# Towards Building A Group-based Unsupervised Representation Disentanglement Framework

arXiv: https://arxiv.org/abs/2102.10303 · HTML: https://mlsanity.com/paper/2102.10303/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 23 of 23)

- [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)
- [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)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEs](https://mlsanity.com/paper/1901.07017/) (2019)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Joint Disentangling and Adaptation for Cross-Domain Person Re-Identification](https://mlsanity.com/paper/2007.10315/) (2020)
- [Cross-Dataset Person Re-Identification via Unsupervised Pose Disentanglement and Adaptation](https://mlsanity.com/paper/1909.09675/) (2019)
- [Symmetry-Based Disentangled Representation Learning requires Interaction with Environments](https://mlsanity.com/paper/1904.00243/) (2019)
- [Disentangling by Subspace Diffusion](https://mlsanity.com/paper/2006.12982/) (2020)
- [High-Fidelity Synthesis with Disentangled Representation](https://mlsanity.com/paper/2001.04296/) (2020)
- [Linear Disentangled Representations and Unsupervised Action Estimation](https://mlsanity.com/paper/2008.07922/) (2020)
- [Addressing the Topological Defects of Disentanglement via Distributed Operators](https://mlsanity.com/paper/2102.05623/) (2021)
- [Learning Group Structure and Disentangled Representations of Dynamical Environments](https://mlsanity.com/paper/2002.06991/) (2020)
- [Bayes-Factor-VAE: Hierarchical Bayesian Deep Auto-Encoder Models for Factor Disentanglement](https://mlsanity.com/paper/1909.02820/) (2019)
- [Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling](https://mlsanity.com/paper/2010.13187/) (2020)

## Built on by (most cited first, 22 of 22)

- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models](https://mlsanity.com/paper/2301.13721/) (2023)
- [Diffusion Model with Cross Attention as an Inductive Bias for Disentanglement](https://mlsanity.com/paper/2402.09712/) (2024)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [Visual Concepts Tokenization](https://mlsanity.com/paper/2205.10093/) (2022)
- [When are Post-hoc Conceptual Explanations Identifiable?](https://mlsanity.com/paper/2206.13872/) (2022)
- [A Flexible Diffusion Model](https://mlsanity.com/paper/2206.10365/) (2022)
- [Closed-Loop Unsupervised Representation Disentanglement with β-VAE Distillation and Diffusion Probabilistic Feedback](https://mlsanity.com/paper/2402.02346/) (2024)
- [Vector-based Representation is the Key: A Study on Disentanglement and Compositional Generalization](https://mlsanity.com/paper/2305.18063/) (2023)
- [Disentanglement Learning via Topology](https://mlsanity.com/paper/2308.12696/) (2023)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncoder](https://mlsanity.com/paper/2401.08897/) (2024)
- [ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networks](https://mlsanity.com/paper/2405.15268/) (2024)
- [Symbolic Disentangled Representations for Images](https://mlsanity.com/paper/2412.19847/) (2024)
- [Equivariant Disentangled Transformation for Domain Generalization under Combination Shift](https://mlsanity.com/paper/2208.02011/) (2022)
- [Disentangled Representation Learning via Modular Compositional Bias](https://mlsanity.com/paper/2510.21402/) (2025)
- [ProtoVAE: Prototypical Networks for Unsupervised Disentanglement](https://mlsanity.com/paper/2305.09092/) (2023)
- [Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs](https://mlsanity.com/paper/2502.03740/) (2025)
- [Disentangled Representation Learning through Unsupervised Symmetry Group Discovery](https://mlsanity.com/paper/2603.11790/) (2026)

## Abstract (arXiv)

Disentangled representation learning is one of the major goals of deep learning, and is a key step for achieving explainable and generalizable models. A well-defined theoretical guarantee still lacks for the VAE-based unsupervised methods, which are a set of popular methods to achieve unsupervised disentanglement. The Group Theory based definition of representation disentanglement mathematically connects the data transformations to the representations using the formalism of group. In this paper, built on the group-based definition and inspired by the n-th dihedral group, we first propose a theoretical framework towards achieving unsupervised representation disentanglement. We then propose a model, based on existing VAE-based methods, to tackle the unsupervised learning problem of the framework. In the theoretical framework, we prove three sufficient conditions on model, group structure, and data respectively in an effort to achieve, in an unsupervised way, disentangled representation per group-based definition. With the first two of the conditions satisfied and a necessary condition derived for the third one, we offer additional constraints, from the perspective of the group-based definition, for the existing VAE-based models. Experimentally, we train 1800 models covering the most prominent VAE-based methods on five datasets to verify the effectiveness of our theoretical framework. Compared to the original VAE-based methods, these Groupified VAEs consistently achieve better mean performance with smaller variances.