Likelihood-based Permutation Invariant Loss Function for Probability Distributions
We propose a permutation-invariant loss function designed for the neural networks reconstructing a set of elements without considering the order within its vector representation. Unlike popular approaches for encoding and decoding a set, our work does not rely on a carefully engineered network topology nor by any additional sequential algorithm. The proposed method, Set Cross Entropy, has a natural information-theoretic interpretation and is related to the metrics defined for sets. We evaluate the proposed approach in two object reconstruction tasks and a rule learning task.
 The paper is understandable and the question addressed is interesting. The use of log likelihoods to metrize distances between sets, although not new, is used quite effectively to address the issue of label switching in sets. Although the run time is O(N^2), the metric can be computed in a parallelized manner. The question of comparing sets of different sample sizes would be a valuable extension to the work. Although I think the proposed loss function addresses some important issues, would like to defer the question of acceptance/rejection to other reviewers due to lack of expertise in related areas.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Likelihood-based Permutation Invariant Loss Function for Probability Distributions
We propose a permutation-invariant loss function designed for the neural networks reconstructing a set of elements without considering the order within its vector representation. Unlike popular approaches for encoding and decoding a set, our work does not rely on a carefully engineered network topology nor by any additional sequential algorithm. The proposed method, Set Cross Entropy, has a natural information-theoretic interpretation and is related to the metrics defined for sets. We evaluate the proposed approach in two object reconstruction tasks and a rule learning task.
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 paper is understandable and the question addressed is interesting. The use of log likelihoods to metrize distances between sets, although not new, is used quite effectively to address the issue of label switching in sets. Although the run time is O(N^2), the metric can be computed in a parallelized manner. The question of comparing sets of different sample sizes would be a valuable extension to the work. Although I think the proposed loss function addresses some important issues, would like to defer the question of acceptance/rejection to other reviewers due to lack of expertise in related areas.
assistant
 The paper is understandable and the question addressed is interesting. The use of log likelihoods to metrize distances between sets, although not new, is used quite effectively to address the issue of label switching in sets. Although the run time is O(N^2), the metric can be computed in a parallelized manner. The question of comparing sets of different sample sizes would be a valuable extension to the work. Although I think the proposed loss function addresses some important issues, would like to defer the question of acceptance/rejection to other reviewers due to lack of expertise in related areas.