VNE: An Effective Method for Improving Deep Representation by Manipulating Eigenvalue Distribution
This work addresses a general problem in deep learning for researchers and practitioners by offering a widely applicable method to enhance representation properties, though it appears incremental as it builds on existing regularization techniques.
The authors tackled the challenge of improving deep representation quality by proposing to regularize von Neumann entropy (VNE), which effectively manipulates eigenvalue distributions of representation autocorrelation matrices, and demonstrated its applicability across domain-generalization, meta-learning, self-supervised learning, and generative models.
Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.