Improving Covariance Conditioning of the SVD Meta-layer by Orthogonality
This work addresses a specific issue in neural network training for visual recognition, offering incremental improvements to existing orthogonal techniques.
The paper tackles the problem of ill-conditioned covariance in SVD meta-layers, which harms training stability and generalization, by proposing Nearest Orthogonal Gradient and Optimal Learning Rate to enforce orthogonality without performance loss, achieving improved conditioning and generalization in decorrelated Batch Normalization and Global Covariance Pooling applications.
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.