The Usual Suspects? Reassessing Blame for VAE Posterior Collapse
In narrow asymptotic settings Gaussian VAE models of continuous data have been shown to possess global optima aligned with ground-truth distributions. Even so, it is well known that poor solutions whereby the latent posterior collapses to an uninformative prior are sometimes obtained in practice. However, contrary to conventional wisdom that largely assigns blame for this phenomena on the undue influence of KL-divergence regularization, we will argue that posterior collapse is, at least in part, a direct consequence of bad local minima inherent to the loss surface of deep autoencoder networks. In particular, we prove that even small nonlinear perturbations of affine VAE decoder models can produce such minima, and in deeper models, analogous minima can force the VAE to behave like an aggressive truncation operator, provably discarding information along all latent dimensions in certain circumstances. Regardless, the underlying message here is not meant to undercut valuable existing explanations of posterior collapse, but rather, to refine the discussion and elucidate alternative risk factors that may have been previously underappreciated.
This paper tries to establish an explanation for the posterior collapse by linking the phenomenon to local minima. If I am understanding correctly, the final conclusion reads along the lines of *if the reconstruction error is high, then the posterior distribution will follow the prior distribution*. They also provide some experimental data to suggest that when the reconstruction error is high, the distribution of the latents tend to follow the prior distribution more closely. Although I really liked section 3 where authors establish the different ways in which `posterior collapse* can be defined, overall I am not sure if I can extract a useful insight or solution out of this paper. When the reconstruction error is large, the VAE is practically not useful. Also, I don*t think I am on board with continuing to use the standard Gaussian prior. Several papers (such as the cited Vampprior paper) showed that one can very successfully use GMM like priors, which reduces the burden on the autoencoder. Even though I liked the exposition in the first half of the paper, I don*t think I find the contributions of this paper very useful, as one can actually learn the prior and get good autoencoder reconstructions while obtaining a good match between the prior and the posterior, without having degenerate posterior distribution which is independent from the data distribution. All in all, I think using a standard gaussian prior is not a good idea, and that fact renders the explanations provided in this paper obsolete in my opinion. Is there any reason why we would want to utilize a simplistic prior such as the standard Gaussian prior? Do you have any insights with regards to whether the explanations in this paper would still hold with more expressive prior distributions? In general, I have found section 5 hard follow. And to reiterate, the main arguments seem to be centered around autoencoders which cannot reconstruct well, as the authors also consider the deterministic autoencoder. If the autoencoder can not reconstruct well, it is not reasonable to expect a regularized autoencoder such as VAE to reconstruct, better, and therefore the VAE is already is a regime where it is not useful anyhow. I think the authors should think about the cases where the reconstruction error is low, and see if there is an issue of posterior collapse in those setups.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
The Usual Suspects? Reassessing Blame for VAE Posterior Collapse
In narrow asymptotic settings Gaussian VAE models of continuous data have been shown to possess global optima aligned with ground-truth distributions. Even so, it is well known that poor solutions whereby the latent posterior collapses to an uninformative prior are sometimes obtained in practice. However, contrary to conventional wisdom that largely assigns blame for this phenomena on the undue influence of KL-divergence regularization, we will argue that posterior collapse is, at least in part, a direct consequence of bad local minima inherent to the loss surface of deep autoencoder networks. In particular, we prove that even small nonlinear perturbations of affine VAE decoder models can produce such minima, and in deeper models, analogous minima can force the VAE to behave like an aggressive truncation operator, provably discarding information along all latent dimensions in certain circumstances. Regardless, the underlying message here is not meant to undercut valuable existing explanations of posterior collapse, but rather, to refine the discussion and elucidate alternative risk factors that may have been previously underappreciated.
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>



This paper tries to establish an explanation for the posterior collapse by linking the phenomenon to local minima. If I am understanding correctly, the final conclusion reads along the lines of *if the reconstruction error is high, then the posterior distribution will follow the prior distribution*. They also provide some experimental data to suggest that when the reconstruction error is high, the distribution of the latents tend to follow the prior distribution more closely. Although I really liked section 3 where authors establish the different ways in which `posterior collapse* can be defined, overall I am not sure if I can extract a useful insight or solution out of this paper. When the reconstruction error is large, the VAE is practically not useful. Also, I don*t think I am on board with continuing to use the standard Gaussian prior. Several papers (such as the cited Vampprior paper) showed that one can very successfully use GMM like priors, which reduces the burden on the autoencoder. Even though I liked the exposition in the first half of the paper, I don*t think I find the contributions of this paper very useful, as one can actually learn the prior and get good autoencoder reconstructions while obtaining a good match between the prior and the posterior, without having degenerate posterior distribution which is independent from the data distribution. All in all, I think using a standard gaussian prior is not a good idea, and that fact renders the explanations provided in this paper obsolete in my opinion. Is there any reason why we would want to utilize a simplistic prior such as the standard Gaussian prior? Do you have any insights with regards to whether the explanations in this paper would still hold with more expressive prior distributions? In general, I have found section 5 hard follow. And to reiterate, the main arguments seem to be centered around autoencoders which cannot reconstruct well, as the authors also consider the deterministic autoencoder. If the autoencoder can not reconstruct well, it is not reasonable to expect a regularized autoencoder such as VAE to reconstruct, better, and therefore the VAE is already is a regime where it is not useful anyhow. I think the authors should think about the cases where the reconstruction error is low, and see if there is an issue of posterior collapse in those setups.
assistant
This paper tries to establish an explanation for the posterior collapse by linking the phenomenon to local minima. If I am understanding correctly, the final conclusion reads along the lines of *if the reconstruction error is high, then the posterior distribution will follow the prior distribution*. They also provide some experimental data to suggest that when the reconstruction error is high, the distribution of the latents tend to follow the prior distribution more closely. Although I really liked section 3 where authors establish the different ways in which `posterior collapse* can be defined, overall I am not sure if I can extract a useful insight or solution out of this paper. When the reconstruction error is large, the VAE is practically not useful. Also, I don*t think I am on board with continuing to use the standard Gaussian prior. Several papers (such as the cited Vampprior paper) showed that one can very successfully use GMM like priors, which reduces the burden on the autoencoder. Even though I liked the exposition in the first half of the paper, I don*t think I find the contributions of this paper very useful, as one can actually learn the prior and get good autoencoder reconstructions while obtaining a good match between the prior and the posterior, without having degenerate posterior distribution which is independent from the data distribution. All in all, I think using a standard gaussian prior is not a good idea, and that fact renders the explanations provided in this paper obsolete in my opinion. Is there any reason why we would want to utilize a simplistic prior such as the standard Gaussian prior? Do you have any insights with regards to whether the explanations in this paper would still hold with more expressive prior distributions? In general, I have found section 5 hard follow. And to reiterate, the main arguments seem to be centered around autoencoders which cannot reconstruct well, as the authors also consider the deterministic autoencoder. If the autoencoder can not reconstruct well, it is not reasonable to expect a regularized autoencoder such as VAE to reconstruct, better, and therefore the VAE is already is a regime where it is not useful anyhow. I think the authors should think about the cases where the reconstruction error is low, and see if there is an issue of posterior collapse in those setups.