Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs
We consider a simple and overarching representation for permutation-invariant functions of sequences (or set functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.
 In this paper, the authors presented a new pooling method called Janossy Pooling (JP), which is designed to better capture high-order information by addressing two limitations of existing works - fixed pooling function and fixed-size inputs. The studied problem is important and the motivation is clear, where the inputs are sets of objects such as values or vectors and how we can learn a good aggregation function to maximally preserve the information in the original sequence. The authors attacked this problem by firstly formally formulating this problem and introducing a general approach as well as a few of approximation methods to realize it in practice. They also discussed the connections of this work and some existing works such as deep set, which I found is quite useful. In general, JP was proposed to learn permutation-invariant function for aggregating the information of the input sequence. The basic idea of JP is to simply take all generated order of sequences from the original sequence input, which however I found is not new since it has been conceptually discussed already in the literature. Since this approach is computationally prohibitive, there are several ways of approximations to approach the solution. As the authors are aware of the existing works in the literature, these approaches were discussed before either in the same context or in some particular learning tasks. From this perspective, the proposed solutions are not novel either. The experimental results are particularly weak. It is little interesting on the first toy problem and the results on graph embedding are not promising. In Table 2, it is clearly shown that the LSTM aggregation functions on the randomly sampled sequences are really beating the simple mean aggregation function. I think the authors need much more experiments to demonstrate why we need LSTM based pooling for realizing JP in terms of both the final accuracy and computational cost. ------------------------------------------------- After reading the authors* rebuttals, they have addressed part of my concerns but I still think the current form is not below the acceptance threshold due to its weak experimental results and unclear technical details.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs
We consider a simple and overarching representation for permutation-invariant functions of sequences (or set functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.
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>



 In this paper, the authors presented a new pooling method called Janossy Pooling (JP), which is designed to better capture high-order information by addressing two limitations of existing works - fixed pooling function and fixed-size inputs. The studied problem is important and the motivation is clear, where the inputs are sets of objects such as values or vectors and how we can learn a good aggregation function to maximally preserve the information in the original sequence. The authors attacked this problem by firstly formally formulating this problem and introducing a general approach as well as a few of approximation methods to realize it in practice. They also discussed the connections of this work and some existing works such as deep set, which I found is quite useful. In general, JP was proposed to learn permutation-invariant function for aggregating the information of the input sequence. The basic idea of JP is to simply take all generated order of sequences from the original sequence input, which however I found is not new since it has been conceptually discussed already in the literature. Since this approach is computationally prohibitive, there are several ways of approximations to approach the solution. As the authors are aware of the existing works in the literature, these approaches were discussed before either in the same context or in some particular learning tasks. From this perspective, the proposed solutions are not novel either. The experimental results are particularly weak. It is little interesting on the first toy problem and the results on graph embedding are not promising. In Table 2, it is clearly shown that the LSTM aggregation functions on the randomly sampled sequences are really beating the simple mean aggregation function. I think the authors need much more experiments to demonstrate why we need LSTM based pooling for realizing JP in terms of both the final accuracy and computational cost. ------------------------------------------------- After reading the authors* rebuttals, they have addressed part of my concerns but I still think the current form is not below the acceptance threshold due to its weak experimental results and unclear technical details.
assistant
 In this paper, the authors presented a new pooling method called Janossy Pooling (JP), which is designed to better capture high-order information by addressing two limitations of existing works - fixed pooling function and fixed-size inputs. The studied problem is important and the motivation is clear, where the inputs are sets of objects such as values or vectors and how we can learn a good aggregation function to maximally preserve the information in the original sequence. The authors attacked this problem by firstly formally formulating this problem and introducing a general approach as well as a few of approximation methods to realize it in practice. They also discussed the connections of this work and some existing works such as deep set, which I found is quite useful. In general, JP was proposed to learn permutation-invariant function for aggregating the information of the input sequence. The basic idea of JP is to simply take all generated order of sequences from the original sequence input, which however I found is not new since it has been conceptually discussed already in the literature. Since this approach is computationally prohibitive, there are several ways of approximations to approach the solution. As the authors are aware of the existing works in the literature, these approaches were discussed before either in the same context or in some particular learning tasks. From this perspective, the proposed solutions are not novel either. The experimental results are particularly weak. It is little interesting on the first toy problem and the results on graph embedding are not promising. In Table 2, it is clearly shown that the LSTM aggregation functions on the randomly sampled sequences are really beating the simple mean aggregation function. I think the authors need much more experiments to demonstrate why we need LSTM based pooling for realizing JP in terms of both the final accuracy and computational cost. ------------------------------------------------- After reading the authors* rebuttals, they have addressed part of my concerns but I still think the current form is not below the acceptance threshold due to its weak experimental results and unclear technical details.