Title: Identifying Informative Latent Variables Learned by GIN via Mutual Information. Abstract: How to learn a good representation of data is one of the most important topics of machine learning.  Disentanglement of representations, though believed to be the core feature of good representations, has caused a lot of debates and discussions in recent. Sorrenson et al. (2020), using the techniques developed in nonlinear independent analysis theory, show that general incompressible-flow networks (GIN) can recover the underlying latent variables that generate the data, and thus can provide a compact and disentangled representation. However, in this paper, we point out that the method taken by GIN for informative latent variables identification is not theoretically supported and can be disproved by experiments.  We propose to use the mutual information between latent variables and the auxiliary variable to correctly identify informative latent variables.  We directly verify the improvement brought by our method in experiments on synthetic data.  We further show the advantage of our method on various downstream tasks including classification, outlier detection and adversarial attack defence.