# Operationalizing Quantized Disentanglement

arXiv: https://arxiv.org/abs/2511.20927 · HTML: https://mlsanity.com/paper/2511.20927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [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)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [The Hessian Penalty: A Weak Prior for Unsupervised Disentanglement](https://mlsanity.com/paper/2008.10599/) (2020)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Function Classes for Identifiable Nonlinear Independent Component Analysis](https://mlsanity.com/paper/2208.06406/) (2022)
- [Disentanglement via Latent Quantization](https://mlsanity.com/paper/2305.18378/) (2023)
- [Disentanglement of Correlated Factors via Hausdorff Factorized Support](https://mlsanity.com/paper/2210.07347/) (2022)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [DCI-ES: An Extended Disentanglement Framework with Connections to Identifiability](https://mlsanity.com/paper/2210.00364/) (2022)
- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Tripod: Three Complementary Inductive Biases for Disentangled Representation Learning](https://mlsanity.com/paper/2404.10282/) (2024)
- [On the Identifiability of Quantized Factors](https://mlsanity.com/paper/2306.16334/) (2023)

## Abstract (arXiv)

Recent theoretical work established the unsupervised identifiability of quantized factors under any diffeomorphism. The theory assumes that quantization thresholds correspond to axis-aligned discontinuities in the probability density of the latent factors. By constraining a learned map to have a density with axis-aligned discontinuities, we can recover the quantization of the factors. However, translating this high-level principle into an effective practical criterion remains challenging, especially under nonlinear maps. Here, we develop a criterion for unsupervised disentanglement by encouraging axis-aligned discontinuities. Discontinuities manifest as sharp changes in the estimated density of factors and form what we call cliffs. Following the definition of independent discontinuities from the theory, we encourage the location of the cliffs along a factor to be independent of the values of the other factors. We show that our method, Cliff, outperforms the baselines on all disentanglement benchmarks, demonstrating its effectiveness in unsupervised disentanglement.