# Disentanglement and Generalization Under Correlation Shifts

arXiv: https://arxiv.org/abs/2112.14754 · HTML: https://mlsanity.com/paper/2112.14754/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 89 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 30 of 60)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [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)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Are we done with ImageNet?](https://mlsanity.com/paper/2006.07159/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [AttGAN: Facial Attribute Editing by Only Changing What You Want](https://mlsanity.com/paper/1711.10678/) (2017)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [Swapping Autoencoder for Deep Image Manipulation](https://mlsanity.com/paper/2007.00653/) (2020)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)

## Built on by (most cited first, 8 of 8)

- [Disentanglement of Correlated Factors via Hausdorff Factorized Support](https://mlsanity.com/paper/2210.07347/) (2022)
- [Conditional Mutual Information for Disentangled Representations in Reinforcement Learning](https://mlsanity.com/paper/2305.14133/) (2023)
- [Disentangling representations of retinal images with generative models](https://mlsanity.com/paper/2402.19186/) (2024)
- [Counterfactual Generation Under Confounding](https://mlsanity.com/paper/2210.12368/) (2022)
- [On Counterfactual Data Augmentation Under Confounding](https://mlsanity.com/paper/2305.18183/) (2023)
- [XFACTORS: Disentangled Information Bottleneck via Contrastive Supervision](https://mlsanity.com/paper/2601.21688/) (2026)
- [Coordinated Disentanglement with Iterative Mode Discovery Under Hidden Correlations](https://mlsanity.com/paper/2607.17264/) (2026)
- [The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning](https://mlsanity.com/paper/2608.16245/) (2026)

## Abstract (arXiv)

Correlations between factors of variation are prevalent in real-world data. Exploiting such correlations may increase predictive performance on noisy data; however, often correlations are not robust (e.g., they may change between domains, datasets, or applications) and models that exploit them do not generalize when correlations shift. Disentanglement methods aim to learn representations which capture different factors of variation in latent subspaces. A common approach involves minimizing the mutual information between latent subspaces, such that each encodes a single underlying attribute. However, this fails when attributes are correlated. We solve this problem by enforcing independence between subspaces conditioned on the available attributes, which allows us to remove only dependencies that are not due to the correlation structure present in the training data. We achieve this via an adversarial approach to minimize the conditional mutual information (CMI) between subspaces with respect to categorical variables. We first show theoretically that CMI minimization is a good objective for robust disentanglement on linear problems. We then apply our method on real-world datasets based on MNIST and CelebA, and show that it yields models that are disentangled and robust under correlation shift, including in weakly supervised settings.