  This paper describes a new method for representing embedding tables of graph
neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We
consider the scenario where (a) the graph data that lack node features, thereby
requiring the learning of embeddings during training; and (b) we wish to
exploit GPU platforms, where smaller tables are needed to reduce host-to-GPU
communication even for large-memory GPUs. The use of TT enables a compact
parameterization of the embedding, rendering it small enough to fit entirely on
modern GPUs even for massive graphs. When combined with judicious schemes for
initialization and hierarchical graph partitioning, this approach can reduce
the size of node embedding vectors by 1,659 times to 81,362 times on large
publicly available benchmark datasets, achieving comparable or better accuracy
and significant speedups on multi-GPU systems. In some cases, our model without
explicit node features on input can even match the accuracy of models that use
node features.
