Disentanglement through Nonlinear ICA with General Incompressible-flow Networks (GIN)
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.
Based on a recent work on identifying the joint distribution over observed and latent variables, the paper presents an extension of it, where the dimension of the latent space is not assumed to be known. Moreover, the authors propose a new neural network architecture based on previous propositions (RealNVP and NICE) to perform this identification. The paper*s presentation is relatively clear, although all the theoretical results are relegated to the appendix. The extension to unknown latent space dimension seems to be quite straightforward, given the recent work that this paper is based on. However, the experimental results performed on EMNIST are quite convincing and the results are interesting. Overall, I think this paper would be interesting to the ICLR audience. It seems currently that there is a need to choose a dimension to be large enough (i.e., larger than the true dimension of the latent space). I would have appreciated some discussion (and some experiments) if this dimension is chosen too small. Also, when the dimension is chosen large enough, the non-informative learned latent variables are determined by looking at their standard deviations. Do they always have to be small compared to the informative latent variables?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Disentanglement through Nonlinear ICA with General Incompressible-flow Networks (GIN)
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.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



Based on a recent work on identifying the joint distribution over observed and latent variables, the paper presents an extension of it, where the dimension of the latent space is not assumed to be known. Moreover, the authors propose a new neural network architecture based on previous propositions (RealNVP and NICE) to perform this identification. The paper*s presentation is relatively clear, although all the theoretical results are relegated to the appendix. The extension to unknown latent space dimension seems to be quite straightforward, given the recent work that this paper is based on. However, the experimental results performed on EMNIST are quite convincing and the results are interesting. Overall, I think this paper would be interesting to the ICLR audience. It seems currently that there is a need to choose a dimension to be large enough (i.e., larger than the true dimension of the latent space). I would have appreciated some discussion (and some experiments) if this dimension is chosen too small. Also, when the dimension is chosen large enough, the non-informative learned latent variables are determined by looking at their standard deviations. Do they always have to be small compared to the informative latent variables?
assistant
Based on a recent work on identifying the joint distribution over observed and latent variables, the paper presents an extension of it, where the dimension of the latent space is not assumed to be known. Moreover, the authors propose a new neural network architecture based on previous propositions (RealNVP and NICE) to perform this identification. The paper*s presentation is relatively clear, although all the theoretical results are relegated to the appendix. The extension to unknown latent space dimension seems to be quite straightforward, given the recent work that this paper is based on. However, the experimental results performed on EMNIST are quite convincing and the results are interesting. Overall, I think this paper would be interesting to the ICLR audience. It seems currently that there is a need to choose a dimension to be large enough (i.e., larger than the true dimension of the latent space). I would have appreciated some discussion (and some experiments) if this dimension is chosen too small. Also, when the dimension is chosen large enough, the non-informative learned latent variables are determined by looking at their standard deviations. Do they always have to be small compared to the informative latent variables?