  Graph Neural Networks (GNNs) are attracting growing attention due to their
effectiveness and flexibility in modeling a variety of graph-structured data.
Exiting GNN architectures usually adopt simple pooling operations (eg. sum,
average, max) when aggregating messages from a local neighborhood for updating
node representation or pooling node representations from the entire graph to
compute the graph representation. Though simple and effective, these linear
operations do not model high-order non-linear interactions among nodes. We
propose the Tensorized Graph Neural Network (tGNN), a highly expressive GNN
architecture relying on tensor decomposition to model high-order non-linear
node interactions. tGNN leverages the symmetric CP decomposition to efficiently
parameterize permutation-invariant multilinear maps for modeling node
interactions. Theoretical and empirical analysis on both node and graph
classification tasks show the superiority of tGNN over competitive baselines.
In particular, tGNN achieves the most solid results on two OGB node
classification datasets and one OGB graph classification dataset.
