@article{5b1d6b2542134354842d6056d188f184,

title = "Deep Linear Networks for Matrix Completion-an Infinite Depth Limit",

abstract = "The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is defined by the architecture of the network and the loss function is defined by the learning task. We extend this geometric framework, obtaining explicit expressions for the volume form, including the case when the network has infinite depth. We investigate the link between the Riemannian geometry and the training asymptotics for matrix completion with rigorous analysis and numerics. We propose that under small initialization, implicit regularization is a result of bias towards high state space volume.",

keywords = "Riemannian gradient flow, deep linear network, generalizability, implicit regularization, matrix completion",

author = "Nadav Cohen and Govind Menon and Zsolt Veraszto",

note = "Publisher Copyright: {\textcopyright} 2023 Society for Industrial and Applied Mathematics.",

year = "2023",

doi = "10.1137/22M1530653",

language = "אנגלית",

volume = "22",

pages = "3208--3232",

journal = "SIAM Journal on Applied Dynamical Systems",

issn = "1536-0040",

publisher = "Society of Industrial and Applied Mathematics",

number = "4",

}