ISA-VAE: Independent Subspace Analysis with Variational Autoencoders
Recent work has shown increased interest in using the Variational Autoencoder (VAE) framework to discover interpretable representations of data in an unsupervised way. These methods have focussed largely on modifying the variational cost function to achieve this goal. However, we show that methods like beta-VAE simplify the tendency of variational inference to underfit causing pathological over-pruning and over-orthogonalization of learned components. In this paper we take a complementary approach: to modify the probabilistic model to encourage structured latent variable representations to be discovered. Specifically, the standard VAE probabilistic model is unidentifiable: the likelihood of the parameters is invariant under rotations of the latent space. This means there is no pressure to identify each true factor of variation with a latent variable. We therefore employ a rich prior distribution, akin to the ICA model, that breaks the rotational symmetry. Extensive quantitative and qualitative experiments demonstrate that the proposed prior mitigates the trade-off introduced by modified cost functions like beta-VAE and TCVAE between reconstruction loss and disentanglement. The proposed prior allows to improve these approaches with respect to both disentanglement and reconstruction quality significantly over the state of the art.
 The authors point out several issues in current VAE approaches, including the rotational symmetric Gaussian prior commonly used. A new perspective on the tradeoff between reconstruction and orthogonalization is provided for VAE, beta-VAE, and beta-TCVAE. By introducing several non rotational-invariant priors, the latent variables* dimensions are more interpretable and disentangled. Competitive quantitative experiment results and promising qualitative results are provided. Overall, I think this paper has proposed some new ideas for the VAE models, which is quite important and should be considered for publication. Here I have some suggestions and I think the authors should be able to resolve these issues in a revision before the final submission: 1) The authors should describe how the new priors proposed work with the "reparameterization trick". 2) The authors should at least provide the necessary implementation details in the appendix, the current manuscript doesn*t seem to contain enough information on the models* details. 3) The description on the experiments and results should be more clear, currently some aspects of the figures may not be easily understood and need some imagination. 4) There are some minor mistakes in both the text and the equations, and there are also some inconsistency in the notations.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
ISA-VAE: Independent Subspace Analysis with Variational Autoencoders
Recent work has shown increased interest in using the Variational Autoencoder (VAE) framework to discover interpretable representations of data in an unsupervised way. These methods have focussed largely on modifying the variational cost function to achieve this goal. However, we show that methods like beta-VAE simplify the tendency of variational inference to underfit causing pathological over-pruning and over-orthogonalization of learned components. In this paper we take a complementary approach: to modify the probabilistic model to encourage structured latent variable representations to be discovered. Specifically, the standard VAE probabilistic model is unidentifiable: the likelihood of the parameters is invariant under rotations of the latent space. This means there is no pressure to identify each true factor of variation with a latent variable. We therefore employ a rich prior distribution, akin to the ICA model, that breaks the rotational symmetry. Extensive quantitative and qualitative experiments demonstrate that the proposed prior mitigates the trade-off introduced by modified cost functions like beta-VAE and TCVAE between reconstruction loss and disentanglement. The proposed prior allows to improve these approaches with respect to both disentanglement and reconstruction quality significantly over the state of the art.
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>



 The authors point out several issues in current VAE approaches, including the rotational symmetric Gaussian prior commonly used. A new perspective on the tradeoff between reconstruction and orthogonalization is provided for VAE, beta-VAE, and beta-TCVAE. By introducing several non rotational-invariant priors, the latent variables* dimensions are more interpretable and disentangled. Competitive quantitative experiment results and promising qualitative results are provided. Overall, I think this paper has proposed some new ideas for the VAE models, which is quite important and should be considered for publication. Here I have some suggestions and I think the authors should be able to resolve these issues in a revision before the final submission: 1) The authors should describe how the new priors proposed work with the "reparameterization trick". 2) The authors should at least provide the necessary implementation details in the appendix, the current manuscript doesn*t seem to contain enough information on the models* details. 3) The description on the experiments and results should be more clear, currently some aspects of the figures may not be easily understood and need some imagination. 4) There are some minor mistakes in both the text and the equations, and there are also some inconsistency in the notations.
assistant
 The authors point out several issues in current VAE approaches, including the rotational symmetric Gaussian prior commonly used. A new perspective on the tradeoff between reconstruction and orthogonalization is provided for VAE, beta-VAE, and beta-TCVAE. By introducing several non rotational-invariant priors, the latent variables* dimensions are more interpretable and disentangled. Competitive quantitative experiment results and promising qualitative results are provided. Overall, I think this paper has proposed some new ideas for the VAE models, which is quite important and should be considered for publication. Here I have some suggestions and I think the authors should be able to resolve these issues in a revision before the final submission: 1) The authors should describe how the new priors proposed work with the "reparameterization trick". 2) The authors should at least provide the necessary implementation details in the appendix, the current manuscript doesn*t seem to contain enough information on the models* details. 3) The description on the experiments and results should be more clear, currently some aspects of the figures may not be easily understood and need some imagination. 4) There are some minor mistakes in both the text and the equations, and there are also some inconsistency in the notations.