# Structured Disentangled Representations

arXiv: https://arxiv.org/abs/1804.02086 · HTML: https://mlsanity.com/paper/1804.02086/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2018.

## Built on by (most cited first, 30 of 62)

- [Generalization and Robustness Implications in Object-Centric Learning](https://mlsanity.com/paper/2107.00637/) (2021)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [ConceptMix: A Compositional Image Generation Benchmark with Controllable Difficulty](https://mlsanity.com/paper/2408.14339/) (2024)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [Compositional Generalization in Unsupervised Compositional Representation Learning: A Study on Disentanglement and Emergent Language](https://mlsanity.com/paper/2210.00482/) (2022)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [A survey on Variational Autoencoders from a GreenAI perspective](https://mlsanity.com/paper/2103.01071/) (2021)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [I Don't Need u: Identifiable Non-Linear ICA Without Side Information](https://mlsanity.com/paper/2106.05238/) (2021)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [When does compositional structure yield compositional generalization? A kernel theory](https://mlsanity.com/paper/2405.16391/) (2024)
- [Can Models Learn Skill Composition from Examples?](https://mlsanity.com/paper/2409.19808/) (2024)
- [3D Shape Variational Autoencoder Latent Disentanglement via Mini-Batch Feature Swapping for Bodies and Faces](https://mlsanity.com/paper/2111.12448/) (2021)
- [Interpretable Molecular Graph Generation via Monotonic Constraints](https://mlsanity.com/paper/2203.00412/) (2022)
- [Disentangled Representations from Non-Disentangled Models](https://mlsanity.com/paper/2102.06204/) (2021)
- [Benchmarks, Algorithms, and Metrics for Hierarchical Disentanglement](https://mlsanity.com/paper/2102.05185/) (2021)
- [The Role of Pretrained Representations for the OOD Generalization of Reinforcement Learning Agents](https://mlsanity.com/paper/2107.05686/) (2021)
- [Is Fairness Only Metric Deep? Evaluating and Addressing Subgroup Gaps in Deep Metric Learning](https://mlsanity.com/paper/2203.12748/) (2022)
- [Disentangling representations in Restricted Boltzmann Machines without adversaries](https://mlsanity.com/paper/2206.11600/) (2022)
- [LADIS: Language Disentanglement for 3D Shape Editing](https://mlsanity.com/paper/2212.05011/) (2022)
- [Enhancing Feature Diversity Boosts Channel-Adaptive Vision Transformers](https://mlsanity.com/paper/2405.16419/) (2024)
- [Semi-Supervised Disentanglement of Class-Related and Class-Independent Factors in VAE](https://mlsanity.com/paper/2102.00892/) (2021)
- [eVAE: Evolutionary Variational Autoencoder](https://mlsanity.com/paper/2301.00011/) (2023)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [3D Generative Model Latent Disentanglement via Local Eigenprojection](https://mlsanity.com/paper/2302.12798/) (2023)
- [Vector-based Representation is the Key: A Study on Disentanglement and Compositional Generalization](https://mlsanity.com/paper/2305.18063/) (2023)
- [Leveraging Relational Information for Learning Weakly Disentangled Representations](https://mlsanity.com/paper/2205.10056/) (2022)
- [Decomposing Normal and Abnormal Features of Medical Images into Discrete Latent Codes for Content-Based Image Retrieval](https://mlsanity.com/paper/2103.12328/) (2021)
- [Adversarial robustness of VAEs through the lens of local geometry](https://mlsanity.com/paper/2208.03923/) (2022)

## Abstract (arXiv)

Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a two-level hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the trade-offs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors.