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Wednesday, December 08, 2021

Math of Knots and Machine Learning

Big interest in the natural and useful topology of knots

UK AI Helps Untangle the Math of Knots

Nature. Davide Castelvecchi, December 1, 2021

Researchers at U.K.-based artificial intelligence (AI) laboratory DeepMind worked with mathematicians to use AI to identify patterns that humans had overlooked in a theory of knots and the study of symmetry, via machine learning. Knot theorists determined the saliency maps technique would be most useful in finding a pattern that linked two knot properties, which led to a formula that appeared correct in all testable cases. The University of Oxford's Marc Lackenby and András Juhász devised a proof that the formula applied to a large class of knots. Geordie Williamson and colleagues at Australia's University of Sydney used AI to discover a technique for guessing precisely which graphs and polynomials originated from the same symmetries. DeepMind's Alex Davies said the mathematicians had to customize AI techniques to the mathematical problems. Said Juhász, "Any area of mathematics where sufficiently large datasets can be generated could benefit from this approach."

Full Article  https://www.nature.com/articles/d41586-021-03593-1

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