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.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Domain Adaptation | PACS | Average Accuracy | 88.3 | VNE (ResNet-50, SWAD) |
| Domain Adaptation | Office-Home | Average Accuracy | 71.1 | VNE (ResNet-50, SWAD) |
| Domain Adaptation | VLCS | Average Accuracy | 79.7 | VNE (ResNet-50, SWAD) |
| Domain Adaptation | TerraIncognita | Average Accuracy | 51.7 | VNE (ResNet-50, SWAD) |
| Image Classification | Mini-Imagenet 5-way (5-shot) | Accuracy | 67.52 | VNE (BOIL) |
| Image Classification | Mini-Imagenet 5-way (1-shot) | Accuracy | 50.95 | VNE (BOIL) |
| Image Classification | ImageNet - 10% labeled data | Top 1 Accuracy | 69.1 | I-VNE+ (ResNet-50) |
| Image Classification | ImageNet - 10% labeled data | Top 5 Accuracy | 89.9 | I-VNE+ (ResNet-50) |
| Image Classification | ImageNet - 1% labeled data | Top 1 Accuracy | 55.8 | I-VNE+ (ResNet-50) |
| Image Classification | ImageNet - 1% labeled data | Top 5 Accuracy | 81 | I-VNE+ (ResNet-50) |
| Image Classification | ImageNet | Top 1 Accuracy | 72.1 | I-VNE+ (ResNet-50) |
| Image Classification | ImageNet | Top 5 Accuracy | 91 | I-VNE+ (ResNet-50) |
| Few-Shot Image Classification | Mini-Imagenet 5-way (5-shot) | Accuracy | 67.52 | VNE (BOIL) |
| Few-Shot Image Classification | Mini-Imagenet 5-way (1-shot) | Accuracy | 50.95 | VNE (BOIL) |
| Semi-Supervised Image Classification | ImageNet - 10% labeled data | Top 1 Accuracy | 69.1 | I-VNE+ (ResNet-50) |
| Semi-Supervised Image Classification | ImageNet - 10% labeled data | Top 5 Accuracy | 89.9 | I-VNE+ (ResNet-50) |
| Semi-Supervised Image Classification | ImageNet - 1% labeled data | Top 1 Accuracy | 55.8 | I-VNE+ (ResNet-50) |
| Semi-Supervised Image Classification | ImageNet - 1% labeled data | Top 5 Accuracy | 81 | I-VNE+ (ResNet-50) |
| Domain Generalization | PACS | Average Accuracy | 88.3 | VNE (ResNet-50, SWAD) |
| Domain Generalization | Office-Home | Average Accuracy | 71.1 | VNE (ResNet-50, SWAD) |
| Domain Generalization | VLCS | Average Accuracy | 79.7 | VNE (ResNet-50, SWAD) |
| Domain Generalization | TerraIncognita | Average Accuracy | 51.7 | VNE (ResNet-50, SWAD) |