  Graph Neural Nets (GNNs) have received increasing attentions, partially due
to their superior performance in many node and graph classification tasks.
However, there is a lack of understanding on what they are learning and how
sophisticated the learned graph functions are. In this work, we propose a
dissection of GNNs on graph classification into two parts: 1) the graph
filtering, where graph-based neighbor aggregations are performed, and 2) the
set function, where a set of hidden node features are composed for prediction.
To study the importance of both parts, we propose to linearize them separately.
We first linearize the graph filtering function, resulting Graph Feature
Network (GFN), which is a simple lightweight neural net defined on a
\textit{set} of graph augmented features. Further linearization of GFN's set
function results in Graph Linear Network (GLN), which is a linear function.
Empirically we perform evaluations on common graph classification benchmarks.
To our surprise, we find that, despite the simplification, GFN could match or
exceed the best accuracies produced by recently proposed GNNs (with a fraction
of computation cost), while GLN underperforms significantly. Our results
demonstrate the importance of non-linear set function, and suggest that linear
graph filtering with non-linear set function is an efficient and powerful
scheme for modeling existing graph classification benchmarks.
