  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.
