# CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncoder

arXiv: https://arxiv.org/abs/2401.08897 · HTML: https://mlsanity.com/paper/2401.08897/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 17 Jan 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (2021)
- [Learning Discrete and Continuous Factors of Data via Alternating Disentanglement](https://mlsanity.com/paper/1905.09432/) (2019)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [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)
- [Addressing the Topological Defects of Disentanglement via Distributed Operators](https://mlsanity.com/paper/2102.05623/) (2021)
- [An Empirical Study on Disentanglement of Negative-free Contrastive Learning](https://mlsanity.com/paper/2206.04756/) (2022)
- [Unsupervised Object Representation Learning using Translation and Rotation Group Equivariant VAE](https://mlsanity.com/paper/2210.12918/) (2022)
- [Generative Flows with Matrix Exponential](https://mlsanity.com/paper/2007.09651/) (2020)

## Built on by (most cited first, 2 of 2)

- [Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs](https://mlsanity.com/paper/2502.03740/) (2025)
- [Commutator-Induced Uncertainty in VAEs](https://mlsanity.com/paper/2605.23449/) (2026)

## Abstract (arXiv)

Symmetries of input and latent vectors have provided valuable insights for disentanglement learning in VAEs. However, only a few works were proposed as an unsupervised method, and even these works require known factor information in the training data. We propose a novel method, Composite Factor-Aligned Symmetry Learning (CFASL), which is integrated into VAEs for learning symmetry-based disentanglement in unsupervised learning without any knowledge of the dataset factor information. CFASL incorporates three novel features for learning symmetry-based disentanglement: 1) Injecting inductive bias to align latent vector dimensions to factor-aligned symmetries within an explicit learnable symmetry code-book 2) Learning a composite symmetry to express unknown factors change between two random samples by learning factor-aligned symmetries within the codebook 3) Inducing a group equivariant encoder and decoder in training VAEs with the two conditions. In addition, we propose an extended evaluation metric for multi-factor changes in comparison to disentanglement evaluation in VAEs. In quantitative and in-depth qualitative analysis, CFASL demonstrates a significant improvement of disentanglement in single-factor change, and multi-factor change conditions compared to state-of-the-art methods.