High-Order Pooling for Graph Neural Networks with Tensor Decomposition

TL;DR

This paper introduces tGNN, a novel graph neural network architecture that uses tensor decomposition to model high-order non-linear interactions among nodes, surpassing traditional pooling methods in classification tasks.

Contribution

The paper proposes tGNN, which employs symmetric CP tensor decomposition to efficiently capture complex node interactions, enhancing GNN expressiveness.

Findings

tGNN outperforms baseline models on OGB node classification datasets.

tGNN achieves superior results on OGB graph classification dataset.

Theoretical analysis confirms the model's ability to capture high-order interactions.

Abstract

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.