BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexei Vernitski (Essex) DTSTART:20220701T130000Z DTEND:20220701T140000Z DTSTAMP:20260423T003246Z UID:CompAlg/2 DESCRIPTION:Title: Using machine learning to solve mathematical problems and to search for ex amples and counterexamples in pure maths research\nby Alexei Vernitski (Essex) as part of Machine Learning Seminar\n\n\nAbstract\nOur recent res earch can be generally described as applying state-of-the-art technologies of machine learning to suitable mathematical problems. As to machine lear ning\, we use both reinforcement learning and supervised learning (underpi nned by deep learning). As to mathematical problems\, we mostly concentrat e on knot theory\, for two reasons\; firstly\, we have a positive experien ce of applying another kind of artificial intelligence (automated reasonin g) to knot theory\; secondly\, examples and counter-examples in knot theor y are finite and\, typically\, not very large\, so they are convenient for the computer to work with.\n\nHere are some successful examples of our re cent work\, which I plan to talk about.\n\n1. Some recent studies used mac hine learning to untangle knots using Reidemeister moves\, but they do not describe in detail how they implemented untangling on the computer. We in vested effort into implementing untangling in one clearly defined scenario \, and were successful\, and made our computer code publicly available.\n2 . We found counterexamples showing that some recent publications claiming to give new descriptions of realisable Gauss diagrams contain an error. We trained several machine learning agents to recognise realisable Gauss dia grams and noticed that they fail to recognise correctly the same counterex amples which human mathematicians failed to spot.\n3. One problem related to (and "almost" equivalent to) recognising the trivial knot is colouring the knot diagram by elements of algebraic structures called quandles (I wi ll define them). We considered\, for some types of knot diagrams (includin g petal diagrams)\, how supervised learning copes with this problem.\n LOCATION:https://researchseminars.org/talk/CompAlg/2/ END:VEVENT END:VCALENDAR