We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information. The proposed feature-crossing layer fuses intermediate features between two scales for mutual enhancement by improving information flow and enriching multiscale features at hidden layers.

We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information.

Additional Feedback: This paper proposes GXN for modeling graph data. Overall, the proposed approach is quite intuitive, and extensive experiment on graph classification and vertex classification proves the effectiveness of the approach. I have the following concerns regarding the paper: 1. The relation to existing graph pooling techniques is not clear. One key component of GXN is vertex informax pooling, which is used to create multi-scale graphs and is thus related to existing graph pooling techniques.

The paper make a novel contribution by introducing graph cross networks, and demonstrate it usefulness in practical example. While initial concern related to the clarity of the paper, the reviewers found that the authors have done a good job in summarizing their work and addressed most of their concerns in the rebuttal. The two key components of GXN are a novel vertex infomax pooling, which creates multiscale graphs in a trainable manner and a novel feature crossing layer, enabling feature interchange across scales. This work has been compared their work with prior methods and surpassed all of them, which meets the bar for a NeurIPS presentation. While it does not impact the decision, during the discussion, the following points were left unanswered, and it would be great if the authors could take the following points in their reviews: (1) In VIPool, P_v, P_n, P_{v,n} are all discrete distributions (although the feature vector can be continuous, as there are V nodes, the sample from P_v can only have at most V values, so it is a discrete distribution).

We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information.