Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)

TL;DR

This paper extends nonlinear ICA theory to real-world data by handling unknown intrinsic dimensions and introduces GIN, a modified invertible neural network, demonstrating successful latent variable disentanglement in experiments.

Contribution

It generalizes nonlinear ICA to unknown dimensions and proposes GIN, a new neural network architecture for effective disentanglement in complex data.

Findings

Informative latent variables are automatically separated from noise.

Recovered latent variables correspond to true generative factors.

Experimental validation on artificial data and EMNIST confirms theoretical predictions.

Abstract

A central question of representation learning asks under which conditions it is possible to reconstruct the true latent variables of an arbitrarily complex generative process. Recent breakthrough work by Khemakhem et al. (2019) on nonlinear ICA has answered this question for a broad class of conditional generative processes. We extend this important result in a direction relevant for application to real-world data. First, we generalize the theory to the case of unknown intrinsic problem dimension and prove that in some special (but not very restrictive) cases, informative latent variables will be automatically separated from noise by an estimating model. Furthermore, the recovered informative latent variables will be in one-to-one correspondence with the true latent variables of the generating process, up to a trivial component-wise transformation. Second, we introduce a modification of the RealNVP invertible neural network architecture (Dinh et al. (2016)) which is particularly suitable for this type of problem: the General Incompressible-flow Network (GIN). Experiments on artificial data and EMNIST demonstrate that theoretical predictions are indeed verified in practice. In particular, we provide a detailed set of exactly 22 informative latent variables extracted from EMNIST.