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

arXiv: https://arxiv.org/abs/2304.01434 · HTML: https://mlsanity.com/paper/2304.01434/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 98 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 30 of 69)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)

## Built on by (most cited first, 17 of 17)

- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Matrix Information Theory for Self-Supervised Learning](https://mlsanity.com/paper/2305.17326/) (2023)
- [HYPO: Hyperspherical Out-of-Distribution Generalization](https://mlsanity.com/paper/2402.07785/) (2024)
- [Rethinking the Representation in Federated Unsupervised Learning with Non-IID Data](https://mlsanity.com/paper/2403.16398/) (2024)
- [CIFAR-10-Warehouse: Broad and More Realistic Testbeds in Model Generalization Analysis](https://mlsanity.com/paper/2310.04414/) (2023)
- [AHA: Human-Assisted Out-of-Distribution Generalization and Detection](https://mlsanity.com/paper/2410.08000/) (2024)
- [Out-of-Distribution Learning with Human Feedback](https://mlsanity.com/paper/2408.07772/) (2024)
- [AdaDim: Dimensionality Adaptation for SSL Representational Dynamics](https://mlsanity.com/paper/2505.12576/) (2025)
- [Learning to Embed Distributions via Maximum Kernel Entropy](https://mlsanity.com/paper/2408.00549/) (2024)
- [FroSSL: Frobenius Norm Minimization for Efficient Multiview Self-Supervised Learning](https://mlsanity.com/paper/2310.02903/) (2023)
- [WeedCLR: Weed Contrastive Learning through Visual Representations with Class-Optimized Loss in Long-Tailed Datasets](https://mlsanity.com/paper/2310.12465/) (2023)
- [Improving Forward Compatibility in Class Incremental Learning by Increasing Representation Rank and Feature Richness](https://mlsanity.com/paper/2403.15517/) (2024)
- [Exploring Information-Theoretic Metrics Associated with Neural Collapse in Supervised Training](https://mlsanity.com/paper/2409.16767/) (2024)
- [Countering Multi-modal Representation Collapse through Rank-targeted Fusion](https://mlsanity.com/paper/2511.06450/) (2025)
- [Unveiling Key Aspects of Fine-Tuning in Sentence Embeddings: A Representation Rank Analysis](https://mlsanity.com/paper/2405.11297/) (2024)
- [Vision and Language Integration for Domain Generalization](https://mlsanity.com/paper/2504.12966/) (2025)
- [NexusFlow: Unifying Disparate Tasks under Partial Supervision via Invertible Flow Networks](https://mlsanity.com/paper/2512.06251/) (2025)

## Abstract (arXiv)

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.