BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Laurent Lafforgue (Huawei Research Centre France) DTSTART:20240208T130000Z DTEND:20240208T143000Z DTSTAMP:20260423T022720Z UID:bM2L/4 DESCRIPTION:Title: Som e sketches for a topos-theoretic AI\nby Laurent Lafforgue (Huawei Rese arch Centre France) as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nThe purpose of this talk will be to sketc h a partial outline for building a new version of AI based on Grothendieck Topos Theory.\n\n We will first review some key facts which make Grot hendieck toposes a natural interface between logic and topology or geometr y. We will explain in particular in which sense the semantics of any first -order "geometric" theory can be incarnated by a topos\, so by a mathemati cal object to which all intuitions of topological nature still apply.\n\n Based on that\, we will consider anew the problem of designing good de scription languages for any type of real objects which we could want to re present mathematically\, with the aim of processing their representations. This would require the choice of a vocabulary. After such a description vocabulary is chosen\, basic principles of Topos Theory yield a process fo r deriving from instances of the type of real objects under consideration some grammar rules relating the elements of vocabulary. These grammar rul es incarnate an interpretation principle for the type of objects under con sideration. The way they are derived using principles of Topos Theory can be considered as a modellization of inductive reasoning.\n\n Supposing a good description language\, consisting in chosen elements of vocabulary and derived grammar rules\, has been elaborated\, the next and most diffic ult step would be to construct a topos-based process for extracting inform ation. This would be a topos-theoretic version of Deep Learning. We will p ropose a general form for such topos-based processes and describe an indu ced framework which allows at least to think about this problem in a mathe matical way.\n LOCATION:https://researchseminars.org/talk/bM2L/4/ END:VEVENT END:VCALENDAR