Venue: NAACL 2022

# Incorporating Centering Theory into Neural Coreference Resolution

Haixia Chai and Michael Strube

Heidelberg Institute for Theoretical Studies gGmbH

Schloss-Wolfsbrunnenweg 35

69118 Heidelberg, Germany

{haixia.chai, michael.strube}@h-its.org

###### Abstract

In recent years, transformer-based coreference resolution systems have achieved remarkable improvements on the CoNLL dataset. However, how coreference resolvers can benefit from discourse coherence is still an open question. In this paper, we propose to incorporate centering transitions derived from centering theory in the form of a graph into a neural coreference model. Our method improves the performance over the SOTA baselines, especially on pronoun resolution in long documents, formal well-structured text, and clusters with scattered mentions.1

Footnote 1: Our code and model are publicly available at: [https://github.com/HaixiaChai/CT-Coref](https://github.com/HaixiaChai/CT-Coref) Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 2996 - 3002 July 10-15, 2022 ©2022 Association for Computational Linguistics

## 1 Introduction

Coreference resolution is the task to find all expressions which refer to the same entity. The coreferential mentions could occur anywhere in the discourse. In recent years, many transformer-based models Joshi et al. (2019); Joshi et al. (2020); Kirstain et al. (2021) achieved improvements on the CoNLL benchmark Pradhan et al. (2012). In contrast to using transformers such as BERT Devlin et al. (2019) which learn the text input sequentially in limited chunks, how knowledge about the structure of discourse can benefit coreference resolution is less explored in the neural NLP era.

Coreference plays an essential role in discourse coherence. A referring expression using a reduced linguistic form (e.g., pronoun) indicates a referential relation to its antecedent in previous utterances. The referring expression connects utterances and contributes to discourse coherence implicitly. On the other hand, coreference resolution can benefit from a coherent discourse. It has long been acknowledged that coherence structure can impose constraints on referential accessibility from a linguistic perspective Asher and Lascarides (2003). Centering theory Joshi and Weinstein (1981); Grosz et al. (1983, 1995); Walker et al. (1998) is a method to formally describe discourse coherence by using attentional state (i.e., the focus of attention of the participants at each utterance of the discourse). Figure 1 shows how the coherence structure of an example text is built by means of tracking the changes in the local attentional state.2 By applying centering theory Gordon and Scearce (1995) investigate how local coherence influences the interpretation of ambiguous pronouns. From reading-time experiments, they observe that utterances with pronouns were read faster in the centering continue than in the shift status, while utterances with noun phrases containing rich lexical information were read more quickly in the centering shift than in the continue status. We conjecture that this pattern could contribute to coreference resolution.

Footnote 2: The example is based on Gordon and Scarce (1995).

In this work, we explore the effect of changes in attentional state in the discourse on entity coreference resolution in a neural approach. Inspired by Jeon and Strube (2020), we capture the most salient mentions of each sentence as centers to compute the local centering transition relations in accordance with centering theory. We then extend the coherence structure globally in the form of a graph. It makes the centering transitions available between any two sentences. Lastly, we fuse the novel discourse structure into a neural coreference model Kirstain et al. (2021). From the results, our

Figure 1: An example text shows how foci change sentence by sentence. The words in bold are the focus of each sentence. The arrows indicate centering transitions with two different transition types, continuue and shift.



proposed method improves the SOTA models up to 80.9 F1 score. Our extensive analysis shows that our approach performs better on pronoun resolution in long documents, formal well-structured text such as magazine and newswire genres, and documents with scattered mentions of clusters. Overall, we observe that incorporating discourse structure derived from centering theory can benefit coreference resolution.

## 2 Related Work

Discourse for Coreference.In early work, some structural features of the discourse were used in machine learning approaches, such as sentential position and distance between two mentions in sentences, phrases or mentions Soon et al. (2001); Sapena et al. (2013). In the deep learning period, only a few researchers incorporated discourse information into a coreference model to our knowledge. Recently, Khosla et al. (2021) use rhetorical structure theory (RST) Mann and Thompson (1988) to capture the hierarchical discourse structure of documents, from which they encode three distance features for the candidate and query mentions on different levels (i.e., word-level, discourse-unit-level and discourse subtree). Held et al. (2021) apply discourse coherence Grosz (1977, 1978); Grosz and Sidner (1986) to cross-document coreference resolution. They retrieve candidate mentions by modeling the attentional state within a latent embedding space as a set of nearest neighbors for a query mention. As a pruning method, these neighborhoods constrain the search space for their following pairwise classifier. Different from the approaches above, we use centering theory to extract centering transitions between sentences through attentional state. We then use these relations to construct a discourse structure that shows how centers change as discourse proceeds dynamically.

Centering Theory.Since centering theory is a linguistic theory, a great number of early works Walker et al. (1994); Di Eugenio (1998); Turan (1998); Strube and Hahn (1999) were dedicated to transform it to a computational one for various languages. Lately, Jeon and Strube (2020) is the first work that applies centering theory in a neural model for discourse coherence explicitly. They capture the relationships sentence by sentence for assessing text coherence. In the coreference resolution task, coreferent mentions could occur anywhere in the discourse rather than the adjacent sentence only. Thus, we propose a fully connected centering transitions graph in our model. In addition, Jeon and Strube compute the centers of each sentence on a token-level, while we do it on the span-level.

## 3 Model

### Baseline

We study the model proposed by Kirstain et al. (2021) as our baseline. It is a _start-to-end_**(s2e)** coreference resolution model that only considers boundary points of a span to compute the mention and antecedent scores without additional handcrafted features. Similar to the method of Lee et al. (2018), they measure how likely a candidate mention \(c\) is to be an antecedent of a query mention \(q\) by a scoring function \(f(c,q)\). The function is the addition of two mention scores \(f_{m}(c)\), \(f_{m}(q)\) and an antecedent score \(f_{a}(c,q)\). Our model is based on this scoring function.3

Footnote 3: For more details, we refer to the original Kirstain et al. (2021) paper.

### Incorporating Centering Transitions

According to centering theory, we formulate centering transitions among utterances -- sentences specifically -- in our approach. Figure 2 shows our model architecture.

Centering Theory.Centering theory describes the local coherence and its relationship to attentional state within a discourse segment. From each utterance, one can extract (1) a set of _forward-looking centers_ (\(C_{f}\)) ranked according to their prominence, (2) a single _backward-looking center_ (\(C_{b}\)) connected with one of the \(C_{f}\) of the immediately preceding utterance, and (3) a _preferred center_ (\(C_{p}\)) which is the most salient center in \(C_{f}\). Following Jeon and Strube (2020), Table 1 presents all relations of centering transition at the local level. The relationships between discourse segments and

\begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{1}{r}{\(C_{b}(s_{i})\)} & \multicolumn{1}{r}{\(C_{b}(s_{i})\)} & No \\  & \(\approx C_{b}(s_{i-1})\) & \(\neq C_{b}(s_{i-1})\) & \(C_{b}(s_{i})\) \\ \hline \multicolumn{5}{l}{\(C_{b}(s_{i})\)} & Continue \\ \(\approx C_{p}(s_{i})\) & \multirow{2}{*}{Retain} & \multirow{2}{*}{Shift} & \multirow{2}{*}{None} \\ \cline{1-1} \multicolumn{5}{l}{\(C_{b}(s_{i})\)} & \\ \(\neq C_{p}(s_{i})\) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Centering transition relations. For instance, continue indicates that the center of utterance \(s_{i}\) is similar to the one in its previous utterance \(s_{i-1}\).

 

utterances then provide the fundamental structural centering relations for discourse.

**Scoring Function.** To combine the structure of the centering transitions with the coreference model, we add sentence score \(f_{s}(c,q)\) to the scoring function as shown below. The last item measures the relationship of the encoded sentences where two examined mentions are located. Especially, if the query mention is a singleton, we set the scoring function to 0.

\[f(c,q)=f_{m}(c)+f_{m}(q)+f_{a}(c,q)+f_{s}(c,q)\]

**Centering Transitions.** Having the mention scores \(f_{m}(\cdot)\), we use top \(\lambda n\) mentions for further processing of centering transitions (where \(n\) is the number of input tokens). Inspired by Jeon and Strube (2020), the remaining mentions with their positions in each sentence are encoded and fed into a multi-head self-attention matrix -- \(softmax\left(\frac{QKT^{T}}{\sqrt{d_{k}}}\right)\) -- to compute the attention score Vaswani et al. (2017). Q and K stand for the observed mentions of the sentence. From the ranked diagonal elements of the self-attention matrix, we take the top \(m\) mentions as \(C_{f}\), and the first most salient mention as \(C_{p}\). As for \(C_{b}\) of the sentence \(s_{i}\), we select the mention from \(C_{f}\) of its previous adjacent sentence \(s_{i-1}\), which has the highest semantic similarity with the current sentence \(s_{i}\). Here, we simply use the averaged token representations as the sentence embedding \(\mathbf{e}_{s_{i}}\). Finally, we generate centering transition relations (i.e., continue, retain and shift) between each two adjacent sentences by computing cosine similarity according to the rules in Table 1.

**Sentence Score.** Sometimes, a candidate mention is more than one sentence away from the query mention. Thus, we apply centering transitions not only at a local level but also to all other sentences in discourse globally. Treating sentences as nodes and transition relations as edges, each sentence can be encoded with its neighbouring nodes weighted by the edges which are connected to it, including self-connections. Then, we calculate the sentence score for each pair of mentions by using the embeddings of the sentences \(\mathbf{e}_{s}\) where the candidate and query mentions belong to.

\[f_{s}(c,q)=\mathbf{A}\cdot\mathbf{e}_{s_{c}}\cdot\mathbf{B}\cdot\mathbf{e}_{ s_{q}}\]

Figure 2: The figure shows our model architecture incorporating centering transitions for the sentence score. There are three example sentences in blue, red and green colors. A string of squares refers to a mention comprising a different number of tokens. The mention with a darker color indicates that it is a more salient center in a sentence.

 

In the above formula, **A** refers to an adjacency matrix, which represents the centering transitions between sentences by numerical values (i.e., continue: 3, retain: 2, shift: 1, and none: 0). They are induced from the above parts. Then, we use a bilinear product over the resulting representations with trainable parameter **B** to compute the sentence score.4 We examine this setting in our experiment **s2e+se_ct**. When **A** is an identity matrix (i.e., the matrix with ones on the main diagonal and zeros elsewhere), the aggregation over \({\bf e}_{\text{s}}\) does not occur. We use this setting **s2e+se** as our simple baseline system for comparative evaluation.

Footnote 4: We only adopt adjacency matrix to aggregate \(e_{s_{c}}\) rather than to aggregate both \(e_{s_{c}}\) and \(e_{s_{q}}\), as the former performs better based on our experiments.

## 4 Experiments

Settings.We train and evaluate our models on the English OntoNotes 5.0 dataset Pradhan et al. (2012). The results are reported using the CoNLL F1 score -- the average of MUC Vilain et al. (1995), B3 Bagga and Baldwin (1998), CEAFe Luo (2005) -- and LEA Moosavi and Strube (2016).

In our experiments, we examine two models, **s2e+se** and **s2e+se_ct**, as explained in SS3. We have 8 self-attention heads for the attention mechanisms, select the top 5 mentions for \(C_{f}\) of each sentence, and set the threshold of cosine similarity as 0.8 for computing the centering transition relations. Following the baseline, We also use Longformer Beltagy et al. (2020) as our pretrained model, which can process a sequence up to 4096 tokens. We set the other parameters the same as the baseline Kirstain et al. (2021).5 All our experiments are performed on a single NVIDIA Tesla V100 32G GPU.

Footnote 5: [https://github.com/yuwalkirstain/s2e-coref](https://github.com/yuwalkirstain/s2e-coref)

Results.Table 2 shows our results. The model **s2e+se_ct** achieves the best result with 80.9 F1 on OntoNotes. Though both examined models outperform the baselines only by a small margin, it suggests that incorporating centering transitions is helpful to some extent for coreference resolution. To thoroughly utilize the discourse structure, a graph or tree-based coreference model would be a promising research direction. One option would be latent trees which have been explored by Bjorkelund and Kuhn (2014) and Martschat and Strube (2015) for providing a more reliable basis for coreference resolution before the neural NLP era.

Analyses.First, we check the performance of our model for pronoun resolution on: (1) GAP dataset Webster et al. (2018); and (2) OntoNotes test dataset in which we only keep the resolved clusters containing pronouns in both gold and system outputs. Table 3 shows the marginal differences between the baseline and our model on the GAP benchmark.

GAP is gender-balanced corpus of ambiguous pronouns sampled from Wikipedia, in which most of examples are short texts. We compute the distributions of lengths of examples by sentence on both GAP and OntoNotes. As shown in the Table 4, the large majority of examples in GAP are 2-4 sentences texts, while the test set of OntoNotes has many documents longer than 5 sentences.

The experiment on OntoNotes in Table 5 shows that our model outperforms the baseline across all evaluation metrics. Overall, the two observed results suggest that our model involving centering transition relations between sentences can improve pronoun resoluti

\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{Model} & \multicolumn{3}{c}{MUC} & \multicolumn{3}{c}{B3} & \multicolumn{3}{c}{CEAF\({}_{e}\)} & \multicolumn{3}{c}{LEA} & \multicolumn{3}{c}{CoNLL} \\ \cline{2-17}  & P & R & F1 & P & R & F1 & P & R & F1 & P & R & F1 & F1 \\ \hline
**c2f** & 85.7 & 85.3 & 85.5 & 79.5 & **78.7** & 79.1 & 76.8 & 75.0 & 75.9 & 76.2 & 75.7 & 75.9 & 80.2 \\
**s2e** & 86.5 & 85.1 & 85.8 & 80.3 & 77.9 & 79.1 & 76.8 & **75.4** & 76.1 & 78.3 & 75.8 & 77.0 & 80.3 \\ \hline
**s2e + se** & 87.0 & 85.1 & 86.0 & 80.5 & 78.2 & 79.3 & 77.6 & 74.9 & 76.2 & 78.4 & 76.1 & 77.2 & 80.5 \\
**s2e + se\_ct** & **87.2** & **85.3** & **86.3** & **80.7** & 78.6 & **79.6** & **78.2** & 75.2 & **76.7** & **78.7** & **76.5** & **77.6** & **80.9** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance on the test set of the English OntoNotes 5.0 dataset. **c2f** refers to Joshi et al. (2020).

\begin{table}
\begin{tabular}{l r r r r}  & **Max** & **Fem** & **Bias** & **Overall** \\ \hline
**s2e** & **91.9** & **88.2** & 0.96 & **90.1** \\
**s2e + se\_ct (ours)** & 91.8 & 87.8 & 0.96 & 89.9 \\ \hline \end{tabular}
\end{table}
Table 3: F1 scores of the examined coreference resolvers running on the test set of the GAP dataset.

 

Second, we investigate how models perform on different genres. The CoNLL-2012 data contains broadcast conversation (bc), broadcast news (bn), magazine genre (mz), newswire genre (nw), pivot text (pt), telephone conversation (tc), and web data (wb) genres. In Table 6, we find that our method gets the most improvements on mz and nw genres, in which text is always formal well-structured. In contrast, tc and wb are the most challenging genres for our approach, where disfluent and ungrammatical segments and sentences may occur. Therefore, we summarize that discourse structure information is more beneficial for narrative text than less-formal text like conversation and web data. Resolving coreference in noisy user-generated text such as text on social media platforms is even harder Chai et al. (2020).

Finally, we observe the effect of maximum sentence distance \(d_{c_{i}}\) between any two mentions of each cluster on models. We take the average of all \(d_{c}\) in the same document as the sentence distance of it. Figure 3 depicts that our method performs better when mentions have a distance of more than six sentences. So, utilizing centering transitions globally is helpful for resolving clusters where mentions are more scattered. Our method captures how centers change between not only adjacent sentences but also non-adjacent sentences in the discourse. This is specially designed for coreference resolution based on centering theory. Meanwhile, we observe that it is difficult for both systems to resolve coreference on documents with long sentence distances (i.e., 12+ sentences).

## 5 Conclusion

We present a neural coreference model incorporating discourse structure information based on centering theory. The model captures the centering transition relationships between sentences. Each sentence is encoded with all neighbour sentences in a weighted graph. Our approach outperforms the baseline with 80.9 F1 score. Especially, it helps resolving pronoun in long documents, text in formal genres and clusters with scattered mentions.

### Acknowledgements

The authors thank the anonymous reviewers for their helpful comments and suggestions. This work has been funded by the Klaus Tschira Foundation, Heidelberg, Germany. The first author has been supported by a Heidelberg Institute for Theoretical Studies PhD. scholarship.

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\begin{table}
\begin{tabular}{l c c c c c c c}  & **bc** & **bn** & **maz** & **nw** & **pt** & **tc** & **wb** \\ \hline
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\end{table}
Table 6: Performance of the examined models on the test set for genres. The bottom line shows the improvement over the baseline by our method.

 

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