SlowGuess/NAACL_2022_OCR huggingface dataset:
where  $\delta$  indicates the margin. It enforces HyperMatch to sort the candidate keyphrases  $p^+$  ahead of  $p^-$  within their corresponding document. Through this training objective, our model will tend to extract the keyphrases, which are more relevant to the source document.
Six benchmark keyphrase datasets are used in our experiments, which contain OpenKP (Xiong et al., 2019),  $KP20k$  (Meng et al., 2017), Inspec (Hulth, 2003), Krapivin (Krapivin and Marchese, 2009), Nus (Nguyen and Kan, 2007), and SemEval (Kim et al., 2010). We follow the previous work (Sun et al., 2020) to preprocess each dataset with the same procedure.
Implementation details of HyperMatch are summarized in Table 1. The maximum document length is 512 tokens due to RoBERTa limitations (Liu et al., 2019) and documents are zero-padded or truncated to this length. Our model was implemented in Pytorch  $1.8^{2}$  (Paszke et al., 2019) using the hugging face reimplementation of RoBERTa $^{3}$  (Wolf et al., 2019) and was trained on eight NVIDIA RTX A4000 GPUs to achieve the best performance.
Hyperparameter	Dimension or Value
RoBERTa Embedding (RdC)	768
Hyperbolic Rank (Rdh)	768
Max Sequence Length	512
Maximum Phrase Length (N)	5
c	1
λ	0.5
δ	1.0
Optimizer	AdamW
Batch Size	72
Learning Rate	5 × 10-5
Warm-Up Proportion	10%
Table 1: Parameters used for training HyperMatch.
For the keyphrase extraction task, the performance of the existing models is typically evaluated by comparing the top-  $K$  predicted keyphrases with the target keyphrases (the ground-truth labels). The evaluation cutoff  $K$  can be a fixed number (e.g., F1@5 compares the top-5 keyphrases predicted by the model with the ground-truth to compute an F1 score). Following the previous work (Meng et al., 2017; Sun et al., 2020; Song et al., 2021), we adopt macro-averaged recall and F-measure (F1) as evaluation metrics, and  $K$  is set to be 1, 3, 5, and 10. In the evaluation, we apply Porter Stemmer $^4$  to both the target keyphrases and the extracted keyphrases when determining the exact match of keyphrases.
We compare two kinds of solid baselines to give a comprehensive evaluation of the performance of HyperMatch: unsupervised keyphrase extraction models (e.g., TextRank (Mihalcea and Tarau, 2004) and TFIDF (Jones, 2004)) and supervised keyphrase extraction models (e.g., classification and ranking models based variants of BERT (Sun et al., 2020)). Noticeably, HyperMatch extracts keyphrases without using additional features on the OpenKP dataset. Therefore, for the sake of fairness, we do not compare with the methods (Xiong et al., 2019; Wang et al., 2020) which use additional features to extract keyphrases.
In addition, this paper mainly focuses on exploring keyphrase extraction in hyperbolic space via a matching framework (similar to the ranking model). Hence, the compared baselines we mainly choose are keyphrase extraction methods based on
$^{2}$ https://pytorch.org/
<sup>3</sup>https://huggingface.co/transformers/index.html
<sup>4</sup>https://tartarus.org/martin/PorterStemmer/
Model	OpenKP
P@1	P@3	P@5	R@1	R@3	R@5	F1@1	F1@3	F1@5
Unsupervised Keyphrase Extraction Models
TFIDF	28.3	18.4	13.7	15.0	28.4	34.7	19.6†	22.3†	19.6†
TextRank	7.7	6.2	5.5	4.1	9.8	14.2	5.4†	7.6†	7.9†
Supervised Keyphrase Extraction via Classification Models
BERT-Chunking-KPE	51.1	30.6	22.5	27.1	46.4	55.8	34.0	35.6	31.1
SpanBERT-Chunking-KPE	52.3	32.1	23.5	27.8	48.6	58.1	34.8	37.2	32.4
RoBERTa-Chunking-KPE	53.3	32.2	23.5	28.3	48.6	58.1	35.5	37.3	32.4
Supervised Keyphrase Extraction via Ranking Models
BERT-Ranking-KPE	51.3	32.3	23.5	27.3	48.9	58.2	34.2	37.4	32.5
SpanBERT-Ranking-KPE	53.0	32.7	24.0	28.4	49.7	59.3	35.5	38.0	33.1
RoBERTa-Ranking-KPE	53.8	33.7	24.4	29.0	50.9	60.4	36.1	39.0	33.7
HyperMatch	54.7	33.9	24.7	29.5	51.5	61.2	36.4	39.4	33.8
Table 2: Model performance on the OpenKP dataset. The best results of our model are highlighted in bold. F1@3 is the main evaluation metric (marked in bold) for this dataset (Xiong et al., 2019; Wang et al., 2020).  $\dagger$  denotes these results are not included in the original paper and are estimated with Precision and Recall score. The results of the baselines are reported in their corresponding papers.
the classification and ranking models rather than some existing studies based on integration models (Ahmad et al., 2021; Wu et al., 2021) or multi-task learning (Song et al., 2021).
In this section, we test the performance of HyperMatch on six widely-used benchmark keyphrase extraction datasets (OpenKP, KP20k, Inspec, Krapivin, Nus, and Semeval) from three facets. The first one demonstrates its superiority by comparing HyperMatch with the recent baselines in terms of several metrics. The second one is to verify the effect of each component via ablation tests. The last one is to test the sensitivity of the hyperbolic margin-based triplet loss with different margins.
The experimental results are given in Table 2 and Table 3. Overall, HyperMatch outperforms the recent BERT-based keyphrase extraction models (the results are reported in their own articles) in most cases. Concretely, on the OpenKP and KP20k datasets, HyperMatch achieves better results than the best ranking models RoBERTa-Ranking-KPE. The main reason for this result may be that learning representation in hyperbolic space can capture more latent hierarchical structures than the euclidean space. Meanwhile, compared with the results on the other four zero-shot datasets (Inspec,
Krapivin, Nus, and Semeval) in Table 3, it can be seen that HyperMatch outperforms both unsupervised and supervised baselines. We consider that the main reason is the scaled phrase-document relevance explicitly models a strong connection between phrases and their corresponding document via the Poincaré distance, obtaining more robust performance even in different datasets.
In this section, we report on several ablation experiments to analyze the effect of different components. The ablation experiment on the OpenKP dataset is shown in Table 4.
To measure the effectiveness of hyperbolic space for the keyphrase extraction task, we compare it with the same model in the euclidean space and use the euclidean distance to explicitly model the phrase-document relevance. As shown in Table 4, HyperMatch outperforms EuclideanMatch, which shows that using the hyperbolic space can capture the latent hierarchical structures more effectively than the euclidean space.
To verify the effectiveness of the adaptive mixing layer, we propose a model HyperMatch w/o AML, which indicates HyperMatch without using the adaptive mixing layer module and only uses the last intermediate layer of RoBERTa to embed phrases and documents. As shown in Table 4, the performance of our model HyperMatch without us
Model	Inspec	Krapivin	Nus	SemEval	KP20k
F1@5	F1@10	F1@5	F1@10	F1@5	F1@10	F1@5	F1@10	F1@5	F1@10
TFIDF	22.3	30.4	11.3	14.3	13.9	18.1	12.0	18.4	10.5	13.0
TextRank	22.9	27.5	17.2	14.7	19.5	19.0	17.2	18.1	18.0	15.0
RoBERTa-Ranking-KPE†	28.1	29.1	29.9	23.7	44.6	37.7	35.4	32.6	41.4	34.2
HyperMatch	30.4	32.2	32.8	26.3	45.8	41.3	35.7	36.8	41.6	34.3
Table 3: Results of keyphrase extraction on five benchmark keyphrase datasets. F1 scores on the top 5 and 10 keyphrases are reported.  $\dagger$  indicates that these results are evaluated via the code which is provided by its corresponding paper. The best results are highlighted in bold.
Model	OpenKP
F1@1	F1@3	F1@5
HyperMatch	36.4	39.4	33.7
EuclideanMatch	36.1	38.5	33.4
HyperMatch w/o Relevance	36.1	38.9	33.6
HyperMatch w/o AML	36.3	38.7	33.5
Table 4: Ablation tests on the OpenKP dataset. The best results are highlighted in bold. F1@3 is the main evaluation metric (marked in bold) for this dataset.
ing the adaptive mixing layer drops in all evaluation metrics. These results demonstrate that combining all the intermediate layers of RoBERTa may capture more helpful information (e.g., surface, syntactic, and semantic) for obtaining candidate phrases and documents representations.
Unlike our model, most recent keyphrase extraction methods (e.g., RoBERTa-Ranking-KPE) implicitly model relevance between candidate phrases and their corresponding document by a linear transformation layer as the phrase-document relevance. Therefore, to verify the effectiveness of explicitly modeling the phrase-document relevance, we built the HyperMatch w/o Relevance, which only implicitly computes the phrase-document relevance by the hyperbolic linear transformation layer (Ganea et al., 2018). The results of HyperMatch w/o Relevance show a drop in all evaluation metrics, indicating that explicitly considering the relevance between phrases and the document is essential for estimating the importance of candidate phrases in the keyphrase extraction task.
5.3 Sensitivity of Hyperparameters
In this section, we verify the sensitivity of HyperMatch with different margins  $(\delta)$  of the hyperbolic margin-based triplet loss. For keyphrase extraction methods equipped with the margin-based triplet
Figure 3: Performance of HyperMatch with different margins  $(\delta)$  of the margin-based triplet loss on the OpenKP dataset.
loss, the margin design significantly impacts the final result, where a poor margin usually causes performance degradation. Therefore, we verify the effects of different margins on HyperMatch in Figure 3. We can see that HyperMatch achieves the best results when  $\delta = 1$ .
This section briefly describes the related work from two fields: keyphrase extraction and hyperbolic deep learning.
6.1 Keyphrase Extraction
Most existing KE models are based on the two-stage extraction framework, which consists of two main procedures: candidate keyphrase extraction and keyphrase importance estimation. Candidate keyphrase extraction extracts a set of candidate phrases from the document by some heuristics (e.g., essential n-gram-based phrases (Hulth, 2004; Medelyan et al., 2009; Xiong et al., 2019; Sun et al., 2020; Wang et al., 2020)). Keyphrase importance estimation first represents candidate phrases and documents by the pre-trained language models (Devlin et al., 2019; Liu et al., 2019) and then estimates the phrase-document relevance implicitly as the importance scores. Finally, the candidate phrases are ranked by their importance scores, which can be
learned by either unsupervised (Mihalcea and Tairau, 2004; Liu et al., 2009c) or supervised (Xiong et al., 2019; Sun et al., 2020; Mu et al., 2020) ranking approaches.
Different from the existing KE models, we map phrases and documents representations from the euclidean space to the same hyperbolic space to capture the latent hierarchical structures. Next, we adopt the Poincaré distance to explicitly model the phrase-document relevance as the important score of each candidate phrase. Finally, the hyperbolic margin-based triplet loss is used to optimize the whole model. To the best of our knowledge, we are the first study to explore supervised keyphrase extraction in hyperbolic space.
6.2 Hyperbolic Deep Learning
Recent studies on representation learning (Nickel and Kiela, 2017; Tifrea et al., 2019; Mathieu et al., 2019) demonstrate that hyperbolic space is more suitable for embedding symbolic data with hierarchies than the Euclidean space since the tree-like properties (Hamann, 2018) of the hyperbolic space make it efficient to learn hierarchical representations with low distortion (Sa et al., 2018; Sarkar, 2011). As linguistic ontologies are innately hierarchies, hierarchies are ubiquitous in natural language (Dai et al., 2021). Some recent studies show the superiority of hyperbolic space for many natural language processing tasks (Gulcehre et al., 2019; Zhu et al., 2020). Chen et al. (2021) demonstrate that mapping contextualized word embeddings (i.e., BERT-based embeddings) to the hyperbolic space can capture richer hierarchical structure information than the euclidean space when encoding natural language text. Inspired by the above methods, we transfer the embeddings obtained by the pretrained language models to hyperbolic space for extracting keyphrases.
A new hyperbolic relevance matching model HyperMatch is proposed to map candidate phrases and documents representations into the hyperbolic space and model the relevance between candidate phrases and the document via the Poincaré distance. Specifically, HyperMatch first combines the intermediate layers of RoBERTa via the adaptive mixing layer for capturing richer syntactic and semantic information. Then, phrases and documents are encoded in the same hyperbolic space to cap
ture the latent hierarchical structures. Next, the phrase-document relevance is estimated explicitly via the Poincaré distance as the importance scores of all the candidate keyphrases. Finally, we adopt the hyperbolic margin-based triplet loss to optimize the whole model for extracting keyphrases.
In this paper, we explore keyphrase extraction in hyperbolic space and implicitly model the latent hierarchical structures hidden in natural languages when representing candidate keyphrases and documents. In the future, it will be interesting to introduce external knowledge (e.g., WordNet) to explicitly model the latent hierarchical structures when representing candidate keyphrases and documents. In addition, our code is publicly available to facilitate other research<sup>5</sup>.
This work was supported in part by the National Key Research and Development Program of China under Grant 2020AAA0106800; the National Science Foundation of China under Grant 61822601 and 61773050; the Beijing Natural Science Foundation under Grant Z180006; the Fundamental Research Funds for the Central Universities (2019JBZ110).
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