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DTSTAMP:20250810T075254Z
DESCRIPTION:Title: The Mathematical Foundations of Deep Learning: From Rati
 ng Impossibility to Practical Existence Theorems.\n\nAbstract: Deep learni
 ng is having a profound impact on industry and scientific research. Yet\, 
 while this paradigm continues to show impressive performance in a wide var
 iety of applications\, its mathematical foundations are far from being wel
 l established. In this talk\, I will present recent developments in this a
 rea by illustrating two case studies.\n	\n	First\, motivated by applications
  in cognitive science\, I will present “rating impossibility' theorems. Th
 ey identify frameworks where deep learning is provably unable to generaliz
 e outside the training set for the seemingly simple task of learning ident
 ity effects\, i.e. classifying whether pairs of objects are identical or n
 ot.Second\, motivated by applications in scientific computing\, I will ill
 ustrate “practical existence' theorems. They combine universal approximati
 on results for deep neural networks with compressed sensing and high-dimen
 sional polynomial approximation theory. As a result\, they yield sufficien
 t conditions on the network architecture\, the training strategy\, and the
  number of samples able to guarantee accurate approximation of smooth func
 tions of many variables.Time permitting\, I will also discuss work in prog
 ress and open questions.To receive the announcements with the Zoom link\, 
 please subscribe once to the lists of your choice\n\nWeb site : http://crm
 .umontreal.ca/colloque-sciences-mathematiques-quebec/index.html#csmq\n\nHy
 bride - CRM\, Salle / Room 5340\, Pavillon André Aisenstadt / Zoom (voir s
 urvol/ see overview)\n
DTSTART:20230210T203000Z
DTEND:20230210T213000Z
SUMMARY:Simone Brugiapaglia (Concordia University)
URL:/mathstat/channels/event/simone-brugiapaglia-conco
 rdia-university-345751
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