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Graph Neural Networks (GNNs) are powerful to learn the representation ofgraph-structured data. Most of the GNNs use the message-passing scheme, wherethe embedding of a node is iteratively updated by aggregating the informationof its neighbors. To achieve a better expressive capability of node influences,attention mechanism has grown to be popular to assign trainable weights to thenodes in aggregation. Though the attention-based GNNs have achieved remarkableresults in various tasks, a clear understanding of their discriminativecapacities is missing. In this work, we present a theoretical analysis of therepresentational properties of the GNN that adopts the attention mechanism asan aggregator. Our analysis determines all cases when those attention-basedGNNs can always fail to distinguish certain distinct structures. Those casesappear due to the ignorance of cardinality information in attention-basedaggregation. To improve the performance of attention-based GNNs, we proposecardinality preserved attention (CPA) models that can be applied to any kind ofattention mechanisms. Our experiments on node and graph classification confirmour theoretical analysis and show the competitive performance of our CPAmodels.

Improving Attention Mechanism in Graph Neural Networks via Cardinality Preservation