In a groundbreaking achievement, Google DeepMind has harnessed the power of a large language model to crack a longstanding, unsolved problem in pure mathematics. Researchers Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Matej Balog, M. Pawan Kumar, Emilien Dupont, Francisco J. R. Ruiz, Jordan S. Ellenberg, Pengming Wang, Omar Fawzi, Pushmeet Kohli, and Alhussein Fawzi, affiliated with Google DeepMind, London, UK, University of Wisconsin-Madison, Madison, Wisconsin, USA, and Université de Lyon (Inria, ENS Lyon, UCBL, LIP), Lyon, France, detail their groundbreaking approach in a paper published in Nature. This marks the first time a large language model has been employed to uncover a solution to a challenging scientific puzzle, yielding new and verifiable information that did not previously exist.
Challenging the Stereotype of Large Language Models:
Large language models (LLMs) are renowned for their capabilities in tasks ranging from quantitative reasoning to natural language understanding. However, these models are not immune to confabulations, where they produce plausible yet incorrect statements. This limitation has hindered their application in scientific discovery until now. The introduction of FunSearch, a tool developed by Google DeepMind, challenges this stereotype and demonstrates that LLMs can indeed make groundbreaking discoveries when utilized strategically.
FunSearch: A Revolutionary Approach to Problem Solving:
FunSearch, short for searching in the function space, is an evolutionary procedure that pairs a pre-trained LLM, named Codey, with a systematic evaluator. This novel approach surpasses existing LLM-based methodologies, pushing the boundaries of what was previously thought possible. By applying FunSearch to the cap set problem in extremal combinatorics, the researchers uncovered new constructions of large cap sets, exceeding the previously known solutions in both finite dimensional and asymptotic cases. This breakthrough represents the first time LLMs have contributed to solving established open problems.
Versatility and Real-World Applications:
FunSearch’s versatility is further demonstrated by its application to the algorithmic problem of online bin packing, where it produced new heuristics that outperform widely used baselines. Unlike traditional computer search approaches, FunSearch seeks programs that describe how to solve a problem rather than just providing solutions. This approach enhances interpretability and facilitates feedback loops between domain experts and FunSearch, enabling the deployment of discovered programs in real-world applications.
FunSearch in the Context of DeepMind’s AI Achievements:
FunSearch adds to a series of discoveries in fundamental mathematics and computer science made by DeepMind using artificial intelligence. Unlike previous tools like AlphaTensor and AlphaDev, which did not use large language models, FunSearch takes a different approach. It combines Codey, a fine-tuned version of Google’s PaLM 2, with other systems to reject incorrect answers and refine good ones.
The FunSearch Process:
The researchers initiated the process by outlining the problem in Python, leaving out the lines specifying how to solve it. FunSearch then leverages Codey to suggest code that fills in the blanks. A second algorithm evaluates and scores Codey’s suggestions, saving the best ones to be fed back into Codey for further refinement. After millions of iterations, FunSearch successfully produced correct and previously unknown solutions to mathematical problems, showcasing its potential in discovering new knowledge.
Conclusion:
Google DeepMind’s FunSearch represents a significant leap forward in the integration of large language models into scientific discovery workflows. By challenging preconceived notions and demonstrating the capacity of LLMs to contribute valuable insights, FunSearch opens up new possibilities for researchers and mathematicians. As the scientific community continues to explore the best ways to leverage these powerful tools, FunSearch stands as a promising avenue for harnessing the potential of large language models in solving complex problems and advancing our understanding of the world.
