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SUMMARY:Complexity of real and artificial networks  - Dr. Gueorgui Mihaylo
 v (Haleon.com)
DTSTART:20250306T140000Z
DTEND:20250306T150000Z
UID:TALK223999@talks.cam.ac.uk
CONTACT:Sri Aitken
DESCRIPTION:In this seminar I present some ideas and recent results in the
  space of geometric modelling of complex adaptive systems\, which are driv
 en by applications on real-world networks and deep (Graph) NN architecture
 s. Modelling complexity and emergent phenomena has been an active field of
  research in recent years. Relevant properties of real-world systems are o
 ften collective/emergent. Similarly\, the learning process\, behaviour\, a
 nd key characteristics of deep NN architectures (also complex adaptive sys
 tems) are intrinsically emergent. \n\nThe geometric approach is directly r
 elated to a successful paradigm in modelling emergent phenomena. I introdu
 ce a specific construction of a principal bundle over simplicial complexes
 \, which naturally arises from local multi-agent interactions in a system.
  This construction leads to consistent definitions of discrete analogues o
 f classical obstructions to the integrability of geometric structures on m
 anifolds (which are geometric such as curvature and torsion forms and topo
 logical i.e. captured by characteristic classes). These objects\, ultimate
 ly related to the non-triviality of principal bundles\, are the key elemen
 ts of a consistent and rich gauge theory.  Unsurprisingly these ideas have
  direct relation and potential implications for the more recently develope
 d field of Geometric Deep Learning. \n
LOCATION:East 1/West Hub
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