# Evaluating the Disentanglement of Deep Generative Models through Manifold Topology

arXiv: https://arxiv.org/abs/2006.03680 · HTML: https://mlsanity.com/paper/2006.03680/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2020.

## Built on by (most cited first, 20 of 20)

- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [Activation Landscapes as a Topological Summary of Neural Network Performance](https://mlsanity.com/paper/2110.10136/) (2021)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [The decomposition of the higher-order homology embedding constructed from the k-Laplacian](https://mlsanity.com/paper/2107.10970/) (2021)
- [FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders](https://mlsanity.com/paper/2209.12806/) (2022)
- [Mapping the Multiverse of Latent Representations](https://mlsanity.com/paper/2402.01514/) (2024)
- [Disentanglement Learning via Topology](https://mlsanity.com/paper/2308.12696/) (2023)
- [Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)](https://mlsanity.com/paper/2307.02509/) (2023)
- [Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps](https://mlsanity.com/paper/2203.08189/) (2022)
- [Manifold Characteristics That Predict Downstream Task Performance](https://mlsanity.com/paper/2205.07477/) (2022)
- [Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors](https://mlsanity.com/paper/2210.01760/) (2022)
- [Do Neural Networks Trained with Topological Features Learn Different Internal Representations?](https://mlsanity.com/paper/2211.07697/) (2022)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds](https://mlsanity.com/paper/2402.15058/) (2024)
- [Object Pursuit: Building a Space of Objects via Discriminative Weight Generation](https://mlsanity.com/paper/2112.07954/) (2021)
- [Towards Scalable Topological Regularizers](https://mlsanity.com/paper/2501.14641/) (2025)
- [Commutativity and Disentanglement from the Manifold Perspective](https://mlsanity.com/paper/2210.07857/) (2022)
- [Rethinking Disentanglement under Dependent Factors of Variation](https://mlsanity.com/paper/2408.07016/) (2024)
- [Disentanglement in Difference: Directly Learning Semantically Disentangled Representations by Maximizing Inter-Factor Differences](https://mlsanity.com/paper/2502.03123/) (2025)
- [Disentangled Representation Learning through Unsupervised Symmetry Group Discovery](https://mlsanity.com/paper/2603.11790/) (2026)

## Abstract (arXiv)

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often dependent on an ad-hoc external model or specific to a certain dataset. To address this, we present a method for quantifying disentanglement that only uses the generative model, by measuring the topological similarity of conditional submanifolds in the learned representation. This method showcases both unsupervised and supervised variants. To illustrate the effectiveness and applicability of our method, we empirically evaluate several state-of-the-art models across multiple datasets. We find that our method ranks models similarly to existing methods. We make ourcode publicly available at https://github.com/stanfordmlgroup/disentanglement.