Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: The paper proposed a method to model the graph topological evolution from the spectral domain by developing a new generalized graph kernel. The new graph kernels cover many existing graph kernels as well as their combination and composition as special cases. The idea of spectral graph translation and its integration with deep learning is interesting, especially considering that most previous spectral graph neural networks only transform the graph signal instead of graph structures. However, I do have some concerns of papers.

1.	My major concern is the soundness of keeping eigenvectors unchanged in the evolution. Although the authors claim that in previous studies eigenvectors are found stable in evolution, it is very counter-intuitive, and I am not sure it is the case for all types of graphs. Let us look at the proof of Lemma 3.1, obviously $L^\prime$ does not necessarily have the same eigenvectors, and $U^TL^\prime U$ is not a diagonal matrix, so this loss is actually very large in many cases. That is to say, the evolution model does not have enough expressive power to recover the $L^\prime$.
2.	Spectral graph translation looks interesting, but the main idea comes from Kunegis et al. (2010). Despite of a new designed graph kernel and adding nonlinear activations, the contributions seem not so significant.
3.	In Kunegis et al. (2010), they consider the evolution of adjacency matrix $A$, but in this paper the authors use the Laplacian matrix $L$. If there any reason to make this choice? Also, I think some of the conclusions (e.g. stable eigenvectors) in Kunegis et al. (2010) may not work since $L$ is used instesd of $A$.
4.    The correlation metric is acceptable, but it will be much better if the authors can do more analysis. For example, why not add the link prediction task as in Kunegis et al. (2010)? BTW, is correlation analysis used before in previous graph evolution papers? (if so, please add a reference)  

review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: This paper proposes a spectral graph neural network based on a graph kernel to predict graph evolution. The overall idea is interesting and the biggest advantage is scalability of the framework to large graphs in terms of time and parameter complexity. 
The major drawback of the paper is the lack of experimentation with real datasets. Based on the results from four datasets they used, the efficacy of their proposed method is unclear. The synthetic datasets are hard to admit in this case.
Note: I could not verify the theory in detail yet. 
review_title: Official Blind Review #1

Meta-review: The reviewers kept their scores after the author response period, pointing to continued concerns with methodology, needing increased exposition in parts, and not being able to verify theoretical results. As such, my recommendation is to improve the clarity around the methodological and theoretical contributions in a revision.
Decision: Reject