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

4 Apr 2023CVPR 2023 1arXiv:2304.01434archive 2025-07-28

Jaeill Kim, Suhyun Kang, Duhun Hwang, Jungwook Shin, Wonjong Rhee

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.

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jaeill/CVPR23-VNE officialmentioned in papermentioned on GitHubpytorchMIT report

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Tasks

DisentanglementDomain GeneralizationFew-Shot Image ClassificationGeneral ClassificationImage ClassificationMeta-LearningObject DetectionRepresentation LearningSelf-Supervised Image ClassificationSelf-Supervised LearningSemi-Supervised Image Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Domain Generalization Office-Home VNE (ResNet-50, SWAD) Average Accuracy 71.1 #28 of 45 Archive leaderboard report
Domain Generalization PACS VNE (ResNet-50, SWAD) Average Accuracy 88.3 #30 of 133 Archive leaderboard report
Domain Generalization TerraIncognita VNE (ResNet-50, SWAD) Average Accuracy 51.7 #20 of 30 Archive leaderboard report
Domain Generalization VLCS VNE (ResNet-50, SWAD) Average Accuracy 79.7 #22 of 37 Archive leaderboard report
Few-Shot Image Classification Mini-Imagenet 5-way (1-shot) VNE (BOIL) Accuracy 50.95 #97 of 105 Archive leaderboard report
Few-Shot Image Classification Mini-Imagenet 5-way (5-shot) VNE (BOIL) Accuracy 67.52 #87 of 95 Archive leaderboard report
Self-Supervised Image Classification ImageNet I-VNE+ (ResNet-50) Number of Params 25M #95 of 144 Archive leaderboard report
Self-Supervised Image Classification ImageNet I-VNE+ (ResNet-50) Top 1 Accuracy 72.1 #95 of 144 Archive leaderboard report
Self-Supervised Image Classification ImageNet I-VNE+ (ResNet-50) Top 5 Accuracy 91.0 #95 of 144 Archive leaderboard report
Semi-Supervised Image Classification ImageNet - 1% labeled data I-VNE+ (ResNet-50) Top 1 Accuracy 55.8 #45 of 65 Archive leaderboard report
Semi-Supervised Image Classification ImageNet - 1% labeled data I-VNE+ (ResNet-50) Top 5 Accuracy 81.0 #45 of 65 Archive leaderboard report
Semi-Supervised Image Classification ImageNet - 10% labeled data I-VNE+ (ResNet-50) Top 1 Accuracy 69.1 #42 of 75 Archive leaderboard report
Semi-Supervised Image Classification ImageNet - 10% labeled data I-VNE+ (ResNet-50) Top 5 Accuracy 89.9 #42 of 75 Archive leaderboard report

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