  Inserting an SVD meta-layer into neural networks is prone to make the
covariance ill-conditioned, which could harm the model in the training
stability and generalization abilities. In this paper, we systematically study
how to improve the covariance conditioning by enforcing orthogonality to the
Pre-SVD layer. Existing orthogonal treatments on the weights are first
investigated. However, these techniques can improve the conditioning but would
hurt the performance. To avoid such a side effect, we propose the Nearest
Orthogonal Gradient (NOG) and Optimal Learning Rate (OLR). The effectiveness of
our methods is validated in two applications: decorrelated Batch Normalization
(BN) and Global Covariance Pooling (GCP). Extensive experiments on visual
recognition demonstrate that our methods can simultaneously improve the
covariance conditioning and generalization. Moreover, the combinations with
orthogonal weight can further boost the performances.
