Semantic Interpolation in Implicit Models
In implicit models, one often interpolates between sampled points in latent space. As we show in this paper, care needs to be taken to match-up the distributional assumptions on code vectors with the geometry of the interpolating paths. Otherwise, typical assumptions about the quality and semantics of in-between points may not be justified. Based on our analysis we propose to modify the prior code distribution to put significantly more probability mass closer to the origin. As a result, linear interpolation paths are not only shortest paths, but they are also guaranteed to pass through high-density regions, irrespective of the dimensionality of the latent space. Experiments on standard benchmark image datasets demonstrate clear visual improvements in the quality of the generated samples and exhibit more meaningful interpolation paths.
 The authors discuss a direct Gamma sampling method for the interpolated samples in GANs, and show the improvements over usual normal sampling for CelebA, MNIST, CIFAR and SVHN datasets. The method involves a nice, albeit minor, trick, where the chi-squared distribution of the sum of the z_{i}^{2} has its dependence on the dimensionality removed. However I am not convinced by the distribution of .|z^.prime.|^{2} in the first place (eqn (2)): the samples from the gaussian will be approximately orthogonal in high dimensions, but the inner product will be at least O(1). Thus although the .|z_{0}.|^{2} and .|z_{1}.|^{2} are chi-squared/gamma, I don*t think .|z^.prime.|^{2} is exactly gamma in general. The experiments do show that the interpolated samples are qualitatively better, but a thorough empirical analysis for different dimensionalities would be welcome. Figures 2 and 3 do not add anything to the story, since 2 is just a plot of gamma pdfs and 3 shows the difference between the constant KL and the normal case that is linear in d. Overall I think the trick needs to be motivated better, and the experiments improved to really show the import of the d-independence of the KL. Thus I think this paper is below the acceptance threshold.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Semantic Interpolation in Implicit Models
In implicit models, one often interpolates between sampled points in latent space. As we show in this paper, care needs to be taken to match-up the distributional assumptions on code vectors with the geometry of the interpolating paths. Otherwise, typical assumptions about the quality and semantics of in-between points may not be justified. Based on our analysis we propose to modify the prior code distribution to put significantly more probability mass closer to the origin. As a result, linear interpolation paths are not only shortest paths, but they are also guaranteed to pass through high-density regions, irrespective of the dimensionality of the latent space. Experiments on standard benchmark image datasets demonstrate clear visual improvements in the quality of the generated samples and exhibit more meaningful interpolation paths.
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 discuss a direct Gamma sampling method for the interpolated samples in GANs, and show the improvements over usual normal sampling for CelebA, MNIST, CIFAR and SVHN datasets. The method involves a nice, albeit minor, trick, where the chi-squared distribution of the sum of the z_{i}^{2} has its dependence on the dimensionality removed. However I am not convinced by the distribution of .|z^.prime.|^{2} in the first place (eqn (2)): the samples from the gaussian will be approximately orthogonal in high dimensions, but the inner product will be at least O(1). Thus although the .|z_{0}.|^{2} and .|z_{1}.|^{2} are chi-squared/gamma, I don*t think .|z^.prime.|^{2} is exactly gamma in general. The experiments do show that the interpolated samples are qualitatively better, but a thorough empirical analysis for different dimensionalities would be welcome. Figures 2 and 3 do not add anything to the story, since 2 is just a plot of gamma pdfs and 3 shows the difference between the constant KL and the normal case that is linear in d. Overall I think the trick needs to be motivated better, and the experiments improved to really show the import of the d-independence of the KL. Thus I think this paper is below the acceptance threshold.
assistant
 The authors discuss a direct Gamma sampling method for the interpolated samples in GANs, and show the improvements over usual normal sampling for CelebA, MNIST, CIFAR and SVHN datasets. The method involves a nice, albeit minor, trick, where the chi-squared distribution of the sum of the z_{i}^{2} has its dependence on the dimensionality removed. However I am not convinced by the distribution of .|z^.prime.|^{2} in the first place (eqn (2)): the samples from the gaussian will be approximately orthogonal in high dimensions, but the inner product will be at least O(1). Thus although the .|z_{0}.|^{2} and .|z_{1}.|^{2} are chi-squared/gamma, I don*t think .|z^.prime.|^{2} is exactly gamma in general. The experiments do show that the interpolated samples are qualitatively better, but a thorough empirical analysis for different dimensionalities would be welcome. Figures 2 and 3 do not add anything to the story, since 2 is just a plot of gamma pdfs and 3 shows the difference between the constant KL and the normal case that is linear in d. Overall I think the trick needs to be motivated better, and the experiments improved to really show the import of the d-independence of the KL. Thus I think this paper is below the acceptance threshold.