On the Identifiability of Quantized Factors

TL;DR

This paper introduces a new form of identifiability called quantized factor identifiability, demonstrating that quantized latent factors can be recovered under certain conditions even with nonlinear mappings, expanding the scope of disentanglement theory.

Contribution

It proves that quantized latent factors are identifiable under nonlinear diffeomorphisms with minimal assumptions, a significant advancement over previous impossibility results.

Findings

Quantized factors can be recovered under generic nonlinear transformations.

Identifiability holds when latent factors have independent discontinuities.

The work broadens the understanding of disentanglement in nonlinear models.

Abstract

Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.