Orthogonal SVD Covariance Conditioning and Latent Disentanglement

TL;DR

This paper introduces methods to improve covariance conditioning in neural networks by enforcing orthogonality, enhancing training stability, generalization, and latent disentanglement across various applications.

Contribution

It proposes the Nearest Orthogonal Gradient and Optimal Learning Rate techniques to improve covariance conditioning without harming performance.

Findings

Enhanced covariance conditioning and generalization in visual recognition tasks.

Improved latent disentanglement in generative models.

Orthogonal treatments combined with weight orthogonality 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 covariance conditioning and generalization. The combinations with orthogonal weight can further boost the performance. Moreover, we show that our orthogonality techniques can benefit generative models for better latent disentanglement through a series of experiments on various benchmarks. Code is available at: \href{https://github.com/KingJamesSong/OrthoImproveCond}{https://github.com/KingJamesSong/OrthoImproveCond}.