Paper:
Graph neural networks have been adopted in numerous applications ranging from learning relational representations to modeling data on irregular domains such as point clouds, social graphs, and molecular structures. Though diverse in nature, graph neural network architectures remain limited by the graph convolution operator whose input and output graphs must have the same structure. Due to this restriction, representational hierarchy can only be built by graph convolution operations followed by non-parameterized pooling or expansion layers. This is very much like early convolutional network architectures, which later have been replaced by more effective parameterized strided and transpose convolution operations in combination with skip connections. In order to bring a similar change to graph convolutional networks, here we introduce the bipartite graph convolution operation, a parameterized transformation between different input and output graphs. Our framework is general enough to subsume conventional graph convolution and pooling as its special cases and supports multi-graph aggregation leading to a class of flexible and adaptable network architectures, termed BiGraphNet. By replacing the sequence of graph convolution and pooling in hierarchical architectures with a single parametric bipartite graph convolution, we (i) answer the question of whether graph pooling is necessary, and (ii) accelerate computations and lower memory requirements in hierarchical networks by eliminating pooling layers. Further, with concrete examples, we demonstrate that the general BiGraphNet formalism (iii) provides the modeling flexibility to build efficient architectures such as graph skip connections, and graph autoencoders.

Review:
This paper proposes a new graph neural network model named BiGraphNet, which introduces a parameterized bipartite graph convolution operation to perform transformation between input and output graphs. The proposed method is claimed to have advantages over existing deep hierarchical GCN architectures mainly in terms of being able to construct analogous building blocks employed by modern lattice CNN architectures and the reduced computational and memory cost. The main weaknesses of this paper are listed as follows:
1) The motivation is relatively weak, which is to bring in the analogous building blocks in CNN architectures. Although GNN is closely related to CNN and RNN, the graph learning tasks may not have the same property as in computer vision or natural language processing. It would be better to convince the readers from the GNN itself and carefully argue the necessity of the proposed method.
2) The experiments in this paper are rather weak and not convincing. First there is no performance comparison to state-of-the-art GNN models, such as DGCNN, DIFFPOOL and GIN, etc. At least on the D&D dataset, many existing models report graph classification accuracy over 78.0, but the baseline method used in this paper only achieves 72.5. Thus it is not fair to claim the proposed method can retain or improve the performance of existing GNN models.
3) The related work comparison is not sufficient. For example, some existing works have already explored to apply skip connections to the graph neural networks, such as [1], which is not mentioned and compared in this paper.
Based on the above arguments, I would like to recommend a reject for this paper.
[1] Xu, Keyulu, et al. "Representation learning on graphs with jumping knowledge networks." arXiv preprint arXiv:1806.03536 (2018).