[DSC Europe 22] Amazing things that happen with Human-AI synergy - Petar Velickovic
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For the past few years, I have been part of a collaboration with top-tier mathematicians on a challenging project: teaching machines to assist humans with proving difficult theorems and conjecturing new approaches to long-standing open problems. My team has demonstrated that analysing and interpreting the outputs of (graph) neural networks is a concrete solution. Our efforts independently derived novel top-tier mathematical results in areas as diverse as representation theory and knot theory. The significance of our findings was recognised by the journal Nature, where it featured on the cover page. I will share our findings from a personal perspective, with key details of our team’s modelling work.
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[DSC Europe 22] Amazing things that happen with Human-AI synergy - Petar Velickovic
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- 20. Can we discover new structure in pure mathematics with machine learning?
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- 22. “I first believed I was dreaming... But it is absolutely certain and exact that the ratio which exists between the period times of any two planets is precisely the ratio of the 3/2th power of the mean distance.” - Johannes Kepler
- 25. “This paper marks the beginning of a new phase in the use of computers in mathematical research.” “I cannot imagine such a mathematician not using these methods, where available, given that not using them means progressing much more slowly and being unable to analyze very complicated objects and very large datasets.” - Anonymous Reviewers “It feels like Galileo picking up a telescope and being able to gaze deep into the universe of data and see things never detected before.” - Marcus du Sautoy
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- 30. Neural Network Geometric quantities Signature (Algebraic quantity) A relationship was found! Which patterns influenced you to make this decision?
- 33. Conjecture:
- 34. Conjecture:
- 37. Towards combinatorial invariance for Kazhdan-Lusztig polynomials. Blundell, Buesing, Davies, Veličković, Williamson. arXiv: 2111.15161
- 40. Graph Neural Network Polynomial Graph of permutations
- 41. Graph Neural Network Polynomial (65% confidence) Graph of permutations How confident are you in this decision?
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- 46. “In particular, the feeling that extremal reflections seem to play a crucial role [...] is one that I would have expected only from a handful of great world experts in representation theory, and is such a "human" suggestion that it gives me goosebumps.”
- 51. What next?
- 52. Thank you! petarv@deepmind.com | https://petar-v.com In collaboration with Andreea Deac (Mila), Alex Davies, Lars Buesing, Sam Blackwell, Daniel Zheng, Nenad Tomašev, Richard Tanburn, Charles Blundell, Peter Battaglia, András Juhász (Oxford), Marc Lackenby (Oxford), Geordie Williamson (Sydney), Demis Hassabis and Pushmeet Kohli