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UID:1037@cran.univ-lorraine.fr
DTSTART;TZID=Europe/Paris:20250703T104500
DTEND;TZID=Europe/Paris:20250703T113000
DTSTAMP:20250701T165212Z
URL:https://www.cran.univ-lorraine.fr/events/seminaire-de-clara-derand-cra
 n/
SUMMARY:Séminaire de Clara Dérand (CRAN)
DESCRIPTION:Speaker: Clara Dérand (CRAN)\nTitle: Identifiability of Deep 
 Polynomial Neural Networks\n\n\nAbstract: \nPolynomial Neural Networks (P
 NNs) possess a rich algebraic and geometric structure. However\, their ide
 ntifiability -- a key property for ensuring interpretability -- remains po
 orly understood. In this work\, we present a comprehensive analysis of the
  identifiability of deep PNNs\, including architectures with and without b
 ias terms. Our results reveal an intricate interplay between activation de
 grees and layer widths in achieving identifiability. As special cases\, we
  show that architectures with non-increasing layer widths are generically 
 identifiable under mild conditions\, while encoder-decoder networks are id
 entifiable when the decoder widths do not grow too rapidly. Our proofs are
  constructive and center on a connection between deep PNNs and low-rank te
 nsor decompositions\, and Kruskal-type uniqueness theorems. This yields bo
 th generic conditions determined by the architecture\, and effective condi
 tions that depend on the network's parameters. We also settle an open conj
 ecture on the expected dimension of PNN's neurovarieties\, and provide new
  bounds on the activation degrees required for it to reach its maximum.\n\
 nPreprint: https://arxiv.org/abs/2506.17093\n\n\nPlace: Seminar room at 4
 th floor of the FST 1er cycle (Henri Poincaré) building\nAlso available o
 n Teams
CATEGORIES:Département BioSiS,Séminaires projet SiMul
LOCATION:CRAN - FST - 4ème\, Campus Sciences\, Boulevard des Aiguillettes\
 , Vandoeuvre-lès-Nancy\, 54506\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus Sciences\, Boulevard
  des Aiguillettes\, Vandoeuvre-lès-Nancy\, 54506\, France;X-APPLE-RADIUS=
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