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SUMMARY:The Geometry of Random Neural Networks - Domenico Marinucci (Unive
 rsità di Roma Tor Vergata)
DTSTART:20260130T140000Z
DTEND:20260130T150000Z
UID:TALK243034@talks.cam.ac.uk
CONTACT:Po-Ling Loh
DESCRIPTION:We study the geometric properties of random neural networks by
  investigating the boundary volumes of their excursion sets for different 
 activation functions\, as the depth increases. More specifically\, we show
  that\, for activations which are not very regular (e.g.\, the Heaviside s
 tep function)\, the boundary volumes exhibit fractal behavior\, with their
  Hausdorff dimension monotonically increasing with the depth. On the other
  hand\, for activations which are more regular (e.g.\, ReLU\, logistic and
  tanh)\, as the depth increases\, the expected boundary volumes can either
  converge to zero\, remain constant or diverge exponentially\, depending o
 n a single spectral parameter which can be easily computed. Our theoretica
 l results are confirmed in some numerical experiments based on Monte Carlo
  simulations.\n\nBased on joint works with Simmaco Di Lillo\, Michele Salv
 i and Stefano Vigogna.
LOCATION:MR12\, Centre for Mathematical Sciences
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