Title: Memory Augmented Design of Graph Neural Networks. Abstract: The expressive power of graph neural networks (GNN) has drawn much interest recently. Most existent work focused on measuring the expressiveness of GNN through the task of distinguishing between graphs. In this paper, we inspect the representation limits of locally unordered messaging passing (LUMP) GNN architecture through the lens of \emph{node classification}. For GNNs based on permutation invariant local aggregators, we characterize graph-theoretic conditions under which such GNNs fail to discriminate simple instances, regardless of underlying architecture or network depth. To overcome this limitation, we propose a novel framework to augment GNNs with global graph information called \emph{memory augmentation}. Specifically, we allow every node in the original graph to interact with a group of memory nodes. For each node, information from all the other nodes in the graph can be gleaned through the relay of the memory nodes. For proper backbone architectures like GAT and GCN, memory augmented GNNs are theoretically shown to be more expressive than LUMP GNNs. Empirical evaluations demonstrate the significant improvement of memory augmentation. In particular, memory augmented GAT and GCN are shown to either outperform or closely match state-of-the-art performance across various benchmark datasets. 