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Higher-order information brings significant accuracy gains in semantic dependency parsing. However, modeling higher-order information is non-trivial. Graph neural networks (GNNs) have been demonstrated to be an effective tool for encoding higher-order information in many graph learning tasks. Inspired by the success of GNNs, we investigate improving semantic dependency parsing with higher-order information encoded by multi-layer GNNs. Experiments are conducted on the SemEval 2015 Task 18 dataset in three languages (Chinese, English, and Czech). Compared to the previous state-of-the-art parser, our parser yields 0.3% and 2.2% improvement in average labeled F1-score on English in-domain (ID) and out-of-domain (OOD) test sets, 2.6% improvement on Chinese ID test set, and 2.0% and 1.8% improvement on Czech ID and OOD test sets. Experimental results show that our parser outperforms the previous best one on the SemEval 2015 Task 18 dataset in three languages. The outstanding performance of our parser demonstrates that the higher-order information encoded by GNNs is exceedingly beneficial for improving SDP.

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