Improving Covariance Conditioning of the SVD Meta-layer by Orthogonality

TL;DR

This paper introduces methods to improve the covariance conditioning of the SVD meta-layer in neural networks by enforcing orthogonality, leading to better training stability and generalization, validated through experiments on visual recognition tasks.

Contribution

The paper proposes the Nearest Orthogonal Gradient and Optimal Learning Rate methods to enhance covariance conditioning without harming performance, advancing orthogonal treatments in neural network layers.

Findings

Improved covariance conditioning with orthogonality techniques.

Enhanced generalization in visual recognition tasks.

Orthogonal weight combinations further boost performance.

Abstract

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.