# Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning

arXiv: https://arxiv.org/abs/2503.00639 · HTML: https://mlsanity.com/paper/2503.00639/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 80 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 30 of 55)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [cGANs with Projection Discriminator](https://mlsanity.com/paper/1802.05637/) (2018)
- [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)
- [Few-Shot Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1905.01723/) (2019)
- [Coupled Generative Adversarial Networks](https://mlsanity.com/paper/1606.07536/) (2016)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Multi-Level Variational Autoencoder: Learning Disentangled Representations from Grouped Observations](https://mlsanity.com/paper/1705.08841/) (2017)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)

## Built on by (most cited first, 4 of 4)

- [Thought Communication in Multiagent Collaboration](https://mlsanity.com/paper/2510.20733/) (2025)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [PersonaX: Multimodal Datasets with LLM-Inferred Behavior Traits](https://mlsanity.com/paper/2509.11362/) (2025)

## Abstract (arXiv)

Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the distribution of latent variables indicated by auxiliary variables such as domain indices, but acquiring enough domains is often challenging. Alternative approaches exploit structural sparsity assumptions on the mixing procedure, but such constraints are usually (partially) violated in practice. Interestingly, we find that these two seemingly unrelated assumptions can actually complement each other to achieve identifiability. Specifically, when conditioned on auxiliary variables, the sparse mixing procedure assumption provides structural constraints on the mapping from estimated to true latent variables and hence compensates for potentially insufficient distribution changes. Building on this insight, we propose an identifiability theory with less restrictive constraints regarding distribution changes and the sparse mixing procedure, enhancing applicability to real-world scenarios. Additionally, we develop an estimation framework incorporating a domain encoding network and a sparse mixing constraint and provide two implementations based on variational autoencoders and generative adversarial networks, respectively. Experiment results on synthetic and real-world datasets support our theoretical results.