## 6 Conclusions  
This paper aims to exploit GNNs' powerful ability of representation learning in SDP. GNNs are utilized to encode higher-order information to improve the accuracy of semantic dependency parsing. 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 the average labeled F1-score \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**English**} & \multicolumn{2}{c}{**Czech**} \\  & **PSD** & & **PSD** \\  & **ID** & **OOD** & **ID** & **OOD** \\ \hline D\&M [12] & 79.1 & 77.5 & 86.9 & 77.8 \\ GNNSDP(GCN): 1-layer & **83.4** & **81.9** & **87.7** & **78.6** \\ GNNSDP(GCN): 2-layers & **84.2** & **82.6** & **88.0** & **78.6** \\ GNNSDP(GCN): 3-layers & **85.6** & **83.6** & **88.2** & **79.1** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: LF1 scores of GNNSDP with different GNN layers on ID and OOD test set of Chinese and Czech. The bold numbers indicate the current best scores. Figure 4: Parsing results of the biaffine parser and GNNSDP, for the sentence (sent_id = 40504035 in OOD of PSD formalism). Some irrelevant dependency edges are hidden. 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 the 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. In addition, our parser shows greater advantage in longer sentence and complex semantic formalism. Outstanding performances of our parser demonstrates that higher-order information encoded by GNNs is exceedingly beneficial for improving SDP. Despite that significant improvement has been made, the initial graph structure output by the vanilla parser may be noisy, resulting in a performance penalty to some extent. In the future, we would like to apply graph structure learning models to jointly learn graph structure and graph representation, rather than depending on the initial dependency graph output by the vanilla parser. Conceptualization, B.L. and Z.G. ; Methodology, B.L. and Y.F. ; Writing--original draft, B.L. ; Writing--review & editing, Y.F., Y.S., Z.G. and Y.G. All authors have read and agreed to the published version of the manuscript. This research is sponsored by the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No. JSSCBS20210507) and NUPTSF (Grant No. NY220176). Not applicable. Our experiment is conducted on SemEval 2015 Task 18 dataset [35]. The description of this dataset is shown in [[https://alt.qcri.org/semeval2015/task18/](https://alt.qcri.org/semeval2015/task18/)]([https://alt.qcri.org/semeval2015/task18/](https://alt.qcri.org/semeval2015/task18/)) (accessed on 7 May 2021). Trial data has been provided in [[https://alt.qcri.org/semeval2015/task18/index.php?id=data-and-tools](https://alt.qcri.org/semeval2015/task18/index.php?id=data-and-tools)]([https://alt.qcri.org/semeval2015/task18/index.php?id=data-and-tools](https://alt.qcri.org/semeval2015/task18/index.php?id=data-and-tools)) (accessed on 7 May 2021), full data is available in LDC official site [[https://catalog.ldc.upenn.edu/LDC2016T10](https://catalog.ldc.upenn.edu/LDC2016T10)]([https://catalog.ldc.upenn.edu/LDC2016T10](https://catalog.ldc.upenn.edu/LDC2016T10)) (accessed on 7 May 2021). Our code extends this github repository [[https://github.com/yzhangcs/parser](https://github.com/yzhangcs/parser)]([https://github.com/yzhangcs/parser](https://github.com/yzhangcs/parser)) (accessed on 15 October 2021), thanks to it very much. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The following abbreviations are used in this manuscript: