We investigate the problem of efficiently incorporating high-order features into neural graph-based dependency parsing. Instead of explicitly extracting high-order features from intermediate parse trees, we develop a more powerful dependency tree node representation which captures high-order information concisely and efficiently.
We use graph neural networks (GNNs) to learn the representations and discuss several new configurations of GNN's updating and aggregation functions. Experiments on PTB show that our parser achieves the best UAS and LAS on PTB (96.0%, 94.3%) among systems without using any external resources.