Supervised parsing models have achieved impressive results on in-domain texts. However, their performances drop drastically on out-of-domain texts due to the data distribution shift. The shared-private model has shown its promising advantages for alleviating this problem via feature separation, whereas prior works pay more attention to enhancing shared features but neglect the in-depth relevance of specific ones. To address this issue, we for the first time apply a dynamic matching network on the shared-private model for semi-supervised cross-domain dependency parsing. Meanwhile, considering the scarcity of target-domain labeled data, we leverage unlabeled data from two aspects, i.e., designing a new training strategy to improve the capability of the dynamic matching network and fine-tuning BERT to obtain domain-related contextualized representations. Experiments on benchmark datasets show that our proposed model consistently outperforms various baselines, leading to new state-of-the-art results on all domains. Detailed analysis on different matching strategies demonstrates that it is essential to learn suitable matching weights to emphasize useful features and ignore useless or even harmful ones. Besides, our proposed model can be directly extended to multi-source domain adaptation and achieves best performances among various baselines, further verifying the effectiveness and robustness. Dependency parsing aims to capture syntactic and semantic information over input words via a dependency tree. As depicted in Figure 1, given an input sentence s = w 0 w 1 . . . w n , a dependency tree is defined as d = { ( h, m, l ) , 0  h  n, 1  m  n, l  L} , where ( h, m, l ) is a dependency from the head word w h to the modifier word w m with the relation label l  L . Recently, supervised neural models have achieved significant improvements in dependency parsing (Chen and Manning, $ 2014; Andor et al., 2016; Kiperwasser and Goldberg, 2016; Dozat and Manning, 2017; Li et al., 2019a). Particularly, Dozat and Manning (2017) propose a BiAffine parser and achieve good results on various languages. In order to obtain better performance, supervised parsing models rely on sufficient in-domain training data. However, the parsing accuracy degrades significantly when the training data is from out-of-domain that has a large gap between the in-domain data.The main reason can be attributed to different feature distributions between source and target domains. Thus modeling the relevance of these distributions becomes the key challenge for cross-domain dependency parsing. In the past few years, semi-supervised dependency parsing has attracted more attention with the surge of labeled web data that are user-generated non-canonical texts (Yu et al., 2013; Peng et al., 2019; Li et al., 2019b; Dakota et al., 2021). As shown in Figure 2, these approaches for modeling the similarity and discrepancy among different domains can be classified into three categories. The fully-shared model treats source and target domains equally and shares all model parameters, which may extract domain-invariant features but fail to capture domain-specific ones. In contrast, the fully-private model exploits completely independent encoders for each domain, which can better capture domain-specific features but ignore domain-invariant ones. To combine the advantages 1035 BiLSTM (sha) x src x tgt MLP BiAffine of fully-shared and fully-private models, the shared-private model naturally separates domain-invariant and domain-specific features via shared and private encoders (Daum III, 2007; Kim et al., 2016). However, this model still has two issues, i.e., neglecting the in-depth relevance of specific ones and failing to utilize unlabeled data effectively. For the first issue, we investigate feature transfer approaches that encourage the target feature space to learn useful knowledge from source domain (Zagoruyko and Komodakis, 2017; Jang et al., 2019; Wright and Augenstein, 2020; Li et al., 2020a). Particularly, Jang et al. (2019) successfully use meta-learning to learn transfer weights between heterogeneous architectures and tasks. Motivated by this work, we propose a dynamic matching network based on the shared-private model for semi-supervised dependency parsing. Concretely, our model automatically generates matching weights to emphasize useful information and filter useless or even harmful features, thus further improving the power of target feature space. For the second issue, considering that manually annotating samples for a new domain is time-consuming and expensive, we endeavour to effectively utilize target-domain unlabeled data. We design a new training strategy to use unlabeled data to enhance the power of matching network, thus modeling more effective specific features for the target domain. Meanwhile, we fine-tune BERT model with language model loss to obtain more reliable domain-related contextualized representations. Experiments on benchmark datasets show that our proposed model outperforms the top submitted system in the NLPCC-2019 shared task (Li et al., 2019c), leading to new state-of-the-art results on all domains. In addition, detailed analysis on different matching settings reveals insights on the effect of intermediate source features. The extension on multi-source domain adaptation further verifies the effectiveness and robustness of our model. The code is released at https://github.com/ suda-yingli/ACL2022-match to facilitate future research. In this work, we use the simple yet effective BiAffine parser (Dozat and Manning, 2017) as our basic model, which consists of four components, i.e., Input Layer , BiLSTM Encoder , MLPs (multi-layer perceptron) , and BiAffines . Inputs. Each input word w i is mapped into a dense vector x i . The vector is the concatenation of pre-trained word embedding emb word i and its Chinese character representation rep char i , x i = emb word i  rep char i (1) where rep char i is generated by using one-layer BiLSTM to encode the characters of word w i (Lam-ple et al., 2016). In addition, we also use BERT representations to enhance our baseline where emb word i is substituted by rep BERT i simply. BiLSTM. A three-layer BiLSTM is applied to sequentially encode the input vectors x 0 x 1 . . . x n in two independent directions (forward and back-ward), and generates context-aware word representations h  0 h  1 . . . h  n via combining the outputs of both directions. MLPs. Two separate MLPs are used to obtain syntax-related lower-dimensional vectors. i i or a dependent word. BiAffines. The score of a dependency i  j is obtained via BiAffine attention, score ( i  j ) = r H j U 1 r D i + r H j U 2 (3) where U 1 and U 2 are parameters. After obtaining the scores, the parser finds the highest-scoring tree with the dynamic programming algorithm known as maximum spanning tree (McDonald et al., 2005). Then, the classification of dependency labels is treated as a separate task, and the arc-factorization score is computed as follows: score ( i l  j ) = r H j U 3 r D i +( r H j  r D i ) U 4 + b (4) where U 3 , U 4 , and b are parameters, and l is the relation label. Parsing loss. During training, the parser computes two independent cross-entropy losses for each position, i.e., maximizing the probability of its correct head and the correct label between them. where w j is the gold-standard head of w i , and l is the corresponding gold relation label. Semi-supervised dependency parsing aims at learning a parser that generalizes well to the target domain. Although supervised parser has achieved good results on in-domain data, the parsing performance drops dramatically when the training data is mainly from the out-of-domain. The shared-private model has been proven effective for alleviating this problem. However, the model ignores the in-depth relevance of specific ones and fails to directly use unlabeled data for model training. To address these problems, we for the first time apply a dynamic matching network on the shared-private model to learn appropriate matching weights automatically via mimicking well-trained source features. As shown in Figure 3, our model mainly contains two components, i.e., a shared-private schema for feature separation and a dynamic matching network BiLSTM (sha) BiLSTM (tgt) BiLSTM (src) x tgt x src x tgt x tgt x src MLP BiAffine Dynamic Matching Matching Loss Figure 3: The framework of our proposed model. for capturing the relevance of domain-specific features. In addition, we propose a new strategy for our model training to make full use of all labeled and unlabeled data. The framework of vanilla shared-private model is shown in Figure 2(c). First, each input word is encoded by the shared BiLSTM and its private BiLSTM to obtain domain-invariant and domain-specific representations. Then, the two representations are combined as the final context-aware representation h  i , which is fed into shared MLPs to obtain syntax-related information. Next, we obtain the scores of dependency arcs and labels via shared BiAffines. Finally, all model parameters are updated via minimizing the parsing loss. Orthogonality constraints. Although the shared-private model has separated domain-invariant and domain-specific features via the shared and private encoders, the two type features may interfere with each other. To alleviate this problem, we apply orthogonality constraints to encourage the domain-specific features to be mutually exclusive with the shared ones. Following Bousmalis et al. (2016), we define the loss of orthogonality constraints as follows: L ort = (cid:40)(cid:80) ni =0 (cid:13)(cid:13) ( h i ) T s i (cid:13)(cid:13) , if w i  { src } (cid:80) ni =0 (cid:13)(cid:13) ( h i ) T t i (cid:13)(cid:13) , if w i  { tgt } (6) where h i is the output of shared BiLSTM, s i and t i are the outputs of source-domain and target-domain private BiLSTMs. In practical application, some source features are more important than others while some are irrelevant or even harmful depending on the domain differences. Hence, directly neglecting source features seems especially profligate. Motivated by Jang et al. (2019), we for the first time apply a dynamic matching network on the shared-private model to learn matching weights automatically. Thus the model is able to pay more attention on useful source features and ignore the useless ones. Considering the source features are well-trained with sufficient labeled data, mimicking these features may be helpful for enhancing the power of the target feature representational space. Hence, we minimize l 2 objection to transfer the knowledge from source features to the target ones: || f  ( t mi )  s ni || 22 (7) where f  (  ) is a linear transformation, t mi is the m th -layer output of target-domain private BiLSTM, and s ni is the n th -layer output of source-domain private BiLSTM. As shown in Figure 4, the key of dynamic matching network is learning layer matching weights W and element matching weights Q . Layer matching weights W . Intuitively, each intermediate feature of source domain has a completely different effect on the target domain. When we exploit the matching network to learn useful information from the source domain, a key problem is to decide the layer matching pair ( n, m ) . Previous works select the matching pair based on prior knowledge of architectures or semantic similarities between tasks (Romero et al., 2015; Zagoruyko and Komodakis, 2017). To reduce the complexities of matching pair selection, we use a learnable layer matching weight W ( n,m )  0 for each pair ( n, m ) which can decide the amount of feature matching between the n th -layer outputs of source-domain private BiLSTM and the m th -layer outputs of target-domain private BiLSTM. where the Relu function is used to ensure non-negativeness of W . Element matching weights Q . After obtaining layer matching weight W n,m , we need to learn element matching weight Q n,md to emphasize the useful intermediate elements according to their utility on the target domain. The matching loss of matching pair ( n, m ) is L n,m mat = W n,m 1 DD (cid:88) d =1 Q n,md ( f  ( t mi )  s ni ) 2 d (9) where D is the dimension of the BiLSTM output. Q n,md is the non-negative weight of element d with (cid:80) Dd =1 Q n,md = 1 . Since the important elements to transfer can vary for each input word w i , we set element transfer weights as follows: Q n,md = softmax (cid:16) r n,m ( s ni ) (cid:17) d (10) where r n,m (  ) is the linear transformation. After obtaining the element and layer matching weights, the combined matching loss is L mat = 1 K (cid:88) n,m L n,m mat = 1 KD (cid:88) n,m W n,m D (cid:88) d =1 Q n,md ( f  ( t mi )  s ni ) 2 d (11) where n, m  { 1 , 2 , 3 } are the layer number of BiLSTM, and K = 3  3 = 9 is the number of matching pairs. In order to make full use of all available training data, our model adopts a joint training strategy as shown in Algorithm 1. Here we split parameters in the model into two groups: 1) parsing parameters  include all parameters of shared-private model and the linear function f  (  ) ; 2) matching parameters  include the parameters of all functions that generate matching weights. To balance the parsing and matching tasks, we give them different loss weights and update the dynamic matching parameters with a smaller learning rate. In the joint training process, minibatches of source domain and target domain take turns to train (lines 3-5 and 6-11, respectively). When the minibatch is from the source domain, we update the parsing parameters  with parsing and orthogonality losses. When the minibatch comes from target domain, if the data is annotated, the total model (  &  ) is jointly trained with parsing, orthogonality and matching losses; otherwise only matching parameters  are updated with the matching loss. Datasets. We use the Chinese multi-domain dependency parsing datasets released at the NLPCC-2019 shared task 1 , containing four domains: one source domain which is a balanced corpus (BC) from news-wire, three target domains which are the product comments (PC) data from Taobao, the product blog (PB) data from Taobao headline, and a web fiction data named ZhuXian (ZX). Table 1 shows the detailed data statistics. Evaluation. We use unlabeled attachment score (UAS) and labeled attachment score (LAS) to two-evaluate the dependency parsing accuracy (Hajic et al., 2009). Each model is trained for at most 1 , 000 iterations, and the performance is evaluated on the dev data after each iteration for model selection. We stop the training if the peak performance does not increase in 100 consecutive iterations. Hyper-parameters. We set the dimension of char embedding to 100. We train word2vec (Mikolov et al., 2013) on Chinese Gigaword Third Edition to obtain pre-trained word embeddings. To see the effect of contextualized representations, we use the released Chinese BERT-Base model 2 to 1 http://hlt.suda.edu.cn/index.php/ Nlpcc-2019-shared-task 2 https://github.com/google-research/ bert yield BERT representations for each word. The averaged sum of the top four layer outputs is reduced into a dimension of 100 via an MLP. The learning rate for feature matching network and loss weights  and  are set as 10  4 , 0 . 01 , and 0 . 01 . For other hyper-parameters, we keep the default configuration in BiAffine parser (Dozat and Manning, 2017). Baseline models. To verify the effectiveness of our proposed model, we select the following models as our strong baselines. FulSha (Fully-shared). The FulSha model, shown as Figure 2(a), directly trains the BiAffine parser with all labeled data from source and target domains. FulPri (Fully-private). The FulPri model, shown as Figure 2(b), exploits two independent BiLSTMs to separate source and target features absolutely. ShaPri (Shared-private). As shown in Figure 2(c), the ShaPri model can combine the advantages of fully-shared and fully-private models. It captures domain-invariant and domain-specific features simultaneously via utilizing two private and one shared BiLSTMs. DoEmb (Domain Embedding). The DoEmb model, proposed by Li et al. (2019b), has been proven effective for semi-supervised dependency parsing. The key idea is to use an extra domain embedding to indicate which domain the input sentence comes from. ADE (Adversarial Domain Embedding). Li et al. (2020b) successfully apply adversarial learning on the Doemb model and achieve good performances on semi-supervised dependency parsing. They leverage an extra domain embedding to capture domain-related information and adversarial network to extract more shared knowledge across different domains. To gain more insights on the data distribution of different domains, we give a detailed analysis on our benchmark datasets from both lexical and syntactic aspects. On the one hand, we calculate word distributions for each domain. Figure 5 clearly shows that the same word appearing in different domains has completely different distributional probabilities. For example, the distributional probabilities 1039 Figure 5: Word distributional probabilities of different domains. of word    are 0.46 in BC domain, 0.43 in PC domain, 0.35 in PB domain, and 0.26 in ZX domain. Thus, it may inevitably lead to the shift of data distributions between different domains. On the other hand, we count sentence distributions for each domain based on the punctuation of input sentences. As shown in Figure 6, we find that the sentence distribution of source domain (BC) is similar to target domains (PB and ZX), but it is much different from the PC domain. The main reason is that the data of PC domain is non-canonical and contains a lot of ellipsis phenomena. Hence, not all source domain knowledge is equally important for the target domain, and it is necessary to automatically select the useful information from the source domain to enhance the performance on the target domain. In this work, we leverage unlabeled data from two aspects: 1) learning more appropriate matching weights via enhancing the power of the dy-77 namic matching network; 2) obtaining more reliable domain-related word representations by fine-tuning BERT. Since the amount of labeled data on target domain is much smaller than the source domain, we attempt to utilize target-domain unlabeled data to help the model to learn matching weights. Figure 7 illustrates the influence of unlabeled data sizes on dev data. In each curve, we fix the size of source-domain labeled data and incrementally add a random subset of target-domain unlabeled data. On the one hand, enlarging the size of unlabeled data leads to consistent improvements when the ratio is less than 3/4. This shows that the unlabeled data plays an important role in the matching weights learning. On the other hand, we can see that the parsing performance slightly degrades when the ratio increases larger than 1, indicating that the usefulness of the unlabeled data becomes limited when the size is too large. Additionally, we leverage large-scale target-domain unlabeled data to fine-tune BERT model parameters, and detailed comparative experimental results are shown in Table 2. First, we observe that the model with fine-tuned BERT consistently outperforms the one with primary BERT representations, demonstrating that fine-tuning BERT is able to learn domain-related knowledge. Second, even the accuracy gap between different models reduces, our proposed model still achieves better per-1040 PC PB ZX AVG UAS LAS UAS LAS UAS LAS UAS LAS Results of previous works Yu (19) * 72.18 64.12 82.57 77.83 80.53 75.84 78.43 72.60 Peng (19) FE 73.16 64.33 83.05 78.57 82.09 77.08 79.43 73.33 Li (19) FB* 75.25 67.77 85.53 81.51 86.14 81.65 82.30 76.98 Li (20) FB 75.93 68.34 85.07 80.99 85.94 81.45 82.31 76.93 Compare with baseline models FulPri 70.02 61.43 79.60 74.74 76.56 71.05 75.39 69.07 FulSha 69.66 61.21 80.03 75.26 79.42 74.55 76.37 70.34 ShaPri 70.47 62.06 80.14 75.10 79.27 74.21 76.63 70.46 DoEmb 70.31 61.45 79.71 74.67 79.65 74.61 76.56 70.24 ADE 71.41 63.16 80.35 75.55 80.26 75.30 77.34 71.33 Our 71.91 63.88 81.24 76.61 80.44 75.58 77.86 72.03 Enhance models with BERT representations FulPri 72.75 65.08 83.96 79.64 83.08 78.48 79.93 74.40 FulSha 73.87 66.12 84.21 79.98 84.75 80.23 80.94 75.44 ShaPri 73.88 66.35 84.50 80.15 84.73 80.29 81.03 75.59 DoEmb 74.10 66.39 84.10 79.79 84.93 80.46 81.04 75.55 ADE 74.61 66.81 84.77 80.62 85.06 80.60 81.48 76.01 Our 75.24 67.36 85.38 81.21 85.87 81.54 82.16 76.71 Our FB 76.73 69.38 86.06 81.63 86.56 82.49 83.12 77.83 Table 3: Final results on test data where FE denotes model with fine-tuned ELMo, FB denotes model with fine-tuned BERT, and * denotes model ensam-ble. formance than the ShaPri model, which further verifies the effectiveness of feature matching network. Overall, unlabeled data is extremely helpful to enhance the feature representations that contribute for semi-supervised dependency parsing via fine-tuning BERT or enhancing the power of feature matching network. Table 3 shows the final results on test data and makes a comparison with previous works. First, we can see that the ShaPri model achieves better performance than FulPri and FulSha models, demonstrating that both domain-invariant and domain-specific features are helpful for semi-supervised dependency parsing. More specially, the FulSha model outperforms the FulPri one on PB and ZX domains but slightly declines on PC domain, possibly because the huge divergence between source and target domains leads to the interference for shared features learning. Although the ShaPri model already achieves better parsing accuracy, our model still outperforms it by 1.5% improvement in averaged LAS, indicating that the dynamic matching network is useful for enhancing the capability of target feature representational space via learning information from source domain. Second, the utilization of BERT boosts all model performances by a large margin. Fine-tuning BERT with unlabeled data can further enhance the model performance. Even the baseline models with BERT become much stronger, our proposed model still achieves the best 77 78 ZXdata 76 77 LAS ( % ) PBdata None 1to3 2to3 3to3 1to2 2to2 3to2 1to1 2to1 3to1 62 63 MatchingPair PCdata Figure 8: Accuracy curves regarding matching pairs. performance, which further demonstrates the effectiveness of our proposed model. Finally, we present the remarkable results of previous works in the top block. Yu et al. (2019) combine self-training and model ensemble approaches to improve the model performance. Peng et al. (2019) re-implement the DoEmb model with fine-tuned ELMo using the codes released by Li et al. (2019b). The top system submitted by Li et al. (2019c) joints the advantages of tri-training, model ensemble, and BERT for the model training. (Li et al., 2020b) propose the ADE model and utilize fine-tuned BERT for semi-supervised dependency parsing, achieving competitive performances with the top system. Our proposed single model outperforms all these baseline models, leading to new state-of-the-art results on all domains. Because there still lacks related studies of feature transfer on semi-supervised dependency parsing, we for the first time design detailed comparative experiments to gain more insight on the impact of migrating the intermediate features from source to target domain. Here, One-to-one means only selecting a matching pair with the matching weight 1 ; All-to-all means that all matching pairs are used with matching weights 1 ; Learned matching means that all matching pairs are used with generated matching weights by our matching network. Figure 8 shows results of different One-to-one models where 1to3 means learning information from the 1 th -layer outputs of source-domain private BiLSTM to the 3 th -layer outputs of target-domain private BiLSTM. First, we can see that almost all 1041 PC PB ZX AVG UAS LAS UAS LAS UAS LAS UAS LAS FulPri 68.44 59.96 79.35 74.60 74.43 70.22 74.07 68.26 FulSha 70.19 62.11 81.42 76.62 81.84 76.87 77.82 71.81 ShaPri 69.87 61.87 81.33 76.71 82.20 77.15 77.80 71.91 DoEmb 70.26 62.00 81.19 76.75 82.37 77.52 77.91 72.09 ADE 70.80 62.69 81.57 76.92 82.57 77.84 78.31 72.48 Our 71.36 63.67 82.00 77.53 82.45 78.16 78.61 73.12 Table 5: Results of multi-source domain adaptation on dev data. One-to-one models outperform the None one, demonstrating that the model can learn some useful information from source domain to target domain via a simple feature matching process. Second, the model achieves a slight improvement when we transform features from the source domain to the higher layer outputs of target private BiLSTM. The reason may be that the higher layer outputs of BiLSTM contain much syntax-related information which has a higher domain relevance. Finally, we find that different domains have different trends in the curves, so it is difficult to select an explicit matching setting that adapts all domains. Table 4 presents that the best One-to-one model achieves better performances than All-to-all. We suspect the reason may be that All-to-all model treats all matching pairs equally, thus may lead to potential conflicts between different matching pairs. Additionally, Learned matching boosts the All-to-all performance by a large margin, indicating that our model is extremely useful for learning matching weights and alleviating the conflicts of feature transfer. Overall, the results can clearly demonstrate that modeling appropriate matching weights to emphasize useful information and filter out harmful knowledge is crucial to improve the capability of domain adaptation. Table 5 presents the parsing accuracy on dev data where each model is trained with multi-source domain training data. For example, if the target domain is PC, its training data comes from BC, PB, and ZX domains. On the one hand, we observe that the same model trained with multi-source domains slightly outperforms it trained with only one source domain. The reason may be that although multi-source domains can provide more knowledge for the target domain, the data distribution shift leads to the negative transfer. Therefore, using all source domains simultaneously always requires more sophisticated hand-crafted configurations of the feature transfer. On the other hand, we can see that our proposed model achieves the best performance over various baselines. It demonstrates that the learned matching weights are helpful for constructing the relationships between target and multiply source domains, thus further boosting the parsing accuracy of the target domain. Domain adaptation generally falls into two categories: semi-supervised where large-scale labeled data for the source and small-scale labeled data for the target are available and unsupervised where only the labeled data for the source domain is given. Due to the lack of target-domain labeled data, previous works focus on unsupervised domain adaptation. One stream of work attempts to create pseudo training samples for the target domain via self-training, co-training, or tri-training processes (Yarowsky, 1995; Blum and Mitchell, 1998; Clark et al., 2003; Sgaard and Rishj, 2010; Yu et al., 2015; Li et al., 2019c; Saito et al., 2020). As a coin has two sides, self-training has been proven effective on cross-domain constituency parsing (Mc-Closky et al., 2006) and dependency parsing (Yu et al., 2015), but Charniak (1997) reports either mi-nor improvements or significant damage for parsing by self-training. Clark et al. (2003) show the same findings on POS-tagging. Both Sarkar (2001) and Steedman et al. (2003) demonstrate that co-training is helpful for cross-domain dependency parsing. Li et al. (2019c) successfully use tri-training and fine-tuned BERT to improve the parsing accuracy. However, these approaches often require both caution and experience for selecting the appropriate pseudo samples. Another stream of work focuses on learning the feature representations from multiple source domain via mixture of experts. Kim et al. (2017) combine the predictions of domain experts via attention. Guo et al. (2018) propose a mixture of experts which uses a point to set metric. (Wright and Augenstein, 2020) extend the mixture of experts method on large pre-trained transformer models, leading to significant improvements. Motivated by these works, our work attempts to learn the relationship between different domain-specific representations. 5.2 Semi-supervised domain adaptation In the past few years, semi-supervised domain adaptation for dependency parsing has achieved great improvements with the development of parsing communities (Chen et al., 2013; Yu et al., 2013; Li et al., 2019b; Peng et al., 2019). Feature separation , as a strand work of semi-supervised domain adaptation, is first proposed by Daum III (2007) and achieves good results on sequence labeling tasks. Finkel and Manning (2009) extend this method by using a hierarchical Bayesian prior. Kim et al. (2016) apply it on neural-based model which uses a shared and multiple private BiLSTMs to separate domain-invariant and domain-specific features. Adversarial learning is a common method to encourage the shared encoder to extract more pure domain-invariant features via cheating the domain classifier (Ganin and Lempitsky, 2015; Bousmalis et al., 2016; Cao et al., 2018). Most relatively, Sato et al. (2017) apply adversarial learning on shared-private model but find slight improvements for semi-supervised dependency parsing. Li et al. (2020b) also exploit adversarial learning on the shared-private and domain embedding models with two strategies and achieves better performances than no-adversarial ones. Another strand work is feature transformation . Ando and Zhang (2005) design a variety of auxiliary problems to learn various aspects of the target problem from unlabeled data. Chen et al. (2013) propose the traditional feature transformation for dependency parsing which is similar as a way of doing feature smoothing. Jang et al. (2019) utilize the meta-learning to learn transfer weights of heterogeneous networks and tasks, leading to great improvements. Hu et al. (2021) propose a multi-view framework which combines multiple source models into an aggregated source view at language, sentence, or sub-structure levels. However, there still lacks related researches on the neural-based model for cross-domain dependency parsing. This work proposes a feature matching shared-private model for semi-supervised dependency parsing. Meanwhile, we utilize unlabeled data to enhance the power of feature matching network and the BERT representations. Our proposed approach achieves consistent improvements among various baseline models, leading to new state-of-the-art results on all domains. The detailed analysis shows that compared with manual matching setting, the automatically learned matching weights by our designed dynamic matching network can improve the parsing accuracy. Furthermore, our proposed model can be directly extended to multi-source domain adaptation and achieves the best performance among various baselines, further demonstrating the effectiveness and robustness of our proposed method. We thank our anonymous reviewers for their helpful comments. We are very grateful to Zhenghua Li for his careful guidance of our work. We also thank Chen Gong, Qingrong Xia, Yu Zhang, Houquan Zhou, Yahui Liu, and Tong Zhu for their help in paper writing and polishing. This work was supported by National Natural Science Foundation of China (Grant No. 62036004) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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