  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.
