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UID:9025@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260414T143000
DTEND;TZID=Europe/Paris:20260414T153000
DTSTAMP:20260216T143012Z
URL:https://www.i2m.univ-amu.fr/evenements/resnets-of-all-shapes-and-sizes
 -quantitative-large-scale-theory-of-training-dynamics/
SUMMARY:Louis-Pierre CHAINTRON (École Polytechnique Fédérale de Lausanne
 ): ResNets of All Shapes and Sizes: Quantitative Large-Scale Theory of Tra
 ining Dynamics
DESCRIPTION:Louis-Pierre CHAINTRON: We study the convergence of the trainin
 g dynamics\nof residual neural networks (ResNets)\ntowards their joint inf
 inite depth–width limit.\nWe focus on ResNets with two-layer perceptron 
 blocks\,\nwhose shape is determined by the depth L\,\nhidden width M\, and
  embedding dimension D\,\nand we adopt the residual scaling O(√D/√(LM)
 )\nrecently identified as necessary for local feature learning.\nWe show t
 hat after a bounded number of training steps\,\nthe error between the fini
 te ResNet and its infinite-size limit\nis O(1/L + √D/√(LM) + 1/√D)\,
  and numerical experiments suggest\nthat this bound is tight in the early 
 training phase.\nFrom a probabilistic viewpoint\,\nthe D → ∞ limit amo
 unts to a mean-field limit\nover the coordinates of the embedding\,\nwhere
  some interactions scale in 1/√D\ncontrary to the usual 1/D setting .\nO
 ur analysis is a rigorous and quantitative instance\nof the Dynamical Mean
  Field Theory (DMFT)\nfrom statistical physics\;\nit combines propagation 
 of chaos arguments\nwith the cavity method at a functional level.\n
CATEGORIES:Séminaire,ALEA,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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