Computational Modelling of Undercuts in Real-world Arguments (2024)

Abstract: Argument Mining (AM) is the task of automatically analysing arguments, such that the unstructured information contained in them is converted into structured representations. Undercut is a unique structure in arguments, as it challenges the relationship between a premise and a claim, unlike direct attacks which challenge the claim or the premise itself. Undercut is also an important counterargument device as it often reflects the value of arguers. However, undercuts have not received the attention in the filed of AM they should have — there is neither much corpus data about undercuts, nor an existing AM model that can automatically recognise them. In this paper, we present a real-world dataset of arguments with explicitly annotated undercuts, and the first computational model that is able to recognise them. The dataset consists of 400 arguments, containing 326 undercuts. On this dataset, our approach beats a strong baseline in undercut recognition, with F1 = 38.8%, which is comparable to the performance on recognising direct attacks. We also conduct experiments on a benchmark dataset containing no undercuts, and prove that our approach is as good as the state of the art in terms of recognising the overall structure of arguments. Our work pioneers the systematic analysis and computational modelling of undercuts in real-world arguments, setting a foundation for future research in the role of undercuts in the dynamics of argumentation.

heading: 1 Introduction
text: Social media allows people to express divergent opinions on the same subject and to reach many more people than was possible in earlier times. However, the ubiquity of the internet and social media also has some negative consequences. One of these is the growing polarisation between individuals holding different beliefs and opinions. It is thus increasingly important to promote productive communication and understanding among people
with opposing perspectives. This is where Argument Mining (AM) comes into play. AM aims to automatically identify and extract arguments from natural language texts (Peldszus and Stede, 2013; Green et al., 2014). It can convert unstructured textual information into structured argument data, which not only identifies the argumentative text segments in the text but also the relations between them (Prakken and Vreeswijk, 2002; Lawrence and Reed, 2020).
A critical aspect of AM is recognising and understanding various argumentative structures, including undercuts. An undercut challenges the relationship between a premise and a claim (Pollock, 1987), unlike direct attacks that challenge the claim or the premise itself. Due to its complex structure, it is difficult to annotate undercuts or to computationally model them. There exist some AM datasets with annotation of undercuts (Peldszus and Stede, 2015a; Visser et al., 2020), but they are often limited in the size, the quality of source text, or the annotation scheme. To our best knowledge, there is no existing AM models that can automatically recognise undercuts.
To addresses this gap, in this paper we present a novel dataset of real-world arguments from Quora1, a popular question-answering platform. Our dataset consists of 400 arguments, including 326 explicitly annotated undercuts, making it the largest AM dataset with such annotations to date. We also develop the first computational approach capable of recognising undercuts, proposing an innovative undercut-inclusive dependency representation and a GNN-based neural dependency parser.
Our work contributes to the field of AM in several ways. Firstly, we provide a comprehensive dataset with detailed annotations of undercuts, offering a valuable resource for future research. Secondly, our undercut-inclusive representation allows
1https://www.quora.com
59
existing neural dependency parsers to process undercuts effectively, preserving their unique status within argument structures. Lastly, our experimental results demonstrate that our GNN-based parser outperforms existing biaffine parsers in recognising undercuts and maintains state-of-the-art performance in the general AM task.

heading: 2 Related Work
text: Our work is closely related to existing approaches to AM, and the studies on undercuts in the field of AM.

heading: 2.1 AM Approaches
text: There are two kinds of approaches to AM in general, pipelined and end-to-end. Pipelined approaches break down AM into several subtasks and process them sequentially, such as in Persing and Ng (2016), Mayer et al. (2020), and RuizDolz et al. (2021). End-to-end approaches to argument mining allow for the prediction of the full argument structure with a single model, and have been gaining popularity due to their advantages over pipelined approaches, including avoiding error propagation and eliminating the need for designing different models for different subtasks (Ye and Teufel, 2021).
The tree or graph structure of arguments enables some end-to-end approaches to formulate argument mining as a dependency parsing problem. For example, Morio et al. (2020) use bidirectional LSTMs (BiLSTMs) (He et al., 2016) to encode argument components, and a biaffine dependency parser (Dozat and Manning, 2018) to classify components and their relations. Bao et al. (2021) propose a neural transition-based model to predict the dependency structure of arguments. These approaches all assume that the input text is already segmented.
In contrast, Eger et al. (2017) and Ye and Teufel (2021) take raw text as input in their end-to-end approaches based on dependency parsing. Ye and Teufel (2021) report better results than those by Eger et al. (2017), crediting the improvement to their token-level dependency representation of argument and the biaffine dependency parser they use. Our approach is based on the work by Ye and Teufel (2021), except that ours can computationally model undercuts.

heading: 2.2 Studies on Undercuts
text: Undercuts play a critical role in challenging the soundness or validity of an argument. They have been well defined in various theoretical argumentation models, such as Pollock’s argumentation model (Pollock, 1987) and Besnard and Hunter’s argumentation model (Besnard and Hunter, 2009).
In the field of AM, some datasets based on the Argument Interchange Format (Chesnevar et al., 2006) may include undercuts, for example, the QT30 corpus by Hautli-Janisz et al. (2022). However, their inclusion of undercuts is incidental and will form a small part of the overall dataset.
The Microtext dataset (Peldszus and Stede, 2015a) is one of the few AM datasets that contain explicitly annotated undercuts. The source text was produced in a highly controlled text generation experiment. The size of this dataset is small (7,846 tokens in total), each document only containing about five segments. Also, its creators do not categorise these undercuts or provide any automatic method to recognise them in their follow-up experiments. Mim et al. (2022) present some ideas that touch upon the phenomenon of undercuts in their dataset, although they do not explicitly mention undercuts when doing so. But nobody has studied which kinds of undercut strategies exist, nor is there large corpus data about them available. In contrast, to the best of our knowledge, the QuoraAM dataset we present is the biggest AM dataset that contains annotation of undercuts. We provide a taxonomy of undercuts after manually examining the annotation of our dataset, along with its distribution in our dataset. Moreover, we propose the first approach to computationally modelling undercuts.

heading: 3 The QuoraAM Dataset
text: We collected 400 arguments from Quora, and named this dataset as the QuoraAM dataset.
Compared to user-generated content on other online discussion platforms such as ChangeMyView, Kialo, idebate.org, and Twitter, arguments on Quora are more in line with our research interest. On Quora, users can present detailed and well-reasoned points of view in their answers to a question. As a result, each answer on Quora can be seen as containing a stand-alone cogently structured complete argument, often supplemented with explanations and supporting evidence. Platforms including ChangeMyView, Kialo and idebate.org are specifically designed for interactive debates and
discussions, with a focus on the process of changing one’s mind through constructive conversations. Each post on such platforms may only contain an incomplete argument, and intertextual referencing is frequent among posts, making the analysis of such posts more difficult. Twitter, unlike those previous platforms, is a more open and informal platform, where arguments can take on a more combative tone. As a result, arguments there may not always be rational and often lack the depth and nuance seen on the other platforms. Additionally, due to Twitter’s character limit, arguments in tweets tend to be very short, with structures that may be too simplistic to warrant a detailed analysis. Therefore, we chose Quora over other online discussion platforms.
We first manually pre-segmented the QuoraAM dataset, and then trained two annotators to annotate this dataset using our annotation scheme. This dataset will be used for our experiments in this paper. To the best of our knowledge, this is the biggest argument mining dataset that contains explicit annotation of undercuts.

heading: 3.1 Annotation Scheme
text: Our scheme is illustrated in Figure 1. It includes four argument component categories and two argument relation types.
The unit of annotation for components is a segment that can be part of a sentence, a sentence or a sequence of sentences. We define four component categories in our annotation scheme, including PROPOSITION, STAKE, ANECDOTE, and ANALOGY. These categories are decided based on our manual observation of arguments on Quora and the argumentation schemes by Walton et al. (2008).
Our scheme only has two relation categories,
namely SUPPORT (e.g. component 2 supporting component 1) and ATTACK (e.g. component 7 attacking component 3). In our scheme, the representation of undercuts does not rely on relation labels, but on the target of an attacking relation: if the target is a relation, an undercut occurs (e.g. component 4 undercutting the relation between component 5 and component 2); otherwise it is just a typical direct SUPPORT.
Component 9 in Figure 1 is a STAKE, and is a stand-alone component, In our scheme, STAKEs are always stand-alone components, which do not hold any relation to other components or relations.

heading: 3.2 Dataset Creation
text: In order to collect 400 answers from Quora, we first selected the first 20 topics in the topic catalogue on Kialo2 (e.g. “Politics”, “Society”, and “Technology”). Under each topic, we identified the top five popular questions, resulting in 100 candidate questions (5 questions per topic). These Kialo questions were then used to search for corresponding questions on Quora.
In the second step, we aimed to select one relevant question on Quora for each topic. We used the full string of each Kialo question as a query on Quora. Suitable questions were those relevant to the Kialo query and with at least 50 answers. If no suitable question was found, we refined our search using key terms from the Kialo question. If we still could not find a suitable Quora question, we proceeded to the next Kialo question. This process yielded 20 selected Quora questions.
In the third step, we chose 20 answers for each selected Quora question. A qualified answers must: 1) directly address the topic; 2) contain at least 30% argumentative material; and 3) be between 60 and 800 wordpieces after being tokenised by the BERT WordPiece tokeniser (Wolf et al., 2020).
Using this data collection method, we selected 400 (20×20) answers that cover various topics such as politics, environment, education, and equality. Since arguments on Quora happen in a questionanswering context, each answer was appended to its corresponding question, forming a “document” for our dataset.
We manually segmented the raw text in the QuoraAM dataset and trained two annotators to apply our annotation scheme. The two annotators first
2https://www.kialo.com. We turned to Kialo for topic selection because Quora does not provide such a catalogue.
annotated the same 60 documents for the annotation study. The remaining 340 documents were randomly split into two equal subsets. Each subset was assigned to one annotator for annotation. The annotation process took approximately 80 hours per annotator. To compile the final collection of 400 annotated documents, we randomly selected one of the doubly annotated documents from the first step and combined it with the 340 documents from the second step.
Inter-annotator agreement was measured using Krippendorff’s alpha (Krippendorff, 2018) for component classification and graph similarity measures (Kirschner et al., 2015; Putra et al., 2022) for relation identification. For component classification, the score of Krippendorff’s alpha is α = 0.78 (N = 7, 883, n = 2, k = 5). According to the interpretation scale in Krippendorff (2018), this score is acceptable for “drawing tentative conclusions” (α ≥ 0.67), and is close to the threshold (α ≥ 0.80) for being considered “reliable”. For relation identification, the graph similarity scores are: Kirschnermean = 0.69, Kirschnerf = 0.67, MARlink = 0.64, MARpath = 0.54, and MARdSet = 0.84.

heading: 3.3 Dataset Statistics
text: Table 1 shows the statistics of the QuoraAM dataset. The dataset contains a total of 118,573 tokens, which is much larger than the Microtext dataset (7,846 tokens). There are over 7,800 segments in the dataset, with approximately 56% being argumentative. The QuoraAM dataset as distributed is randomly divided into three subsets: 280 documents for training, 40 for development, and 80 for testing.
Table 2 shows the distribution of components and relations. The dataset includes over 4,000 PROPOSITIONS, around 200 ANALOGIES, 79 ANECDOTES, and 28 STAKES. Due to the small number of STAKES, we merged them with ANEC-
DOTES in our experiments in Section 5, though the original categories are preserved in the dataset for future research.
In terms of relations, the QuoraAM dataset includes 2,752 instances of SUPPORT and 1,190 instances of ATTACK. There are 326 undercuts in the dataset, which constitutes approximately 27% of all ATTACKs. This result confirms the prevalence of undercuts in Quora arguments.

heading: 3.4 Categories of Undercuts
text: We manually examined all undercuts in the QuoraAM dataset, classifying them into three categories:
• Rejection: Rejecting the relation by denying the relevance between the source component and the target component.
• Low importance: Questioning the importance of the relation, or providing more important reasons.
• Alternative option: Stating that the current solution is not the only option, or providing alternative options. This kind of undercuts often appears in arguments about policies.
Figure 2 shows the distribution of undercuts in the QuoraAM dataset. “Low importance” (41%) is the most frequent, followed by “Alternative option” (36%), “Rejection” (15%), and others (8%). This indicates that Quora authors prefer less direct methods of undercutting relations, often pointing out weaknesses or suggesting alternatives rather than outright rejection.
Rejection Low impor tance Alternative option Others
0
20
40
60
80
100
120 140 Fr eq ue nc y
49
15%
135
41%
117
36%
25 8%
Figure 2: Distribution of undercuts in the QuoraAM dataset.

heading: 4 Computational Modelling of Undercuts
text: Through a redesign of an existing dependency representation of arguments by Ye and Teufel (2021), we are able to directly use existing neural dependency parsers to computationally model undercuts. We also apply a modified GNN-based dependency parser for improved performance.

heading: 4.1 Undercut-inclusive Dependency Representation
text: Following Ye and Teufel (2021), we also frame AM as a dependency parsing task. They propose a token-level dependency representation for arguments in order to approach argument mining in an end-to-end fashion. However, their dependency representation cannot be used for arguments containing undercuts, as undercuts involve relations between a component and a relation, and a relation cannot be a dependent or a head in typical dependency representations. Therefore, we designed an undercut-inclusive dependency representation for arguments (shown in Figure 3) to allow existing neural parsers to process undercuts directly. It is a modification of the undercut-exclusive representation by Ye and Teufel (2021). This figure uses the category labels in the Persuasive Essays dataset (Stab and Gurevych, 2017) to be consistent with the figure in Ye and Teufel (2021). New features of our undercut-inclusive representation are as follows:
• A relation node (shown as dashed-line nodes in Figure 3) for each token in the argument is added. Each relation node is indexed with the token number of its corresponding token, followed by a prime. The relation nodes are meant to represent relations. This is very different from the undercut-exclusive representation, where relations are represented by edges.
• The relation node (e.g. relation node 7 ′ ) of
the last token (token 7) in a component is always the head of that token, and represents the relation from that component to its target, or the other way around. The edge label between the last token in a component and its corresponding relation node is written as (segment_label, REL), where REL means “relation”. For example, the label of the edge between token 7 and relation node 7 ′ is (P, REL).
• If the relation is a SUPPORT or a direct ATTACK, the relation node’s outgoing edge points to the last token in the source component. Its incoming edge comes from the last token of the target component. For example, the fact that “it killed much marine life” (tokens 3-7) supports “tourism has threatened nature” (tokens 9-12) is expressed by the incoming edge of relation node 7 ′ from token 12,
and the outgoing edge of relation node 7 ′
to node 7.
• If the relation is an undercut, the relation node’s outgoing edge points to the last token in the undercutting component. The incoming edge comes from another relation node, rather than the last token in a component. For example, the fact that tokens 14-15 undercuts the relation between tokens 3-7 and tokens 9-12 is expressed by the incoming edge of relation node 15 ′ from relation node 7 ′ , and the
outgoing edge of relation node 15 ′ to node 15.
This design treats all relations as nodes, enabling undercuts to be modelled as relations between nodes while preserving their unique status. In this way, existing neural dependency parsers are able to process undercuts directly.

heading: 4.2 GNN-based Neural Dependency Parser
text: We modified the GNN-based dependency parser proposed by Ji et al. (2019), which uses Graph Attention Networks (GANs) (Veličković et al., 2017) to model higher-order dependencies. Compared to the biaffine parser used by Ye and Teufel (2021), we expect our GNN-based parser to capture global argument structure and higher-order dependencies more effectively.
The mathematical description of our GNN-based parser is as follows:
rS = BERT(s1s2...sn) (1)
rROOT = FFN ROOT(mean(rS), axis=0) (2)
R = [rS ; rROOT ], axis=0 (3) He_h, H l_h, He_d, H l_d = FFN(R) (4)
He_hr , H l_h r , H e_d r , H l_d r ={
FFNrel_node(R) if undercut_inclusive ∅ if undercut_exclusive
(5)
He_hG , H l_h G , H e_d G , H l_d G = GNNlayer=2(
([He_h;H l_h], axis=1), ([He_d;H l_d], axis=1),
([He_hr ;H l_h r ], axis=1), ([H e_d r ;H l_d r ], axis=1)
)
(6)
Biaff(x, y) = x⊤Uy +W(x⊕ y) + b (7) scedge = Biaffedge(He_hG , H e_d G ) (8) sclabel = Biaff label(H l_hG , H l_d G ) (9) y ′edge i,j = {sc edge i,j ≥ 0} (10) y ′label i,j = argmax sc label i,j (11)
We calculate four representations for all tokens (He_h, H l_h, He_d, H l_d) in Equations 1-4. Relation nodes’ representations (He_hr , H l_h r , H e_d r , H l_d r ) are produced in Equation 5 when necessary. In Equation 6, the eight representations above are fed into a two-layer GNN encoder, forming a
fully connected graph. The head representation and the dependant representation of each node are concatenated to form a general representation. The general representation of each node is then aggregated and updated through the GNN layers. A detailed explanation can be found in Ji et al. (2019).
The GNN-encoded representations are then used for edge and label prediction, as described in Equations 7-11.
The final loss is calculated in the same way as that in Ji et al. (2019).

heading: 5 Experiments
text: We conducted two experiments in order to test:
• Experiment 1 – the effectiveness of our undercut-inclusive representation and GNNbased parser on undercut recognition;
• Experiment 2 – the impact of our undercutinclusive representation on arguments without undercuts.
Results from these experiments can also be used to test the effectiveness of our GNN-based parser on AM in general.

heading: 5.1 Datasets
text: In Experiment 1, we used our QuoraAM dataset, processing each document as a data point to capture argument relations spanning paragraphs. This is because relations in the QuoraAM dataset are more likely to span across paragraphs, rather than
operating within individual paragraphs, as paragraph breaks are often not used consistently in this dataset. We merged all instances of STAKE and ANECDOTE in the QuoraAM dataset to form a new category called STAKE+ANECDOTE, as discussed in Section 3.3.
In Experiment 2, we used the Persuasive Essays dataset, which is a benchmark constructed by Stab and Gurevych (2017). This dataset is also used in Ye and Teufel (2021). It comprises 402 persuasive essays randomly selected from an online forum, with 322 essays used for training and 80 essays for testing. Considering that most relations hold within paragraphs in this dataset, each paragraph was processed as a separate argument, aligning with Ye and Teufel (2021).
In both experiments, we performed the same post-processing steps as Ye and Teufel (2021).

heading: 5.2 Systems
text: In Experiment 1, since no existing approaches model undercuts computationally, we built a new baseline model Biaff_exc_r, using the biaffine parser in Ye and Teufel (2021) with their undercutexclusive representation. We simulate Peldszus and Stede (2015b)’s approach by transforming all undercuts into direct ATTACKs during training. During inference, we randomly convert all predicted direct ATTACKs to undercuts in proportion to the ratio of undercuts to overall ATTACKs in the original QuoraAM dataset.
In Experiment 2, we selected two baseline models: Biaff_exc (the BiPAM model in Ye and Teufel (2021)), the biaffine parser in Ye and Teufel (2021) with their undercut-exclusive representation; and GNN_exc, our GNN-based parser with the undercut-exclusive representation in Ye and Teufel (2021).
We implemented two models in the two experiments to compare with the baselines: Biaff_inc, the biaffine parser with our undercut-inclusive representation; and GNN_inc, our GNN-based parser with our undercut-inclusive representation.

heading: 6 Results and Discussion
text: Table 3 shows the F1 scores for component and relation identification in Experiment 1. Table 4 shows the results for Experiment 2. We used permutation tests from Ye and Teufel (2021) to test the significance of our results.
In Experiment 1, for undercut recognition, both
models significantly outperform the baseline (i.e. Biaff_exc_r) by a large margin. Biaff_inc outperforms the baseline by 15.8% (Biaff_inc = 21.6%, baseline = 5.8%, p < 0.01), which suggests that our undercut-inclusive representation can significantly improve undercut recognition compared to the undercut-inclusive representation by Ye and Teufel (2021). The increase is 33.0% for GNN_inc (GNN_inc = 38.8%, baseline = 5.8%, p < 0.01). The performance on undercut recognition of GNN_inc is comparable to that on recognising direct ATTACKs (Undercut = 38.8%, DirectAttack = 40.3%). This suggests that undercuts, despite their intricate nature, are structures that can be effectively recognised using our approach. It also shows that the GNN-based parser is better than the biaffine parser at recognising undercuts: GNN_inc significantly outperforms Biaff_inc by 17.2% (GNN_inc = 38.8%, Biaff_inc = 21.6%, p < 0.01).
The results from two experiments suggest that the GNN-based parser is more efficient than the biaffine parser. In Experiment 1, GNN_inc significantly outperforms Biaff_inc by 3.8% for component identification (GNN_inc = 66.2%, Biaff_inc = 62.4%, p < 0.01) and 4.1% for relation identification (GNN_inc = 45.8%, Biaff_inc = 41.7%, p < 0.01); in Experiment 2, GNN_inc significantly outperforms Biaff_inc by 1.0% for component identification (GNN_inc =
73.8%, Biaff_inc = 72.8%, p < 0.01) and 3.5% for relation identification (GNN_inc = 49.4%, Biaff_inc = 45.9%, p < 0.01).
Regarding the comparison between the undercutexclusive and the undercut-inclusive representations in Experiment 2, the results reveals no significant difference in performance. Both representations yield similar F1 scores for component and relation identification, which implies that our undercut-inclusive representation can also be used for arguments containing no undercuts, without performance compromise. This result suggests the flexibility of our undercut-inclusive representation.
6.1 Recognising undercuts: biaffine parser vs. GNN-based parser
To understand the disparity between the biaffine parser and the GNN-based parser in recognising undercuts, we compared the errors made by both parsers, so that we can discern which parts of an undercut are most error-prone for the GNN-based parser.
Figure 4 shows the structure of an undercut with its dependency representation. Nodes 1-3 are components, with nodes 1’ and 2’ as their corresponding relation nodes. An undercut has three elements: an undercutting component (e.g. node 1 in Figure 4), its target relation (“node 2 ⇐ node 2’ ⇐ node 3”), and the link between them (“node 1’ ⇐ node 2”’). Errors can occur in recognising any single element or a combination of them. We focused on three error types illustrated in Figure 4: type I (errors in recognising the undercutting component); type II (errors in recognising the target relation); and type III (errors only in recognising the link between them). Please note that type III only include the cases where the link is incorrectly predicted but the undercutting component and the target relation are correctly predicted.
We performed an error analysis by counting the
errors made by our models. Figure 5 shows the error distribution among all undercuts (N=58) in the test set. Due to the small sample size, we refrain from testing the statistical significance of the results in this figure, and instead interpret the numbers only qualitatively. According to Figure 5, Biaff_inc produces relatively 20% more type I errors and 26% more type II errors than GNN_inc. For type III errors, the difference becomes much bigger, which is 300%. This pattern suggests that the GNN-based parser recognises all three elements of an undercut more effectively, especially the link between the undercutting component and the target relation.
Regarding the disparity in link recognition between the GNN-based parser and the biaffine parser, we hypothesise that the GNN-parser’s advantage in identifying higher-order dependencies is crucial. Figure 6 illustrates the number of hops required for different relation representations: (a) in the undercut-exclusive representation, a direct ATTACK requires one hop; (b) in the undercutinclusive representation, a direct ATTACK requires two hops; (c) in the undercut-inclusive representation, an undercut requires three hops.
A direct ATTACK is a 1-hop relation in the undercut-exclusive representation, but becomes a 2-hop relation in the undercut-inclusive representation. Despite this, performance on the Persuasive Essays dataset shows no significant loss, imply-
ing neither parser suffers from the transition from 1-hop to 2-hop relations.
However, when comparing direct ATTACKs and undercuts in the undercut-inclusive representation (2-hop vs. 3-hop relations), both models show weaker performance for undercuts. According to Table 3, the F1 score of Biaff_inc for undercuts lags by 16.8% compared to direct ATTACKs, while for GNN_inc the difference is only 1.5%. This suggests the GNN-based parser handles the increase from two to three hops better than the biaffine parser, supporting our earlier prediction that the GNN-based parser excels at capturing higher-order dependencies.

heading: 7 Conclusion
text: In this study, we addressed a critical gap in AM by focusing on the computational recognition of undercuts, a complex yet essential structure in arguments. Existing AM research has largely overlooked undercuts, primarily due to the lack of annotated datasets and effective computational models.
To tackle this, we introduced a novel dataset sourced from Quora. This dataset, is the largest that contains undercuts, providing a valuable resource for future AM research. We also developed the first computational approach capable of recognising undercuts, featuring an undercut-inclusive dependency representation and a GNN-based neural dependency parser.
Our experiments indicated that our undercutinclusive representation can be effectively used for undercut recognition, and it does not compromise performance on datasets without undercuts, showcasing its flexibility and robustness. The results also demonstrated that the GNN-based parser is effective in general AM as well as in recognising undercuts. The GNN-based parser’s ability to capture higher-order dependencies was evident, showing a notable advantage in accurately identifying the intricate structures of undercuts.

heading: Future Work
text: This dataset, is the largest that contains undercuts, providing a valuable resource for future AM research. We also developed the first computational approach capable of recognising undercuts, featuring an undercut-inclusive dependency representation and a GNN-based neural dependency parser. Our experiments indicated that our undercutinclusive representation can be effectively used for undercut recognition, and it does not compromise performance on datasets without undercuts, showcasing its flexibility and robustness. The results also demonstrated that the GNN-based parser is effective in general AM as well as in recognising undercuts. The GNN-based parser’s ability to capture higher-order dependencies was evident, showing a notable advantage in accurately identifying the intricate structures of undercuts