# Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions

arXiv: https://arxiv.org/abs/2411.03755 · HTML: https://mlsanity.com/paper/2411.03755/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 30 of 32)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [DRIT++: Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1905.01270/) (2019)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Deep Variational Canonical Correlation Analysis](https://mlsanity.com/paper/1610.03454/) (2016)
- [Harnessing Out-Of-Distribution Examples via Augmenting Content and Style](https://mlsanity.com/paper/2207.03162/) (2022)
- [TransGaGa: Geometry-Aware Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1904.09571/) (2019)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Smoothing the Disentangled Latent Style Space for Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/2106.09016/) (2021)
- [Disentangling Writer and Character Styles for Handwriting Generation](https://mlsanity.com/paper/2303.14736/) (2023)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Collapse by Conditioning: Training Class-conditional GANs with Limited Data](https://mlsanity.com/paper/2201.06578/) (2022)
- [Self-Supervised Disentanglement by Leveraging Structure in Data Augmentations](https://mlsanity.com/paper/2311.08815/) (2023)
- [Generalized Canonical Correlation Analysis: A Subspace Intersection Approach](https://mlsanity.com/paper/2003.11205/) (2020)
- [GP-UNIT: Generative Prior for Versatile Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/2306.04636/) (2023)
- [Revisiting Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2312.13455/) (2023)

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

- [Melodia: Training-Free Music Editing Guided by Attention Probing in Diffusion Models](https://mlsanity.com/paper/2511.08252/) (2025)
- [Content-Style Identification via Differential Independence](https://mlsanity.com/paper/2605.17827/) (2026)

## Abstract (arXiv)

Understanding identifiability of latent content and style variables from unaligned multi-domain data is essential for tasks such as domain translation and data generation. Existing works on content-style identification were often developed under somewhat stringent conditions, e.g., that all latent components are mutually independent and that the dimensions of the content and style variables are known. We introduce a new analytical framework via cross-domain textitlatent distribution matching (LDM), which establishes content-style identifiability under substantially more relaxed conditions. Specifically, we show that restrictive assumptions such as component-wise independence of the latent variables can be removed. Most notably, we prove that prior knowledge of the content and style dimensions is not necessary for ensuring identifiability, if sparsity constraints are properly imposed onto the learned latent representations. Bypassing the knowledge of the exact latent dimension has been a longstanding aspiration in unsupervised representation learning -- our analysis is the first to underpin its theoretical and practical viability. On the implementation side, we recast the LDM formulation into a regularized multi-domain GAN loss with coupled latent variables. We show that the reformulation is equivalent to LDM under mild conditions -- yet requiring considerably less computational resource. Experiments corroborate with our theoretical claims.