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Google DeepMind's FunSearch Solves Old Mathematical Mystery

Leveraging great language models to solve age-old puzzles, thanks to this extraordinary achievement

NEWS  AI  December 16, 2023  Reading time: 2 Minute(s)

mdo Max (RS editor)

Google DeepMind has successfully unraveled a longstanding mathematical mystery using an innovative method known as FunSearch. This triumph marks the first instance of a large language model (LLM) contributing to the resolution of a complex scientific problem. The mathematical enigma in question is none other than the notorious cap set problem in pure mathematics, a challenge that has confounded even the most brilliant human mathematicians for ages.

Published in the esteemed peer-reviewed journal Nature, the research team at Google DeepMind detailed their unprecedented discovery. The researchers declared:

"To the best of our knowledge, this shows the first scientific discovery - a new piece of verifiable knowledge about a notorious scientific problem - using an LLM."

At the heart of this groundbreaking methodology is the union of a pre-trained LLM with an automated "evaluator." FunSearch, as explained by Alhussein Fawzi and Bernardino Romera Paredes, research scientists at Google DeepMind, is designed to transcend the limitations of existing LLM-based approaches. The dynamic duo aims to deliver creative solutions in the form of computer code while mitigating the inherent issues of hallucinations and inaccuracies common in LLMs.

Large Language Models, such as GPT-4, have showcased remarkable abilities in tackling complex problems involving quantitative reasoning and generating predictive text. These models possess the capacity to process extensive information and produce responses indicative of a profound understanding across various domains. FunSearch, in its quest for "functions" encoded in computer language, engages in a continuous interplay between the LLM and the evaluator. This intricate dance transforms initial solutions into new knowledge, ultimately fostering innovation in mathematical problem-solving.

Despite the capabilities of LLMs, they are not without their shortcomings. Confabulation or hallucination, wherein the model produces plausible yet incorrect responses, poses challenges in deploying LLMs for scientific discovery. Reliability is paramount in research and problem-solving, making the collaboration with an evaluator essential in FunSearch. Fawzi and Paredes emphasize that FunSearch's applications extend beyond the cap set problem. They successfully utilized the method to discover more effective algorithms for the "bin-packing" problem, an optimization challenge crucial in efficiently allocating items of varying sizes into a limited number of bins or containers, thereby enhancing the efficiency of data centers.




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