Covariant Compositional Networks For Learning Graphs
Most existing neural networks for learning graphs deal with the issue of permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a limitation on their representation power, and instead propose a new general architecture for representing objects consisting of a hierarchy of parts, which we call Covariant Compositional Networks (CCNs). Here covariance means that the activation of each neuron must transform in a specific way under permutations, similarly to steerability in CNNs. We achieve covariance by making each activation transform according to a tensor representation of the permutation group, and derive the corresponding tensor aggregation rules that each neuron must implement. Experiments show that CCNs can outperform competing methods on some standard graph learning benchmarks.
 The paper presents a generalized architecture for representing generic compositional objects, such as graphs, which is called covariant compositional networks (CCN). Although, the paper is well structured and quite well written, its dense information and its long size made it hard to follow in depth. Some parts of the paper should have been moved to appendix. As far as the evaluation, the proposed method seems to outperform in a number of tasks/datasets compare to SoA methods, but it is not really clear whether the out-performance is of statistical significance. Moreover, in Table 1, training performances shouldn*t be shown, while in Table 3, RMSE it would be nice to be shown in order to gain a complete image of the actual performance.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Covariant Compositional Networks For Learning Graphs
Most existing neural networks for learning graphs deal with the issue of permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a limitation on their representation power, and instead propose a new general architecture for representing objects consisting of a hierarchy of parts, which we call Covariant Compositional Networks (CCNs). Here covariance means that the activation of each neuron must transform in a specific way under permutations, similarly to steerability in CNNs. We achieve covariance by making each activation transform according to a tensor representation of the permutation group, and derive the corresponding tensor aggregation rules that each neuron must implement. Experiments show that CCNs can outperform competing methods on some standard graph learning benchmarks.
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 presents a generalized architecture for representing generic compositional objects, such as graphs, which is called covariant compositional networks (CCN). Although, the paper is well structured and quite well written, its dense information and its long size made it hard to follow in depth. Some parts of the paper should have been moved to appendix. As far as the evaluation, the proposed method seems to outperform in a number of tasks/datasets compare to SoA methods, but it is not really clear whether the out-performance is of statistical significance. Moreover, in Table 1, training performances shouldn*t be shown, while in Table 3, RMSE it would be nice to be shown in order to gain a complete image of the actual performance.
assistant
 The paper presents a generalized architecture for representing generic compositional objects, such as graphs, which is called covariant compositional networks (CCN). Although, the paper is well structured and quite well written, its dense information and its long size made it hard to follow in depth. Some parts of the paper should have been moved to appendix. As far as the evaluation, the proposed method seems to outperform in a number of tasks/datasets compare to SoA methods, but it is not really clear whether the out-performance is of statistical significance. Moreover, in Table 1, training performances shouldn*t be shown, while in Table 3, RMSE it would be nice to be shown in order to gain a complete image of the actual performance.