a secondary algorithm. The most promising suggestions are retained and fed back into Codey for further refinement, creating a cyclical process of improvement.
The research team, led by Alhussein Fawzi, a research scientist at Google DeepMind, initiated the project by delineating the problem in Python, a widely-used programming language, intentionally omitting the lines that dictate how to solve it. This is where FunSearch comes into play, filling in the missing code and proposing solutions to the problem. After undergoing millions of iterations and repetitions, FunSearch triumphantly generated a correct and previously unknown solution to the cap set problem, an esoteric yet pivotal mathematical challenge.
Esteemed mathematician Terence Tao at the University of California, Los Angeles, commends FunSearch’s capabilities as a “promising paradigm,” recognizing its potential to harness the formidable power of large language models. Notably, unlike its predecessor AlphaTensor, FunSearch’s distinctive advantage lies in its adaptability to tackle a wide array of problems, as it produces code—a recipe for the solution—rather than the solution itself.
To validate its versatility, the researchers subjected FunSearch to the bin packing problem, a complex mathematical challenge in computer science. Impressively, FunSearch not only provided a solution but outpaced human-devised methods, underscoring its potential in solving diverse and intricate problems. As mathematicians continue to explore ways to integrate large language models into their research workflow, FunSearch emerges as a promising avenue, offering a unique and potent approach to computational problem-solving.
