Off-Diagonal Orthogonal Regularization

Off-Diagonal Orthogonal Regularization is a modified form of orthogonal regularization originally used in BigGAN. The original orthogonal regularization is known to be limiting so the authors explore several variants designed to relax the constraint while still imparting the desired smoothness to the models. They opt for a modification where they remove diagonal terms from the regularization, and aim to minimize the pairwise cosine similarity between filters but does not constrain their norm:

$R\_{\beta}\left(W\right) = \beta|| W^{T}W \odot \left(\mathbf{1}-I\right) ||^{2}\_{F}$

where $\mathbf{1}$ denotes a matrix with all elements set to 1. The authors sweep $\beta$ values and select $10^{−4}$.