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Since the introduction of deep learning, a wide scope of representationproperties, such as decorrelation, whitening, disentanglement, rank, isotropy,and mutual information, have been studied to improve the quality ofrepresentation. However, manipulating such properties can be challenging interms of implementational effectiveness and general applicability. To addressthese limitations, we propose to regularize von Neumann entropy~(VNE) ofrepresentation. First, we demonstrate that the mathematical formulation of VNEis superior in effectively manipulating the eigenvalues of the representationautocorrelation matrix. Then, we demonstrate that it is widely applicable inimproving state-of-the-art algorithms or popular benchmark algorithms byinvestigating domain-generalization, meta-learning, self-supervised learning,and generative models. In addition, we formally establish theoreticalconnections with rank, disentanglement, and isotropy of representation.Finally, we provide discussions on the dimension control of VNE and therelationship with Shannon entropy. Code is available at:https://github.com/jaeill/CVPR23-VNE.

VNE: An Effective Method for Improving Deep Representation by Manipulating Eigenvalue Distribution