On the Identifiability of Quantized Factors
This provides a theoretical foundation for disentanglement in machine learning, addressing a key limitation in unsupervised learning.
The paper tackles the impossibility of recovering independent latent factors in unsupervised i.i.d. settings by showing that quantized latent factors can be recovered under a generic nonlinear diffeomorphism, assuming independent discontinuities in their density.
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.