Implicit Regularization and Convergence for Weight Normalization. (arXiv:1911.07956v5 [cs.LG] UPDATED)

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight
[Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer
normalization [Baet al., 2016] have been widely used in modern machine
learning. Here, we study the weight normalization (WN) method [Salimans and
Kingma, 2016] and a variant called reparametrized projected gradient descent
(rPGD) for overparametrized least-squares regression. WN and rPGD reparametrize
the weights with a scale g and a unit vector w and thus the objective function
becomes non-convex. We …

arxiv convergence normalization regularization