# Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs

arXiv: https://arxiv.org/abs/2502.03740 · HTML: https://mlsanity.com/paper/2502.03740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [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)
- [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)
- [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)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEs](https://mlsanity.com/paper/1901.07017/) (2019)
- [Joint Disentangling and Adaptation for Cross-Domain Person Re-Identification](https://mlsanity.com/paper/2007.10315/) (2020)
- [Understanding Failures of Deep Networks via Robust Feature Extraction](https://mlsanity.com/paper/2012.01750/) (2020)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Cross-Dataset Person Re-Identification via Unsupervised Pose Disentanglement and Adaptation](https://mlsanity.com/paper/1909.09675/) (2019)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Learning Disentangled Representation by Exploiting Pretrained Generative Models: A Contrastive Learning View](https://mlsanity.com/paper/2102.10543/) (2021)
- [Contrastively Disentangled Sequential Variational Autoencoder](https://mlsanity.com/paper/2110.12091/) (2021)
- [Progressive Learning and Disentanglement of Hierarchical Representations](https://mlsanity.com/paper/2002.10549/) (2020)
- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (2021)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [Learning Discrete and Continuous Factors of Data via Alternating Disentanglement](https://mlsanity.com/paper/1905.09432/) (2019)
- [Learning to Manipulate Individual Objects in an Image](https://mlsanity.com/paper/2004.05495/) (2020)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [The Convolution Exponential and Generalized Sylvester Flows](https://mlsanity.com/paper/2006.01910/) (2020)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Deep Exponential Families](https://mlsanity.com/paper/1411.2581/) (2014)
- [On Incorporating Inductive Biases into VAEs](https://mlsanity.com/paper/2106.13746/) (2021)
- [Bayes-Factor-VAE: Hierarchical Bayesian Deep Auto-Encoder Models for Factor Disentanglement](https://mlsanity.com/paper/1909.02820/) (2019)
- [Generative Flows with Matrix Exponential](https://mlsanity.com/paper/2007.09651/) (2020)

## Abstract (arXiv)

Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains challenging. In this paper, we propose a novel method, called Multiple Invertible and Partial-Equivariant Transformation (MIPE-Transformation), which integrates two main parts: (1) Invertible and Partial-Equivariant Transformation (IPE-Transformation), guaranteeing an invertible latent-to-transformed-latent mapping while preserving partial input-to-latent equivariance in the transformed latent space; and (2) Exponential-Family Conversion (EF-Conversion) to extend the standard Gaussian prior to an approximate exponential family via a learnable conversion. In experiments on the 3D Cars, 3D Shapes, and dSprites datasets, MIPE-Transformation improves the disentanglement performance of state-of-the-art VAEs.