# NashAE: Disentangling Representations through Adversarial Covariance Minimization

arXiv: https://arxiv.org/abs/2209.10677 · HTML: https://mlsanity.com/paper/2209.10677/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradients](https://mlsanity.com/paper/1711.09404/) (2017)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [Deep Convolutional Inverse Graphics Network](https://mlsanity.com/paper/1503.03167/) (2015)
- [Turning a Blind Eye: Explicit Removal of Biases and Variation from Deep Neural Network Embeddings](https://mlsanity.com/paper/1809.02169/) (2018)
- [Natural Language Processing Advancements By Deep Learning: A Survey](https://mlsanity.com/paper/2003.01200/) (2020)
- [Disentangling Factors of Variation by Mixing Them](https://mlsanity.com/paper/1711.07410/) (2017)
- [Reinforcement Learning and Deep Learning based Lateral Control for Autonomous Driving](https://mlsanity.com/paper/1810.12778/) (2018)

## Built on by (most cited first, 13 of 13)

- [InfoDiffusion: Representation Learning Using Information Maximizing Diffusion Models](https://mlsanity.com/paper/2306.08757/) (2023)
- [DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models](https://mlsanity.com/paper/2301.13721/) (2023)
- [Diffusion Bridge AutoEncoders for Unsupervised Representation Learning](https://mlsanity.com/paper/2405.17111/) (2024)
- [Sequential Data Generation with Groupwise Diffusion Process](https://mlsanity.com/paper/2310.01400/) (2023)
- [Adversarial Estimation of Topological Dimension with Harmonic Score Maps](https://mlsanity.com/paper/2312.06869/) (2023)
- [Disentangling Disentangled Representations: Towards Improved Latent Units via Diffusion Models](https://mlsanity.com/paper/2410.23820/) (2024)
- [Denoising Multi-Beta VAE: Representation Learning for Disentanglement and Generation](https://mlsanity.com/paper/2507.06613/) (2025)
- [Disentangling Learning Representations with Density Estimation](https://mlsanity.com/paper/2302.04362/) (2023)
- [ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networks](https://mlsanity.com/paper/2405.15268/) (2024)
- [Disentangled Representation Learning via Flow Matching](https://mlsanity.com/paper/2602.05214/) (2026)
- [Do Counterfactual Examples Complicate Adversarial Training?](https://mlsanity.com/paper/2404.10588/) (2024)
- [Patronus: Interpretable Diffusion Models with Prototypes](https://mlsanity.com/paper/2503.22782/) (2025)
- [Disentangled representations via score-based variational autoencoders](https://mlsanity.com/paper/2512.17127/) (2025)

## Abstract (arXiv)

We present a self-supervised method to disentangle factors of variation in high-dimensional data that does not rely on prior knowledge of the underlying variation profile (e.g., no assumptions on the number or distribution of the individual latent variables to be extracted). In this method which we call NashAE, high-dimensional feature disentanglement is accomplished in the low-dimensional latent space of a standard autoencoder (AE) by promoting the discrepancy between each encoding element and information of the element recovered from all other encoding elements. Disentanglement is promoted efficiently by framing this as a minmax game between the AE and an ensemble of regression networks which each provide an estimate of an element conditioned on an observation of all other elements. We quantitatively compare our approach with leading disentanglement methods using existing disentanglement metrics. Furthermore, we show that NashAE has increased reliability and increased capacity to capture salient data characteristics in the learned latent representation.