The paper also details DeepMind’s work with professor Marc Lackenby and professor András Juhász at the University of Oxford, which explored knots - one of the fundamental objects of study in topology (i.e., the mathematical study of the properties that are preserved through deformations, twistings, and stretchings). We have seen that machine learning can be used to guide intuition, and eventually to prove new theorems.” It has been a fascinating interdisciplinary journey with the teams at DeepMind and Oxford. “Often finding the right way to think about something, even if imprecise, is more useful than another long calculation. Mathematicians inhabit a world rich in imagination, heuristics, and intuition,” Williamson said in a statement. “One might imagine that the work of a mathematician is dry and formulaic. (A directed graph is a set of vertices connected by edges, with each node having a direction associated with it.) Using machine learning techniques, DeepMind was able to gain confidence that such a relationship does indeed exist and to hypothesize that it might be related to structures known as “broken dihedral intervals” and “external reflections.” With this knowledge, professor Williamson was able to create an algorithm that would solve the combinatorial invariance conjecture, which DeepMind computationally verified across more than 3 million examples. Defying progress for nearly 40 years, the combinatorial invariance conjecture states that a relationship should exist between certain directed graphs and polynomials.
In a paper published in the journal Nature, DeepMind describes how it - alongside professor Geordie Williamson at the University of Sydney - used AI to help discover a new approach to a longstanding conjecture in representation theory. Supervised learning is defined by its use of labeled datasets to train algorithms to classify data, predict outcomes, and more, and it’s been applied to domains including fraud detection, sales forecasting, and inventory optimization. What ostensibly sets DeepMind’s work apart, however, is its detection of the existence of patterns in mathematics with supervised learning - and giving insight into these patterns with attribution techniques from AI. One of the formulas created by the machine can be used to compute the value of a constant called Catalan’s number more efficiently than any human-discovered formula. More recently, a group of researchers from the Technion in Israel and Google presented an automated conjecturing system called the Ramanujan Machine, which came up with original formulas for universal constants that show up in mathematics. (In mathematics, a “proof” refers to a logical argument that tries to show that a statement is true.) GPT-f found new proofs that were accepted into a mathematics community, which the researchers claimed at the time was a historic achievement. In 2020, Microsoft-backed AI research lab OpenAI introduced GPT-f, an automated prover and proof assistant for the Metamath formalization language. Separately, the lab has spotlighted its work in the fields of weather forecasting, materials modeling, and atomic energy computation. Earlier this year, DeepMind cofounder Demis Hassabis announced the launch of Isomorphic Labs, which will use machine learning to identify disease treatments that have thus far eluded researchers. But the sciences remain of principle interest to DeepMind, not least of which because of their commercial applications. DeepMind claims that its AI technology helped to uncover a new formula for a previously-unsolved conjecture, as well as a connection between different areas of mathematics elucidated by studying the structure of knots.ĭeepMind’s experiments with AI run the gamut from systems that can win at StarCraft II and Go to machine learning models for app recommendations and datacenter cooling optimization.
Register HereĭeepMind, the AI research laboratory funded by Google’s parent company, Alphabet, today published the results of a collaboration between it and mathematicians to apply AI toward discovering new insights in areas of mathematics. Head over to our on-demand library to view sessions from VB Transform 2023.
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