## 4 Experiments
### Baseline Approaches  
We compare GNNSDP with previous state-of-the-art parsers in Tables 4 and 6. Turku is from Kanerva et al. [42]. Riga is from Barzdins et al. [43]. Peking is a hybrid model from Du et al. [10]. Lisbon is from Almeida and Martins [39]. WCGL [13] is a neural transition-based model. PTS17 is proposed by Peng et al. [11] and Basic is single task parsing, while Freda3 is a multitask parser across three formalisms. D&M [12] is a first-order graph-based model. MF and LBP [8] are a second-order model using mean field variational inference or loopy belief propagation. Lindemann et al. [44] and Lindemann et al. [24] are a compositional semantic parser for SDP and abstract meaning representation. SemPointer [14] is a transition-based model using the Pointer Network. Jia et al. [27] is a semi-supervised parser, only the full-supervised result on DM formalism is shown in their paper. He and Choi [28] uses not only BERT but also contextual string embeddings (called Flair).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{4}{c}{**DM**} & \multicolumn{4}{c}{**PAS**} & \multicolumn{2}{c}{**PSD**} & \multicolumn{2}{c}{**Avg**} \\  & **ID** & **OOD** & **ID** & **OOD** & **ID** & **OOD** & **ID** & **OOD** \\ \hline Peking [10] & 89.1 & 81.8 & 91.3 & 87.2 & 75.7 & 73.3 & 85.3 & 80.8 \\ Lisbon [39] & 88.2 & 81.8 & 90.9 & 86.9 & 76.4 & 74.8 & 85.2 & 81.2 \\ PTS17 [11]: Basic & 89.4 & 84.5 & 92.2 & 88.3 & 77.6 & 75.3 & 86.4 & 82.7 \\ PTS17 [11]: Basic & 90.4 & 85.3 & 92.7 & 89.0 & 78.5 & 76.4 & 87.2 & 83.6 \\ WCGL [13] & 90.3 & 84.9 & 91.7 & 87.6 & 78.6 & 75.9 & 86.9 & 82.8 \\ D\&M [12]: Basic & 91.4 & 86.9 & 93.9 & 90.8 & 79.1 & 77.5 & 88.1 & 85.0 \\ MF [8]: Basic & 93.0 & **88.4** & 94.3 & 91.5 & 80.9 & 78.9 & 89.4 & 86.3 \\ LBP [8]: Basic & 92.9 & **88.4** & 94.3 & 91.5 & 81.0 & 78.8 & 89.4 & 86.2 \\ Lindemann et al. [44]: Basic & 91.2 & 85.7 & 92.2 & 88.0 & 78.9 & 76.2 & 87.4 & 83.3 \\ SemPointer [14]: Basic & 92.5 & 87.7 & 94.2 & 91.0 & 81.0 & 78.7 & 89.2 & 85.8 \\ \hline GNNSDP(GCN): Basic & **93.3** & 88.0 & **94.8** & 91.1 & **85.6** & **83.6** & **91.2** & **87.6** \\ GNNSDP(GAT): Basic & 93.0 & 87.9 & **94.8** & **91.6** & **85.4** & **83.3** & **91.1** & **87.6** \\ \hline D\&M [12]: +Char+Lemma & 93.7 & 88.9 & 93.9 & 90.6 & 81.0 & 79.4 & 89.5 & 86.3 \\ MF [8]: +Char+Lemma & 94.0 & 89.7 & 94.1 & 91.3 & 81.4 & 79.6 & 89.8 & 86.9 \\ LBP [8]: +Char+Lemma & 93.9 & 89.5 & 94.2 & 91.3 & 81.4 & 79.5 & 89.8 & 86.8 \\ Jia et al. [27]: +Lemma & 93.6 & 89.1 & - & - & - & - & - & - \\ SemPointer [14]: +Char+Lemma & 93.9 & 89.6 & 94.2 & 91.2 & 81.8 & 79.8 & 90.0 & 86.9 \\ \hline GNNSDP(GCN): +Char+Lemma & **94.2** & **90.1** & **94.9** & **91.4** & **86.4** & **84.9** & **91.8** & **88.8** \\ GNNSDP(GAT): +Char+Lemma & **94.4** & **89.9** & **95.0** & **91.8** & **86.2** & **84.6** & **91.9** & **88.8** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of labeled F1 scores achieved by our model and previous state-of-the-art in the English dataset. The bold numbers indicate the current best scores. The F1 scores of baseline and our models are averaged over five runs. ID denotes the in-domain (WSJ) test set and OOD denotes the out-of-domain (Brown) test set. +Char, +Lemma, +BERT, and +Flair mean augmenting the token embeddings with character-level, lemma embeddings, BERT embeddings, and Flair embeddings. Semi-SDP only shows the full-supervised result on DM formalism.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Hyper-Parameter** & **Value** \\ \hline \multirow{4}{*}{Trainer} & optimizer & Adam \\  & learning rate & \(1\times 10^{-2}\) \\  & Adam (\(\beta_{1}\), \(\beta_{2}\)) & (0.95, 0.95) \\  & decay rate & 0.75 \\  & decay step length & 5000 \\  & \(\lambda\) & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._