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

TL;DR

This paper introduces a new theoretical framework for identifying content and style variables from unaligned multi-domain data without strict assumptions, enabling more flexible and practical unsupervised representation learning.

Contribution

The authors develop the latent distribution matching (LDM) framework that removes the need for known latent dimensions and independence assumptions, advancing theoretical understanding and practical methods.

Findings

Identifiability is achievable without prior knowledge of latent dimensions.

Sparsity constraints enable content-style separation under relaxed conditions.

The LDM approach is effectively implemented via a regularized multi-domain GAN.

Abstract

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 \textit{latent 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.