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SUMMARY:CayleyPy-Holography: Mathematical and String Theory Methods for AI
DTSTART:20260716T120000Z
DTEND:20260716T130000Z
DTSTAMP:20260727T011200Z
UID:indico-event-16953@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Alexander Chervov (Institute for Theoretical and Exp
 erimental Physics\, Moscow)\n\nWe present a new approach to one of the cen
 tral problems in AI: the construction of embeddings (latent representation
 s) inspired by ideas from holographic string dualities\, in particular the
  AdS/CFT correspondence. Our central conjecture is that\, for a broad cla
 ss of graphs\, there exists a dual polygon together with a map ("holograp
 hy") that sends graph vertices to lattice paths inside the polygon in such
  a way that graph distances are well approximated by the areas enclosed be
 tween the corresponding lattice paths. This can be viewed as a combinatori
 al analogue of the "Complexity = Volume" principle proposed by L. Susskin
 d and collaborators in 2014 in the context of AdS/CFT\, and later explored
  for Cayley graphs by H. Lin\, D. Melnikov\, and others. From the perspec
 tive of AI\, this suggests that effective embeddings of graph vertices may
  be realized as their holographic images. Understanding such holographic r
 epresentations for natural language and other AI systems could provide a n
 ew mathematical framework for constructing more powerful latent representa
 tions and\, ultimately\, more effective AI architectures. As mathematical
  applications of the conjecture\, we explain how it naturally leads to var
 iants of the famous Babai conjecture predicting an n2 upper bound on the d
 iameters of Sn Cayley graphs and conjecture of quasi-polynomiality of the 
 diameters and word metrics. We also discuss connections with limit shapes 
 of Young diagrams\, integrable systems\, and the description of conformal 
 dimensions in conformal field theories arising as large-size limits of gra
 ph families. The talk is based on the CayleyPy series of papers\, in part
 icular CayleyPy-4: AI-Holography. Towards analogs of holographic string du
 alities for AI tasks (https://arxiv.org/abs/2603.22195).\nThe talk will be
  accessible to mathematicians. No prior background in artificial intellige
 nce or string theory will be assumed.\n \n========\nPour être informé d
 es prochains séminaires vous pouvez vous abonner à la liste de diffusion
  en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subs
 cribe seminaire_mathematique PRENOM NOM"(indiquez vos propres prénom et n
 om) et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/ev
 ent/16953/
LOCATION:Bâtiment Alix et Marwan Lahoud (IHES)
URL:https://indico.math.cnrs.fr/event/16953/
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