# A Revisit of Total Correlation in Disentangled Variational Auto-Encoder with Partial Disentanglement

arXiv: https://arxiv.org/abs/2502.02279 · HTML: https://mlsanity.com/paper/2502.02279/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [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)
- [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)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE](https://mlsanity.com/paper/2011.04798/) (2020)
- [Disentanglement via Latent Quantization](https://mlsanity.com/paper/2305.18378/) (2023)
- [Exploring Behavior-Relevant and Disentangled Neural Dynamics with Generative Diffusion Models](https://mlsanity.com/paper/2410.09614/) (2024)
- [Independent Subspace Analysis for Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1909.05063/) (2019)
- [α-TCVAE: On the relationship between Disentanglement and Diversity](https://mlsanity.com/paper/2411.00588/) (2024)

## Built on by (most cited first, 3 of 3)

- [BrainStratify: Coarse-to-Fine Disentanglement of Intracranial Neural Dynamics](https://mlsanity.com/paper/2505.20480/) (2025)
- [A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity](https://mlsanity.com/paper/2511.13899/) (2025)
- [Uncovering Semantic Selectivity of Latent Groups in Higher Visual Cortex with Mutual Information-Guided Diffusion](https://mlsanity.com/paper/2510.02182/) (2025)

## Abstract (arXiv)

A fully disentangled variational auto-encoder (VAE) aims to identify disentangled latent components from observations. However, enforcing full independence between all latent components may be too strict for certain datasets. In some cases, multiple factors may be entangled together in a non-separable manner, or a single independent semantic meaning could be represented by multiple latent components within a higher-dimensional manifold. To address such scenarios with greater flexibility, we develop the Partially Disentangled VAE (PDisVAE), which generalizes the total correlation (TC) term in fully disentangled VAEs to a partial correlation (PC) term. This framework can handle group-wise independence and can naturally reduce to either the standard VAE or the fully disentangled VAE. Validation through three synthetic experiments demonstrates the correctness and practicality of PDisVAE. When applied to real-world datasets, PDisVAE discovers valuable information that is difficult to find using fully disentangled VAEs, implying its versatility and effectiveness.