Add Batch edacbd78-c85a-4f0c-bec5-9f7f01694882 data

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@@ -7129,3 +7129,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2023/Investigating Bias in Multilingual Language Models_ Cross-Lingual Transfer of Debiasing Techniques/ac884595-2bc6-45c5-8d3c-8fe9015e5586_content_list.json

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+        "text": "Manon Reusens<sup>1</sup>, Philipp Borchert<sup>1,2</sup>, Margot Mieskes<sup>3</sup>, Jochen De Weerdt<sup>1</sup>, Bart Baesens<sup>1,4</sup>",
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+        "text": "$^{2}$ IESEG School of Management, 3 Rue de la Digue, 59000 Lille, France",
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+        "type": "text",
+        "text": "<sup>3</sup>University of Applied Sciences Darmstadt",
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+        "type": "text",
+        "text": "$^{4}$ Department of Decision Analytics and Risk, University of Southampton {manon.reusens, philipp.borchert, jochen.deweerdt, bart.daesens} @kuleuven.be margot.mieskes@h-da.de",
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+    {
+        "type": "text",
+        "text": "DISCLAIMER: This paper contains explicit statements that are potentially offensive.",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper investigates the transferability of debiasing techniques across different languages within multilingual models. We examine the applicability of these techniques in English, French, German, and Dutch. Using multilingual BERT (mBERT), we demonstrate that cross-lingual transfer of debiasing techniques is not only feasible but also yields promising results. Surprisingly, our findings reveal no performance disadvantages when applying these techniques to non-English languages. Using translations of the CrowS-Pairs dataset, our analysis identifies SentenceDebias as the best technique across different languages, reducing bias in mBERT by an average of  $13\\%$ . We also find that debiasing techniques with additional pretraining exhibit enhanced cross-lingual effectiveness for the languages included in the analyses, particularly in lower-resource languages. These novel insights contribute to a deeper understanding of bias mitigation in multilingual language models and provide practical guidance for debiasing techniques in different language contexts.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "There has been a growing interest in addressing bias detection and mitigation in Natural Language Processing (NLP) due to their societal implications. Initially, research focused on debiasing word embeddings (Bolukbasi et al., 2016; Zhao et al., 2018b), but recent studies found that pretrained language models also capture social biases present in training data (Meade et al., 2022). Hence, attention has shifted towards debiasing techniques that target sentence representations. These techniques include additional pretraining steps (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019)",
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+    {
+        "type": "image",
+        "img_path": "images/ccbe36bc7cf718d0565ea636470abe47965474edc31478ceb635fccb2d995619.jpg",
+        "image_caption": [
+            "Figure 1: The example of the English CrowS-Pairs dataset illustrates sentence probabilities after debiasing mBERT with SentenceDebias in English, French, German, and Dutch."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "and projection-based methods that assume a bias direction (Liang et al., 2020a; Ravfogel et al., 2020; Liang et al., 2020b).",
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+    {
+        "type": "text",
+        "text": "While debiasing techniques have been developed and evaluated for monolingual, and mostly English models, the effectiveness and transferability of these techniques to diverse languages within multilingual models remain largely unexplored (Stanczak and Augenstein, 2021; Sun et al., 2019). Our research aims to bridge this gap by examining the potential of debiasing techniques applied to one language to effectively mitigate bias in other languages within multilingual large language models. We examine English (EN), French (FR), German (DE), and Dutch (NL). Figure 1 illustrates an example sentence pair included in the English CrowS-Pairs dataset<sup>1</sup>, where the unmodified and modified parts are highlighted in blue and yellow respectively. It shows the predicted probabilities of",
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+    {
+        "type": "page_footnote",
+        "text": "This example assumes gender to be binary. We acknowledge that this fails to capture the full range of gender identities.",
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+    },
+    {
+        "type": "page_number",
+        "text": "2887",
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+    },
+    {
+        "type": "footer",
+        "text": "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 2887-2896 December 6-10, 2023 ©2023 Association for Computational Linguistics",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "the modified part occurring given the unmodified part across different debiasing languages.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This study examines the cross-lingual transferability of debiasing techniques using mBERT. mBERT, trained on Wikipedia data from diverse languages, possesses the capability to process and generate text in various linguistic contexts. Despite balancing efforts, it still performs worse on low-resource languages (Wu and Dredze, 2020; Devlin, 2018). We investigate whether this performance disparity extends to gender, religious, and racial biases. Related studies demonstrate the effectiveness of cross-lingual debiasing for individual techniques and selected bias scopes (Liang et al., 2020b; Lauscher et al., 2021). We show how to reduce bias in mBERT across different languages by conducting a benchmark of state-of-the-art (SOTA) debiasing techniques and providing guidance on its implementation. To facilitate further research and reproducibility, we make the code and additional data available to the research community $^{2}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our contributions can be summarized as follows: 1) We provide a benchmark of different SOTA debiasing techniques across multiple languages in a multilingual large language model. 2) We find that SentenceDebias is the most effective for cross-lingual debiasing, reducing the bias in mBERT by  $13\\%$ . 3) We provide implementation guidelines for debiasing multilingual models and highlight the differences in the cross-lingual transferability of different debiasing techniques. We find that most projection-based techniques applied to one language yield similar predictions across evaluation languages. We also recommend performing the techniques with an additional pretraining step on the lowest resource language within the multilingual model for optimal results.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 Methodology",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This section introduces the data, debiasing techniques, and experimental setup respectively.",
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+    {
+        "type": "text",
+        "text": "2.1 CrowS-Pairs",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "CrowS-Pairs is a benchmark dataset comprising 1508 examples that address stereotypes associated with historically disadvantaged groups in the US, encompassing various types of bias, such as age and religion (Nangia et al., 2020). Following Meade et al. (2022), where different debiasing tech",
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+    {
+        "type": "text",
+        "text": "niques were benchmarked and their effectiveness demonstrated on BERT for gender, race, and religion, we focus on these three types of bias. Néveol et al. (2022) translated the dataset in French. To the best of our knowledge, there are currently no peer-reviewed variants of CrowS-Pairs available in other languages. Therefore, we used three samples of the full dataset and translated them into the respective language to evaluate our experiments.",
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+    {
+        "type": "text",
+        "text": "To create an evaluation set for our experiments, we started from the English CrowS-Pairs dataset (Nangia et al., 2020). We randomly sampled  $N$  instances, where  $N \\in \\{20,30,40,50\\}$ , and measured the performance differences on mBERT and BERT. Through three random seeds, we found that a sample size of 40 resulted in an average performance correlation of more than  $75\\%$  with the full dataset for both models. Thus, we conclude that using 40 instances with three random seeds provides a representative dataset for our evaluation. Further details are shown in Appendix A. Subsequently, we included the translated samples from each language into our dataset, either the corresponding sentences from the French CrowS-Pairs or a translation.",
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+    {
+        "type": "text",
+        "text": "2.2 Debiasing techniques",
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+        "type": "text",
+        "text": "Next, the different debiasing techniques are explained. For more information on the attribute lists used, we refer to Appendix B.",
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+    {
+        "type": "text",
+        "text": "Counterfactual Data Augmentation (CDA) is a debiasing technique that trains the model on an augmented training set (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019). First, the corpus is augmented by duplicating sentences that include words from a predefined attribute list. Next, counterfactual sentences are generated by swapping these attribute words with other variants in the list, for example, swapping  $he$  by  $she$ . We augment  $10\\%$  of the Wikipedia corpus of the respective language and use an additional pretraining step to debias the model for three random seeds and average the results.",
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+    {
+        "type": "text",
+        "text": "Dropout Regularization (DO) is introduced by Webster et al. (2020) as a debiasing technique by implementing an additional pretraining step. We execute this pretraining step while training on  $10\\%$  of the Wikipedia corpus of the respective language using three random seeds and averaging the results.",
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+    {
+        "type": "text",
+        "text": "SentenceDebias (SenDeb) introduced by Liang et al. (2020a) is a projection-based debiasing technique extending debiasing word embeddings",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://github.com/manon-reusens/multilingual.bias",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2888",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "(Bolukbasi et al., 2016) to sentence representations. Attribute words from a predefined list are contextualized by retrieving their occurrences from a corpus and augmented with CDA. Next, the bias subspace is computed using the representations of these sentences through principal component analysis (PCA). The first  $K$  dimensions of PCA are assumed to define the bias subspace as they capture the principle directions of variation of the representations. We debias the last hidden state of the mBERT model and implement SenDeb using  $2.5\\%$  of the Wikipedia text in the respective language.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Iterative Nullspace Projection (INLP) is a projection-based debiasing technique in which multiple linear classifiers are trained to predict biases, such as gender, that are to be removed from the sentence representations (Ravfogel et al., 2020). After training a single classifier, the representations are debiased by projecting them onto the learned linear classifier's weight matrix to gather the rowspace projection. We implement this technique using the  $2.5\\%$  of the Wikipedia text in each language.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "DensRay (DR) is a projection-based debiasing technique first implemented by (Duftner and Schütze, 2019) and adapted for contextualized word embeddings by (Liang et al., 2020b). This technique is similar to SenDeb, but the bias direction is calculated differently. This method aims to find an optimal orthogonal matrix so that the first  $K$  dimensions correlate well with the linguistic features in the rotated space. The second dimension is assumed to be orthogonal to the first one. The bias direction is considered to correspond to the eigenvector of the highest eigenvalue of the matrix. DR is only implemented for a binary bias type and using it for multiclass bias types requires modifying the technique. Therefore, we only apply it to the gender bias type. We implement DR debiasing the last hidden state of mBERT and using  $2.5\\%$  of the Wikipedia text in the respective language.",
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+    {
+        "type": "text",
+        "text": "2.3 Experimental setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We debias mBERT using language  $X$  and evaluating it on language  $Y$  with  $X, Y \\in \\{EN, FR, DE, NL\\}$ . In essence, we debiased the model using one language and evaluated it on another, covering all language combinations in our experiments. We implement mBERT in its base configuration (uncased, 12 layers, 768 hidden size) and utilize the bias score as implemented in Meade et al. (2022). This metric evaluates the percentage",
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+    {
+        "type": "text",
+        "text": "of sentences where the model prefers the more biased sentence over the less biased sentence, with an optimal performance of  $50\\%$ . All experiments are performed on P100 GPUs.",
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+    {
+        "type": "text",
+        "text": "3 Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows the performance of the different debiasing techniques when debiasing in English in terms of the absolute deviation of the ideal unbiased model. This is an average score for all bias types and models trained for the respective evaluation language. Base represents the score that is achieved by mBERT on the respective evaluation language dataset before debiasing. More results are shown in Appendices C and D.",
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+    {
+        "type": "text",
+        "text": "As shown in Table 1, English is relatively unbiased compared to the other languages and shows a small bias increase after debiasing. This observation aligns with the findings of Ahn and Oh (2021), who propose mBERT as a debiasing technique. In cases where the initial bias score is already close to the optimal level, further debiasing can lead to overcompensation, consequently amplifying the total bias. We assume that an unbiased model should equally prioritize both biased and unbiased sentences. However, when debiasing techniques tend to overcorrect, they skew the balance towards favoring the prediction of unbiased sentences over biased ones. Addressing this challenge necessitates the adoption of specialized techniques to effectively mitigate any residual bias.",
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+    {
+        "type": "text",
+        "text": "This phenomenon of overcompensation occurs in several underperforming techniques, as illustrated in Table 1. Notably, we find instances of overcompensation for gender when debiasing using INLP for French and using CDA for German, as well as for race when debiasing using DO for German. Another contributing factor to the poor performance of certain techniques within specific debiasing and evaluation language combinations lies in the inherent ineffectiveness of the debiasing method itself, exemplified by the cases of gender debiasing using CDA for French and religion debiasing using CDA for German. In Tables 5, 6, and 7, we find overcompensation for gender when debiasing with INLP in German and French, evaluating in German, debiasing with Sendeb and DR in French, and evaluating in French, as well as when debiasing in Dutch with INLP and evaluating in French. Moreover, overcompensation for race is also observed when debiasing with CDA in French",
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+    {
+        "type": "page_number",
+        "text": "2889",
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+    {
+        "type": "table",
+        "img_path": "images/3b2d2bd1cc458252bf44eba5c72e377a3e1d4c59441a80fcd55a79174fe13803.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Base</td><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.70↑</td><td>7.78↑</td><td>6.94↑</td><td>13.43↑</td><td>8.70↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.20↑</td><td>10↓</td><td>10.28↓</td><td>12.6↑</td><td>9.44↓</td></tr><tr><td>DE</td><td>9.33</td><td>7.52↓</td><td>6.57↓</td><td>6.84↓</td><td>10.75↑</td><td>9.75↑</td></tr><tr><td>NL</td><td>17.66</td><td>13.96↓</td><td>15.14↓</td><td>16.54↓</td><td>16.84↓</td><td>17.40↓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "and evaluating in German.",
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+    {
+        "type": "text",
+        "text": "Is cross-lingual transferability of debiasing techniques possible? Table 1 shows that cross-lingual transfer is possible using English as debiasing language. Figure 2 confirms this, depicting the bias scores averaged over all debiasing techniques. As discussed, for English, these techniques increase the bias contained in the model due to its already close to optimal performance. For the other evaluation languages, we find better performance after debiasing. Therefore, we conclude that for these four languages, it is possible to debias the mBERT model to some extent using a different debiasing language, except when the bias contained in the model is already relatively low.",
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+    {
+        "type": "text",
+        "text": "To shed some light on the insights that can be gathered from Figure 2, Table 2 offers an overview of the best- and worst-performing techniques per evaluation language. As shown, Dutch is found to be the best debiasing language for English. This is because this debiasing language has shown to overcompensate the gender bias category the least, therefore, resulting in the best performance. In general, we find that using the same debiasing language as evaluation language often results in an overcompensation of the bias, therefore turning around the bias direction. This means that the best-performing debiasing language is often not the same as the evaluation language. However, German is the exception. As this language already has the highest bias score for gender before debiasing, strong debiasing is beneficial and therefore does not result in overcompensation. Besides German being the best-performing debiasing language for German, it also shows the best performance for French because it achieves the best performance on all different evaluation sets. Moreover, it also shows less overcompensation for the gender bias present in the model than other languages such as Dutch.",
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+    {
+        "type": "text",
+        "text": "French is the worst-performing debiasing language for all evaluation languages except for Dutch, where it is the best-performing one. We find that when evaluating in French, the gender bias is over",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ab1533e01bbc82cc6f9156043cb7e9c5e1d0137c9a39e51f2cfec0ecaefe0c18.jpg",
+        "table_caption": [
+            "Table 1: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in English."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Evaluation language</td><td>Best debiasing language</td><td>worst debiasing language</td></tr><tr><td>English</td><td>Dutch</td><td>French</td></tr><tr><td>French</td><td>German</td><td>French</td></tr><tr><td>German</td><td>German</td><td>French</td></tr><tr><td>Dutch</td><td>French</td><td>English</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Overview best- and worst-performing debiasing languages per evaluation language.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/9730fd8a88c0edb9da23f7d55bcdfa07c9f51f298fea8ebc259d0563075d7d42.jpg",
+        "image_caption": [
+            "Figure 2: Average bias scores per evaluation and debi-aising language."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "compensated. For English, both racial and gender bias are overcompensated. The German evaluation shows lower overall performance due to already two ineffective methods (INLP and CDA), which were also due to overcompensating racial bias. Finally, for Dutch, we find that debiasing with French overcompensates gender bias less than Dutch and, therefore, is the best-performing method. As Dutch has the second highest gender bias score before debiasing, it also benefits from strong debiasing and therefore both French and Dutch perform well.",
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+    {
+        "type": "text",
+        "text": "We believe that these results are influenced by the fact that both German and French have a grammatical gender distinction, which may impact debiasing gender to a greater extent. This grammatical gender distinction is not embedded in English and Dutch. Moreover, as the religion category regularly shows limited bias decrease, we find that the performance in the gender and race category often determines whether a technique works well or not.",
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+    {
+        "type": "text",
+        "text": "How are the different techniques affected by cross-lingual debiasing? Table 3 shows the overall percentage increase of the bias score per technique. From this, we conclude that SenDeb is the best-performing technique and reduces bias in mBERT on average by  $13\\%$ . DO is the second best-performing method reducing bias on average by  $10\\%$ . However, Figure 3 shows that DO performs well for all debiasing languages except English, while SenDeb performs consistently well for all languages. The other techniques perform worse overall. Hence, we suggest using SenDeb as cross-lingual debiasing technique for these languages.",
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+    {
+        "type": "page_number",
+        "text": "2890",
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+        "type": "table",
+        "img_path": "images/8b3f2fb8daac0f9163e450fe2c3fceeede6c419a9249801ba5a9e4059f4fbca7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>Dropout</td></tr><tr><td>1.11</td><td>13.21</td><td>7.1</td><td>-0.16</td><td>10.21</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3: Average percentage difference in bias scores of each technique compared to the base model.",
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+    {
+        "type": "image",
+        "img_path": "images/e95201d19415bb36863f645c9b70e4055bc0d942a37c68f83da930823f45e0ce.jpg",
+        "image_caption": [
+            "Figure 3: Average bias score per technique per debiasing language."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "When zooming in on the projection-based techniques, i.e. INLP, SenDeb, and DR, a high performance variation is shown in Table 3 and Figure 3. While SenDeb offers consistent performance for all different debiasing languages, we see more variation and a lower bias decrease for INLP. This is due to the high variation in performance, resulting in a higher overall average. As INLP uses multiple linear classifiers to define the projection matrix, high variability is introduced. Since DR was only implemented for gender, no performance gains can be obtained from the other bias types, therefore resulting in a lower overall performance increase.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Techniques using an additional pretraining step obtain the best results when debiasing in Dutch, as illustrated in Figure 4. Notably, Dutch is the lowest resource language out of these four languages during pretraining (Wu and Dredze, 2020). This additional pretraining step lets the model learn unbiased associations between words while becoming familiar with the lower-resource language resulting in lower overall bias. Therefore, we conclude that, for our set of languages, these techniques are most effective when applied to low-resource languages.",
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+    {
+        "type": "text",
+        "text": "4 Related work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Significant research focuses on the cross-lingual performance of mBERT (Wu and Dredze, 2020; Pires et al., 2019; Libovický et al., 2019). Limited research focuses on the cross-lingual transferability of debiasing techniques in mBERT (Stanczak and Augenstein, 2021; Sun et al., 2019). Liang et al. (2020b) use DensRay in English to debias Chinese",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/3b20bcb64277e02f2f9e6a3ba214f4a93af3f37c1dc0b1696a7b1f9913379497.jpg",
+        "image_caption": [
+            "Figure 4: Average bias score per debiasing languages for both CDA and DO."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "in mBERT for gender. Similarly, Zhao et al. (2020) analyze the cross-lingual transfer of gender bias mitigation using one method. Lauscher et al. (2021) also find that their proposed technique, ADELE, can transfer debiasing across six languages. Other studies analyze biases contained in multilingual language models. Kaneko et al. (2022) evaluate bias across multiple languages in masked language models using a new metric. Ahn and Oh (2021) study ethnic bias and its variability over languages proposing mBERT as debiasing technique. Finally, some studies also explore the cross-lingual transferability of downstream tasks (Levy et al., 2023).",
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+    {
+        "type": "text",
+        "text": "5 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Most studies focus on debiasing techniques for large language models, but rarely explore their cross-lingual transferability. Therefore, we offer a benchmark for SOTA debiasing techniques on mBERT across multiple languages (EN, FR, DE, NL) and show that debiasing is transferable across languages, yielding promising results. We provide guidance for cross-lingual debiasing, highlighting SenDeb as the best-performing method, reducing bias in mBERT by  $13\\%$ . Additionally, we find that, for the studied languages, debiasing with the lowest resource language is effective for techniques involving an additional training step (CDA and DO). This research is a first step into the cross-lingual transferability of debiasing techniques. Further studies should include languages from different cultures and other multilingual large language models to assess generalizability.",
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+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A first limitation concerns the analysis focused on four closely related languages from a similar culture. A broader range of languages should be explored to ensure the generalizability of the findings. Our research was conducted employing a",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "2891",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "single multilingual model, mBERT. Extending this to other multilingual language models would provide valuable insights into the wider applicability of the results. Moreover, the evaluation of outcomes relied primarily on the CrowS-Pairs metric, although efforts were made to enhance the understanding by examining the absolute difference compared to the optimal model. Next, the consideration of gender was limited to binary classification, overlooking non-binary gender identities. This should be further addressed in future research. Furthermore, a comprehensive multilingual dataset to assess stereotypes across different languages is not available, and thus, the English CrowS-Pairs dataset was translated and corresponding sentences of the French dataset were used. Nevertheless, typical stereotypes for other languages were not adequately represented. Furthermore, the dataset used in the study exhibited certain flaws highlighted by Blodgett et al. (2021), such as the influence of selected names on predictions, which was observed to have a significant impact. This needs to be investigated further. Additionally, attribute lists for languages other than English were not available to the same extent. We tried to compile lists for French, Dutch, and German, excluding words with multiple meanings to minimize noise. However, our lists were not exhaustive, and therefore the omission of relevant attributes is possible. It is also worth noting that, in certain cases, the generic masculine form was considered the preferred answer, despite it being included in the attribute lists. Finally, the applicability of downstream tasks should be investigated (e.g. (Levy et al., 2023)). Hence, future research should encompass a wider language scope, include multiple models, address existing dataset flaws, and develop more comprehensive attribute lists for various languages.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ethics Statement",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We would like to address three key ethical considerations in this study that highlight ongoing challenges and complexities associated with mitigating bias in large language models. First, it is important to acknowledge that the gender bias examined in this paper is approached from a binary perspective. However, this does not capture the full range of gender identities present in reality. While we recognize this limitation, it was necessary to simplify the analysis for experimental purposes. In future research, we hope to address this limitation. Second, despite",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "efforts to debias the multilingual large language model, it is important to note that not all forms of bias are completely mitigated. The applied debiasing techniques do lower the bias present in the model, however, there is still bias present in the model both within and outside the targeted bias types. Finally, we recognize that our evaluation datasets do not encompass all the different biases that might be present in the model. Therefore, even if a model would obtain a perfect score, it is still possible that other forms of bias persist.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This research was funded by the Statistics Flanders research cooperation agreement on Data Science for Official Statistics. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            510,
+            407,
+            608,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        "bbox": [
+            114,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Ran Zmigrod, Sabrina J. Mielke, Hanna Wallach, and Ryan Cotterell. 2019. Counterfactual data augmentation for mitigating gender stereotypes in languages with rich morphology. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 1651-1661, Florence, Italy. Association for Computational Linguistics.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A Correlation samples and full dataset",
+        "text_level": 1,
+        "bbox": [
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+            318,
+            465,
+            332
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4 shows the overall correlation between the performance of the respective model on the full dataset and on the sample over three random seeds. Full represents that we looked at all different bias types in the CrowS-Pairs dataset and (3) refers to the three bias types used in this study (gender, religion, and race). We used a threshold of  $75\\%$  to decide on the sample size.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3adc455cd422fe6dfb64d9e3125c1be007d5f0f1add8575301b4c49e5f09bc06.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT full</td><td>mBERT (3)</td><td>BERT full</td><td>BERT (3)</td></tr><tr><td>size 20</td><td>85.71</td><td>66.58</td><td>74.40</td><td>70.58</td></tr><tr><td>size 30</td><td>88.54</td><td>66.80</td><td>80.14</td><td>70.66</td></tr><tr><td>size 40</td><td>93.11</td><td>86.02</td><td>83.78</td><td>75.88</td></tr><tr><td>size 50</td><td>94.21</td><td>86.82</td><td>90.52</td><td>87.32</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 4: Correlation between the sample and full respective model's performance over three random seeds before debiasing.",
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+    },
+    {
+        "type": "text",
+        "text": "B Attribute Lists",
+        "text_level": 1,
+        "bbox": [
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+            278,
+            634
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The different lists of attribute words per language used for CDA, SenDeb, INLP, and DR are listed below. We started from the lists in (Meade et al., 2022; Zhao et al., 2018a; Liang et al., 2020a) and extended these to other languages. For the non-English lists, we first translated the words in the English attribute list if a similar relation is contained in the translated words. Subsequently, we asked a native speaker of the respective language whether there are extra words that contain similar relations which do not exist in English. We added these to the list. However, note that these lists are not exhaustive, as many other words still exist that express the same relationship. Nevertheless, this list already provides a more extensive attribute list than by only translating the English attribute list.",
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+    },
+    {
+        "type": "text",
+        "text": "English",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Gender: (Zhao et al., 2018a) actor, actress, actors, actresses, airman, airwoman, airmen, airwomen, uncle, aunt, uncles, aunts, boy, girl, boys, girls, groom, bride, grooms, brides, brother, sister, brothers, sisters, businessman, businesswoman, businessmen, businesswomen, chairman, chairwoman, chairmen, chairwomen, dude, chick, dudes, chicks, dad, mom, dads, moms, daddy, mommy, daddies, mommies, son, daughter, sons, daughters, father, mother, fathers, mothers, male, female, males, females, guy, gal, guys, gals, gentleman, lady, gentlemen, ladies, grandson, granddaughter, granddaughters, grandsons, granddaughters, guy, girl, guys, girls, he, she, himself, herself, him, her, his, her, husband, wife, husbands, wives, king, queen, kings, queens, lord, lady, lords, ladies, sir, ma'am, man, woman, men, women, sir miss mr. mrs. ms. policeman, policeman woman, prince princess princes princesses spokeseman spokeswoman spokesmen spokeswomen.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Race: (Meade et al., 2022) black, caucasian, asian, african, caucasian, asian, black, white, asian, africa, america, asia, africa, america, china, africa, europe, asia.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Religion: (Liang et al., 2020a) Jewish, christian, muslim, jews, christians, muslims, torah, bible, quran, synagogue, church, mosque, rabbi, priest, imam, judaism, christianity, islam.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "French",
+        "text_level": 1,
+        "bbox": [
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+            542,
+            588,
+            556
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Gender: acteur, actrice, actuurs, actrices, aviateur, aviatrice, aviateurs, aviatrices, oncle, tante, oncle, tantine, tonton, tata, tontons, tatas, oncles, tantes, oncles, tantines, garcon, fille, garcons, filles, marié, mariée, époux, épouse, mariés, mariées, époux, épouses, brother, sister, frère, soeur, frères, soeurs, entrepreneur, entrepriseuse, entrepreneur, entrepriseure, entrepreneurs, entreprisesures, entrepreneurs, entreprisesuses, président, présidente, prêsidents, prêsentes, mec, meuf, gamin, gamine, mecs, meufs, père, mère, pères, mères, papa, maman, papas, mamans, fils, fille, fils, filles, abbe, abbesse, abbés, abbesses, masculin, féminin, malé, femelle, malés, femelles, gars, fille, gars, filles, monsieur, dame, messieurs, dames, petit-fils, petite-fille, petit-fils, petites-filles, il, elle, lui-même, elle-même, lui, elle, mari, femme, maris, femmes, roi, reine, rois, reines, seigneur, seigneuresse, seigneurs, seigneuresses, monsieur, m'dame, monsieur, madame, homme, femme, hommes, femmes, monsieur, mademoiselle, mr, mme, mr, mLle, policier, policière, prince",
+        "bbox": [
+            505,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "2894",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "princesse, princes, princesses, copain, copine, copains, copines, ami, amie, amis, amies, voisin, voisine, docteur, doctoresse, docteur, docteure, boulanger, boulangere, héros, héroîne, employé, employeee, employés, employées, chef, cheffe, chefs, cheffes, cousin, cousine, grand-père, grand-mère, expert, experte, pompier, pompère, pompiers, pompières, agricultrice, agriculteurs, agricultrices, travaillerur, travailluse, infirmier, infirmière, infirmiers, infirmières, patron, patronne, patrons, patronnes.",
+        "bbox": [
+            110,
+            85,
+            489,
+            260
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Race: noir, blanc, asiatique, black, blanc, asiatique, noir, caucasien, asiatique, africain, europeen, asienne, african, americain, asiatique, afrique, amerique, asie, afrique, amerique, chine, afrique, europe, asie.",
+        "bbox": [
+            112,
+            261,
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+            341
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Religion: juif, chretien, musulman, juifs, chretiens, musulmans, torah, bible, coran, synagogue, église, mosquee, rabbin, prétre, imam, judaïisme, christianisme, islam.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "German",
+        "text_level": 1,
+        "bbox": [
+            132,
+            410,
+            203,
+            423
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gender: schauspieler, schauspielerin, koch, kochin, Lehrer, Lehrerin, schüler, schülerin, student, studentin, pilot, pilotin, onkel, tante, jungge, madchen, brautigam, braut, bruder, schwester, geschäftsmann, geschäftsfrau, vorsitzender, vorsitzende, vater, mutter, papa, mama, sohn, tochter, mann, Frau, kerl, madel, herr, dame, enkel, enkelin, großvater, großmutter, cousin, cousine, er, sie, ihm, ihr, sein, ihr, seine, ihre, ehemann, ehefrau, feuerwehrmann, feuerwehrfrau, konig, konigin, fürst, fürstin, herzog, herzogin, mann, Frau, Männer, femmes, hr., fr., polizist, polizistin, prinz, prinzessin, sprecher, sprecherin, kollege, kollegin, mitarbeiter, mitarbeiterin, helfer, helferin, anwalt, anwältin, bauarbeiter, bauarbeiterin, krankenpfleger, krankenpflegerin, chef, chefsin, vorgesetzter, vorgesetzte, sönger, söngerin, kunde, kundin, besucher, besucherin, freund, freundin, arzt, ärtzin, verkäufer, verkäuferin, kanzler, kanzlerin, geschäftsleiter, geschäftsleiterin, pfleger, pflegerin, kellner, kellnerin.",
+        "bbox": [
+            110,
+            429,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Race: dunkelhautig, hellhautig, asiatisch, afrikaner, europäer, asiate, amerikaner, afrika, amerika, asien, china.",
+        "bbox": [
+            112,
+            768,
+            487,
+            814
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Religion: jiudisch, christlich, muslimisch, Jude, christ, muslim, torah, bibel, koran, synagogue, kirche, moschee, rabbiner, pfarrer, imam, judentum, christentum, islam.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Dutch",
+        "text_level": 1,
+        "bbox": [
+            132,
+            883,
+            184,
+            897
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gender: acteur, actrice, actuers, actrices,",
+        "bbox": [
+            132,
+            903,
+            487,
+            917
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "oom, tante, ooms, tantes, nonkel, tante, nonkels, tantes,jongen,meisje,jongens,meisjes,bruidgem, bruid, bruidegommen, bruiden, broer, zus, broers,zussen,zakenman,zakenvrouw,zakenmannen,zakenvrouwen,kerel,griet,kerels,grieten,vader,moeder,vaders,moeders,papa,mama,papa's,mama's,zoon, dochter;zonen,dochters,man,vrouw,mannen,vrouwen,gast,wijf,gasten,wijven,heer,dame,heren,dames,kleinzoon,kleindochter,kleinzonen,kleindochters,vent,vrouw,venten,vrouwen,hij,zij,hemzelf,haarzelf,hem,haar,zijn,haar,mannelijk,vrouwelijk,vriend,vriendin,vrienden,vriendinnen,koning,koningin,koningen,koninginnen,heer,dame,heren,dames,meneer,mevrouw,jongeheer,jongedame,jongeheren,jongedames,jongeheer,juffrouw,jongeheren,juffrouwen,politieagent,politieagente,prins,prinses,prinsen,prinsessen,woordvoerder,wordvoerster,wordvoerders,wordvoersters,brandweerman,brandweervrouw,brandweermannen,brandweervrouwen,timmerman,timmervrouw,timmermannen,timmervrouwen,meester,juf,meesters,juffen,verpleger,verpleegster,verplegers,verpleegsters,bestuurder,bestuurster,bestuurders,bestuursters,kuisman,kuisvrouw,kuismannen,kuisvrouwen,kok,kokkin,kokken,kokkinen,leraar,lerares,directeur,directrice,directeurs,directrices,secretaris,secretaresse,secretaris-SEN,secretaressen,boer,boerin,boeren,boerinnen,held,heldin,gastheer,gastvrouw,gastheren,gastvrouwen,opa,oma,opa's,oma's,grootvader,grootmoeder,grootvaders,grootmoeders.",
+        "bbox": [
+            505,
+            85,
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+            599
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Race: afrikaans, amerikaans, aziatisch, afrikaans, europees, aziatisch, zwart, blank, aziatisch, afrika, amerika, aziè, afrika, amerika, china, afrika, europa, aziè.",
+        "bbox": [
+            507,
+            600,
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+            662
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Religion: joods, christen, moslim, joden, christenen, moslims, thorabijbel, koran, synagogue, kerk, moskee, rabbijn, priester, imam, jodendom, christendom, islam.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "C Averaged results",
+        "text_level": 1,
+        "bbox": [
+            509,
+            741,
+            690,
+            757
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tables 5, 6, and 7 show the different averaged results are the debiasing languages other than English, namely French, German, and Dutch.",
+        "bbox": [
+            507,
+            766,
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+            815
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "D Breakdown results",
+        "text_level": 1,
+        "bbox": [
+            507,
+            828,
+            710,
+            843
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this section, a breakdown of the different scores per category is shown in terms of the bias metric established in (Nangia et al., 2020) in Tables 8, 9, 10, 11. For brevity, we employ the following",
+        "bbox": [
+            507,
+            854,
+            882,
+            917
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "2895",
+        "bbox": [
+            480,
+            928,
+            519,
+            940
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/2144d34d3184fb3991a7cadbf12ded902a8f2661c8513c3be7812838224d5b53.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>10.93↑</td><td>6.94↑</td><td>7.50↑</td><td>9.44↑</td><td>9.07↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.91↓</td><td>12.22↑</td><td>11.67↑</td><td>10.00↓</td><td>10.74↓</td></tr><tr><td>DE</td><td>9.33</td><td>11.11↑</td><td>6.29↓</td><td>6.55↓</td><td>9.45↑</td><td>6.09↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.96↓</td><td>14.86↓</td><td>16.26↓</td><td>15.05↓</td><td>12.94↓</td></tr></table>",
+        "bbox": [
+            124,
+            80,
+            478,
+            131
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/fc9624709299ecc555425c19155cfa389d6fdffb1201b3ea6d5c5b8bc8f83ff5.jpg",
+        "table_caption": [
+            "Table 5: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>9.44↑</td><td>6.94↑</td><td>7.22↑</td><td>10.19↑</td><td>8.43↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.17↓</td><td>7.5↓</td><td>10.28↓</td><td>8.43↓</td><td>7.13↓</td></tr><tr><td>DE</td><td>9.33</td><td>10.20↑</td><td>4.89↓</td><td>6.27↓</td><td>6.38↓</td><td>6.01↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.31↓</td><td>14.59↓</td><td>16.25↓</td><td>17.10↓</td><td>16.65↓</td></tr></table>",
+        "bbox": [
+            124,
+            198,
+            480,
+            250
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/310fe9fdee610f2dba0db479ed9a7a6dbd98e5ae0d38f81d30f802cf148017f4.jpg",
+        "table_caption": [
+            "Table 6: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.80↑</td><td>6.94↑</td><td>7.22↑</td><td>7.69↑</td><td>7.50↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.30↑</td><td>10.28↓</td><td>10.56↓</td><td>9.07↓</td><td>9.17↓</td></tr><tr><td>DE</td><td>9.33</td><td>8.71↓</td><td>6.83↓</td><td>7.39↓</td><td>6.04↓</td><td>5.37↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.68↓</td><td>15.71↓</td><td>16.54↓</td><td>14.69↓</td><td>14.41↓</td></tr></table>",
+        "bbox": [
+            124,
+            316,
+            480,
+            368
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "abbreviations: Gender (G), Race (Ra), and Religion (Re).",
+        "bbox": [
+            112,
+            447,
+            485,
+            478
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/6814c0198842b4c8b70c29d07754f6ea80e966b168f72314dbd9d53c1f4834ca.jpg",
+        "table_caption": [
+            "Table 7: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>51.30</td><td>51.11</td><td>50.28*</td><td>55.28</td><td>50.37</td></tr><tr><td>G</td><td>49.17</td><td>49.17</td><td>49.17</td><td>46.67</td><td>50.83</td><td>51.11</td></tr><tr><td>Ra</td><td>44.17</td><td>41.94</td><td>45.00</td><td>-</td><td>39.72</td><td>39.17</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>59.17</td><td>-</td><td>75.28</td><td>60.83</td></tr><tr><td>FR</td><td>60.56</td><td>57.50</td><td>60.00</td><td>60.28*</td><td>62.59</td><td>58.52</td></tr><tr><td>G</td><td>50.83</td><td>45.56</td><td>50.00</td><td>50.00</td><td>59.72</td><td>60.83</td></tr><tr><td>Ra</td><td>59.17</td><td>56.67</td><td>57.50</td><td>-</td><td>56.39</td><td>50.83</td></tr><tr><td>Re</td><td>71.67</td><td>70.28</td><td>72.50</td><td>-</td><td>71.67</td><td>63.89</td></tr><tr><td>DE</td><td>59.05</td><td>55.93</td><td>54.86</td><td>56.55*</td><td>57.06</td><td>55.50</td></tr><tr><td>G</td><td>60.90</td><td>54.50</td><td>51.71</td><td>53.42</td><td>53.29</td><td>56.70</td></tr><tr><td>Ra</td><td>57.07</td><td>61.35</td><td>57.05</td><td>-</td><td>51.51</td><td>48.42</td></tr><tr><td>Re</td><td>59.17</td><td>51.94</td><td>55.83</td><td>-</td><td>66.39</td><td>61.39</td></tr><tr><td>NL</td><td>67.66</td><td>63.96</td><td>64.59</td><td>65.98*</td><td>66.65</td><td>67.22</td></tr><tr><td>G</td><td>56.32</td><td>54.10</td><td>49.59</td><td>51.28</td><td>56.62</td><td>57.48</td></tr><tr><td>Ra</td><td>65.83</td><td>59.17</td><td>65.00</td><td>-</td><td>66.39</td><td>65.56</td></tr><tr><td>Re</td><td>80.83</td><td>78.61</td><td>79.17</td><td>-</td><td>76.94</td><td>78.61</td></tr></table>",
+        "bbox": [
+            139,
+            489,
+            463,
+            634
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/77aefb112970b3b07b86468549ba29151f870ea8973c40782a416048d66d93bb.jpg",
+        "table_caption": [
+            "Table 8: Overall performance score per evaluation language, debiasing technique, and category averaged over the three random seeds after debiasing in English."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>55.74</td><td>50.28</td><td>50.28*</td><td>54.26</td><td>51.67</td></tr><tr><td>G</td><td>49.17</td><td>52.78</td><td>47.50</td><td>46.67</td><td>49.72</td><td>53.06</td></tr><tr><td>Ra</td><td>44.17</td><td>45.83</td><td>43.33</td><td>-</td><td>46.11</td><td>38.89</td></tr><tr><td>Re</td><td>60.00</td><td>68.61</td><td>60.00</td><td>-</td><td>66.94</td><td>63.06</td></tr><tr><td>FR</td><td>60.56</td><td>54.54</td><td>60.00</td><td>58.89*</td><td>58.15</td><td>57.59</td></tr><tr><td>G</td><td>50.83</td><td>47.22</td><td>46.67</td><td>45.83</td><td>52.22</td><td>55.28</td></tr><tr><td>Ra</td><td>59.17</td><td>47.22</td><td>60.83</td><td>-</td><td>57.50</td><td>51.67</td></tr><tr><td>Re</td><td>71.67</td><td>69.17</td><td>72.50</td><td>-</td><td>64.72</td><td>65.83</td></tr><tr><td>DE</td><td>59.05</td><td>59.68</td><td>55.43</td><td>55.98*</td><td>55.95</td><td>53.09</td></tr><tr><td>G</td><td>60.90</td><td>52.47</td><td>50.85</td><td>51.71</td><td>55.24</td><td>55.83</td></tr><tr><td>Ra</td><td>57.07</td><td>59.91</td><td>58.78</td><td>-</td><td>52.05</td><td>47.04</td></tr><tr><td>Re</td><td>59.17</td><td>66.67</td><td>56.67</td><td>-</td><td>60.56</td><td>56.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>64.31</td><td>65.71*</td><td>65.05</td><td>62.94</td></tr><tr><td>G</td><td>56.32</td><td>49.59</td><td>49.59</td><td>50.45</td><td>54.32</td><td>55.76</td></tr><tr><td>Ra</td><td>65.83</td><td>62.22</td><td>65.00</td><td>-</td><td>62.50</td><td>58.33</td></tr><tr><td>Re</td><td>80.83</td><td>80.83</td><td>78.33</td><td>-</td><td>78.33</td><td>74.72</td></tr></table>",
+        "bbox": [
+            137,
+            715,
+            463,
+            860
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/b23bac938d17d1c4a1ddaa70c5031e06990245b7961eaf724b145a917ecb28c0.jpg",
+        "table_caption": [
+            "Table 9: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.44</td><td>50.28</td><td>50.00*</td><td>52.59</td><td>52.13</td></tr><tr><td>G</td><td>49.17</td><td>46.67</td><td>45.83</td><td>45.83</td><td>45.28</td><td>49.17</td></tr><tr><td>Ra</td><td>44.17</td><td>53.06</td><td>45.00</td><td>-</td><td>44.17</td><td>43.06</td></tr><tr><td>Re</td><td>60.00</td><td>63.61</td><td>60.00</td><td>-</td><td>68.33</td><td>64.17</td></tr><tr><td>FR</td><td>60.56</td><td>56.57</td><td>57.5</td><td>60.28*</td><td>53.80</td><td>53.61</td></tr><tr><td>G</td><td>50.83</td><td>47.48</td><td>50.00</td><td>50.00</td><td>53.89</td><td>55.83</td></tr><tr><td>Ra</td><td>59.17</td><td>60.56</td><td>58.33</td><td>-</td><td>44.44</td><td>45.83</td></tr><tr><td>Re</td><td>71.67</td><td>61.39</td><td>64.17</td><td>-</td><td>63.06</td><td>59.17</td></tr><tr><td>DE</td><td>59.05</td><td>57.64</td><td>53.75</td><td>55.70*</td><td>55.72</td><td>55.35</td></tr><tr><td>G</td><td>60.90</td><td>47.69</td><td>50.00</td><td>50.86</td><td>54.46</td><td>58.41</td></tr><tr><td>Ra</td><td>57.07</td><td>64.38</td><td>57.07</td><td>-</td><td>57.69</td><td>53.47</td></tr><tr><td>Re</td><td>59.17</td><td>60.83</td><td>54.17</td><td>-</td><td>55.00</td><td>54.17</td></tr><tr><td>NL</td><td>67.66</td><td>61.16</td><td>63.48</td><td>65.14*</td><td>67.10</td><td>66.65</td></tr><tr><td>G</td><td>56.32</td><td>49.88</td><td>48.76</td><td>48.76</td><td>56.30</td><td>56.60</td></tr><tr><td>Ra</td><td>65.83</td><td>53.89</td><td>64.17</td><td>-</td><td>69.44</td><td>67.78</td></tr><tr><td>Re</td><td>80.83</td><td>79.72</td><td>77.50</td><td>-</td><td>75.56</td><td>75.56</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/27b1efc400fd21208e7fd61819ee81e06ae0f0bc73ee5a1021b1c1bdbb9233a6.jpg",
+        "table_caption": [
+            "Table 10: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.91</td><td>50.83</td><td>50.56*</td><td>47.69</td><td>51.20</td></tr><tr><td>G</td><td>49.17</td><td>51.94</td><td>48.33</td><td>47.50</td><td>45.56</td><td>52.22</td></tr><tr><td>Ra</td><td>44.17</td><td>50.00</td><td>44.17</td><td>-</td><td>40</td><td>40.83</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>60.00</td><td>-</td><td>57.5</td><td>60.56</td></tr><tr><td>FR</td><td>60.56</td><td>60.37</td><td>60.28</td><td>60.56*</td><td>55.37</td><td>52.50</td></tr><tr><td>G</td><td>50.83</td><td>50.28</td><td>50.83</td><td>50.83</td><td>55.83</td><td>53.89</td></tr><tr><td>Ra</td><td>59.17</td><td>61.94</td><td>61.67</td><td>-</td><td>44.44</td><td>41.11</td></tr><tr><td>Re</td><td>71.67</td><td>68.89</td><td>68.33</td><td>-</td><td>65.83</td><td>62.50</td></tr><tr><td>DE</td><td>59.05</td><td>55.67</td><td>56.55</td><td>56.25*</td><td>48.53</td><td>50.86</td></tr><tr><td>G</td><td>60.90</td><td>47.71</td><td>53.38</td><td>52.52</td><td>53.04</td><td>54.73</td></tr><tr><td>Ra</td><td>57.07</td><td>58.20</td><td>59.59</td><td>-</td><td>45.89</td><td>46.47</td></tr><tr><td>Re</td><td>59.17</td><td>61.11</td><td>56.67</td><td>-</td><td>46.67</td><td>51.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>63.74</td><td>64.57*</td><td>64.51</td><td>63.67</td></tr><tr><td>G</td><td>56.32</td><td>52.92</td><td>47.05</td><td>47.05</td><td>52.97</td><td>53.22</td></tr><tr><td>Ra</td><td>65.83</td><td>59.72</td><td>67.50</td><td>-</td><td>61.67</td><td>57.78</td></tr><tr><td>Re</td><td>80.83</td><td>80.00</td><td>76.67</td><td>-</td><td>78.89</td><td>80.00</td></tr></table>",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Table 11: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch.",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "2896",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    }
+]

2023/Investigating Bias in Multilingual Language Models_ Cross-Lingual Transfer of Debiasing Techniques/ac884595-2bc6-45c5-8d3c-8fe9015e5586_model.json

@@ -0,0 +1,1782 @@
+[
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Investigating Bias in Multilingual Language Models: Cross-Lingual Transfer of Debiasing Techniques"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Manon Reusens<sup>1</sup>, Philipp Borchert<sup>1,2</sup>, Margot Mieskes<sup>3</sup>, Jochen De Weerdt<sup>1</sup>, Bart Baesens<sup>1,4</sup>"
+        },
+        {
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+            "angle": 0,
+            "content": "<sup>1</sup>Research Centre for Information Systems Engineering (LIRIS), KU Leuven"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{2}\\)IESEG School of Management, 3 Rue de la Digue, 59000 Lille, France"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "<sup>3</sup>University of Applied Sciences Darmstadt"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.178,
+                0.215,
+                0.826,
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+            "angle": 0,
+            "content": "\\(^{4}\\)Department of Decision Analytics and Risk, University of Southampton {manon.reusens, philipp.borchert, jochen.deweerdt, bart.daesens} @kuleuven.be margot.mieskes@h-da.de"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.287,
+                0.49,
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+            ],
+            "angle": 0,
+            "content": "DISCLAIMER: This paper contains explicit statements that are potentially offensive."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.262,
+                0.32,
+                0.341,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.142,
+                0.346,
+                0.461,
+                0.688
+            ],
+            "angle": 0,
+            "content": "This paper investigates the transferability of debiasing techniques across different languages within multilingual models. We examine the applicability of these techniques in English, French, German, and Dutch. Using multilingual BERT (mBERT), we demonstrate that cross-lingual transfer of debiasing techniques is not only feasible but also yields promising results. Surprisingly, our findings reveal no performance disadvantages when applying these techniques to non-English languages. Using translations of the CrowS-Pairs dataset, our analysis identifies SentenceDebias as the best technique across different languages, reducing bias in mBERT by an average of \\(13\\%\\). We also find that debiasing techniques with additional pretraining exhibit enhanced cross-lingual effectiveness for the languages included in the analyses, particularly in lower-resource languages. These novel insights contribute to a deeper understanding of bias mitigation in multilingual language models and provide practical guidance for debiasing techniques in different language contexts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.701,
+                0.26,
+                0.715
+            ],
+            "angle": 0,
+            "content": "1 Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.727,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "There has been a growing interest in addressing bias detection and mitigation in Natural Language Processing (NLP) due to their societal implications. Initially, research focused on debiasing word embeddings (Bolukbasi et al., 2016; Zhao et al., 2018b), but recent studies found that pretrained language models also capture social biases present in training data (Meade et al., 2022). Hence, attention has shifted towards debiasing techniques that target sentence representations. These techniques include additional pretraining steps (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.858,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.508,
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+                0.886,
+                0.548
+            ],
+            "angle": 0,
+            "content": "Figure 1: The example of the English CrowS-Pairs dataset illustrates sentence probabilities after debiasing mBERT with SentenceDebias in English, French, German, and Dutch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.576,
+                0.884,
+                0.623
+            ],
+            "angle": 0,
+            "content": "and projection-based methods that assume a bias direction (Liang et al., 2020a; Ravfogel et al., 2020; Liang et al., 2020b)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.625,
+                0.885,
+                0.883
+            ],
+            "angle": 0,
+            "content": "While debiasing techniques have been developed and evaluated for monolingual, and mostly English models, the effectiveness and transferability of these techniques to diverse languages within multilingual models remain largely unexplored (Stanczak and Augenstein, 2021; Sun et al., 2019). Our research aims to bridge this gap by examining the potential of debiasing techniques applied to one language to effectively mitigate bias in other languages within multilingual large language models. We examine English (EN), French (FR), German (DE), and Dutch (NL). Figure 1 illustrates an example sentence pair included in the English CrowS-Pairs dataset<sup>1</sup>, where the unmodified and modified parts are highlighted in blue and yellow respectively. It shows the predicted probabilities of"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.509,
+                0.893,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "This example assumes gender to be binary. We acknowledge that this fails to capture the full range of gender identities."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.52,
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+            ],
+            "angle": 0,
+            "content": "2887"
+        },
+        {
+            "type": "footer",
+            "bbox": [
+                0.16,
+                0.946,
+                0.836,
+                0.973
+            ],
+            "angle": 0,
+            "content": "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 2887-2896 December 6-10, 2023 ©2023 Association for Computational Linguistics"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.486,
+                0.117
+            ],
+            "angle": 0,
+            "content": "the modified part occurring given the unmodified part across different debiasing languages."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.117,
+                0.118,
+                0.49,
+                0.422
+            ],
+            "angle": 0,
+            "content": "This study examines the cross-lingual transferability of debiasing techniques using mBERT. mBERT, trained on Wikipedia data from diverse languages, possesses the capability to process and generate text in various linguistic contexts. Despite balancing efforts, it still performs worse on low-resource languages (Wu and Dredze, 2020; Devlin, 2018). We investigate whether this performance disparity extends to gender, religious, and racial biases. Related studies demonstrate the effectiveness of cross-lingual debiasing for individual techniques and selected bias scopes (Liang et al., 2020b; Lauscher et al., 2021). We show how to reduce bias in mBERT across different languages by conducting a benchmark of state-of-the-art (SOTA) debiasing techniques and providing guidance on its implementation. To facilitate further research and reproducibility, we make the code and additional data available to the research community\\(^{2}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.424,
+                0.49,
+                0.681
+            ],
+            "angle": 0,
+            "content": "Our contributions can be summarized as follows: 1) We provide a benchmark of different SOTA debiasing techniques across multiple languages in a multilingual large language model. 2) We find that SentenceDebias is the most effective for cross-lingual debiasing, reducing the bias in mBERT by \\(13\\%\\). 3) We provide implementation guidelines for debiasing multilingual models and highlight the differences in the cross-lingual transferability of different debiasing techniques. We find that most projection-based techniques applied to one language yield similar predictions across evaluation languages. We also recommend performing the techniques with an additional pretraining step on the lowest resource language within the multilingual model for optimal results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.695,
+                0.264,
+                0.71
+            ],
+            "angle": 0,
+            "content": "2 Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.721,
+                0.489,
+                0.753
+            ],
+            "angle": 0,
+            "content": "This section introduces the data, debiasing techniques, and experimental setup respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.765,
+                0.262,
+                0.78
+            ],
+            "angle": 0,
+            "content": "2.1 CrowS-Pairs"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.787,
+                0.489,
+                0.883
+            ],
+            "angle": 0,
+            "content": "CrowS-Pairs is a benchmark dataset comprising 1508 examples that address stereotypes associated with historically disadvantaged groups in the US, encompassing various types of bias, such as age and religion (Nangia et al., 2020). Following Meade et al. (2022), where different debiasing tech"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.883,
+                0.229
+            ],
+            "angle": 0,
+            "content": "niques were benchmarked and their effectiveness demonstrated on BERT for gender, race, and religion, we focus on these three types of bias. Néveol et al. (2022) translated the dataset in French. To the best of our knowledge, there are currently no peer-reviewed variants of CrowS-Pairs available in other languages. Therefore, we used three samples of the full dataset and translated them into the respective language to evaluate our experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.232,
+                0.885,
+                0.472
+            ],
+            "angle": 0,
+            "content": "To create an evaluation set for our experiments, we started from the English CrowS-Pairs dataset (Nangia et al., 2020). We randomly sampled \\( N \\) instances, where \\( N \\in \\{20,30,40,50\\} \\), and measured the performance differences on mBERT and BERT. Through three random seeds, we found that a sample size of 40 resulted in an average performance correlation of more than \\( 75\\% \\) with the full dataset for both models. Thus, we conclude that using 40 instances with three random seeds provides a representative dataset for our evaluation. Further details are shown in Appendix A. Subsequently, we included the translated samples from each language into our dataset, either the corresponding sentences from the French CrowS-Pairs or a translation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.489,
+                0.722,
+                0.505
+            ],
+            "angle": 0,
+            "content": "2.2 Debiasing techniques"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.513,
+                0.884,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Next, the different debiasing techniques are explained. For more information on the attribute lists used, we refer to Appendix B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.563,
+                0.884,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Counterfactual Data Augmentation (CDA) is a debiasing technique that trains the model on an augmented training set (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019). First, the corpus is augmented by duplicating sentences that include words from a predefined attribute list. Next, counterfactual sentences are generated by swapping these attribute words with other variants in the list, for example, swapping \\( he \\) by \\( she \\). We augment \\( 10\\% \\) of the Wikipedia corpus of the respective language and use an additional pretraining step to debias the model for three random seeds and average the results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.773,
+                0.883,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Dropout Regularization (DO) is introduced by Webster et al. (2020) as a debiasing technique by implementing an additional pretraining step. We execute this pretraining step while training on \\(10\\%\\) of the Wikipedia corpus of the respective language using three random seeds and averaging the results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.872,
+                0.882,
+                0.919
+            ],
+            "angle": 0,
+            "content": "SentenceDebias (SenDeb) introduced by Liang et al. (2020a) is a projection-based debiasing technique extending debiasing word embeddings"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.113,
+                0.892,
+                0.395,
+                0.918
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)https://github.com/manon-reusens/multilingual.bias"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2888"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.085,
+                0.493,
+                0.278
+            ],
+            "angle": 0,
+            "content": "(Bolukbasi et al., 2016) to sentence representations. Attribute words from a predefined list are contextualized by retrieving their occurrences from a corpus and augmented with CDA. Next, the bias subspace is computed using the representations of these sentences through principal component analysis (PCA). The first \\(K\\) dimensions of PCA are assumed to define the bias subspace as they capture the principle directions of variation of the representations. We debias the last hidden state of the mBERT model and implement SenDeb using \\(2.5\\%\\) of the Wikipedia text in the respective language."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.28,
+                0.492,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Iterative Nullspace Projection (INLP) is a projection-based debiasing technique in which multiple linear classifiers are trained to predict biases, such as gender, that are to be removed from the sentence representations (Ravfogel et al., 2020). After training a single classifier, the representations are debiased by projecting them onto the learned linear classifier's weight matrix to gather the rowspace projection. We implement this technique using the \\(2.5\\%\\) of the Wikipedia text in each language."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.443,
+                0.492,
+                0.735
+            ],
+            "angle": 0,
+            "content": "DensRay (DR) is a projection-based debiasing technique first implemented by (Duftner and Schütze, 2019) and adapted for contextualized word embeddings by (Liang et al., 2020b). This technique is similar to SenDeb, but the bias direction is calculated differently. This method aims to find an optimal orthogonal matrix so that the first \\(K\\) dimensions correlate well with the linguistic features in the rotated space. The second dimension is assumed to be orthogonal to the first one. The bias direction is considered to correspond to the eigenvector of the highest eigenvalue of the matrix. DR is only implemented for a binary bias type and using it for multiclass bias types requires modifying the technique. Therefore, we only apply it to the gender bias type. We implement DR debiasing the last hidden state of mBERT and using \\(2.5\\%\\) of the Wikipedia text in the respective language."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.75,
+                0.317,
+                0.767
+            ],
+            "angle": 0,
+            "content": "2.3 Experimental setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.775,
+                0.49,
+                0.921
+            ],
+            "angle": 0,
+            "content": "We debias mBERT using language \\(X\\) and evaluating it on language \\(Y\\) with \\(X, Y \\in \\{EN, FR, DE, NL\\}\\). In essence, we debiased the model using one language and evaluated it on another, covering all language combinations in our experiments. We implement mBERT in its base configuration (uncased, 12 layers, 768 hidden size) and utilize the bias score as implemented in Meade et al. (2022). This metric evaluates the percentage"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.885,
+                0.15
+            ],
+            "angle": 0,
+            "content": "of sentences where the model prefers the more biased sentence over the less biased sentence, with an optimal performance of \\(50\\%\\). All experiments are performed on P100 GPUs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.165,
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+            ],
+            "angle": 0,
+            "content": "3 Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.193,
+                0.885,
+                0.337
+            ],
+            "angle": 0,
+            "content": "Table 1 shows the performance of the different debiasing techniques when debiasing in English in terms of the absolute deviation of the ideal unbiased model. This is an average score for all bias types and models trained for the respective evaluation language. Base represents the score that is achieved by mBERT on the respective evaluation language dataset before debiasing. More results are shown in Appendices C and D."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.339,
+                0.886,
+                0.597
+            ],
+            "angle": 0,
+            "content": "As shown in Table 1, English is relatively unbiased compared to the other languages and shows a small bias increase after debiasing. This observation aligns with the findings of Ahn and Oh (2021), who propose mBERT as a debiasing technique. In cases where the initial bias score is already close to the optimal level, further debiasing can lead to overcompensation, consequently amplifying the total bias. We assume that an unbiased model should equally prioritize both biased and unbiased sentences. However, when debiasing techniques tend to overcorrect, they skew the balance towards favoring the prediction of unbiased sentences over biased ones. Addressing this challenge necessitates the adoption of specialized techniques to effectively mitigate any residual bias."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.599,
+                0.886,
+                0.921
+            ],
+            "angle": 0,
+            "content": "This phenomenon of overcompensation occurs in several underperforming techniques, as illustrated in Table 1. Notably, we find instances of overcompensation for gender when debiasing using INLP for French and using CDA for German, as well as for race when debiasing using DO for German. Another contributing factor to the poor performance of certain techniques within specific debiasing and evaluation language combinations lies in the inherent ineffectiveness of the debiasing method itself, exemplified by the cases of gender debiasing using CDA for French and religion debiasing using CDA for German. In Tables 5, 6, and 7, we find overcompensation for gender when debiasing with INLP in German and French, evaluating in German, debiasing with Sendeb and DR in French, and evaluating in French, as well as when debiasing in Dutch with INLP and evaluating in French. Moreover, overcompensation for race is also observed when debiasing with CDA in French"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.522,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2889"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.133,
+                0.082,
+                0.472,
+                0.133
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Base</td><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.70↑</td><td>7.78↑</td><td>6.94↑</td><td>13.43↑</td><td>8.70↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.20↑</td><td>10↓</td><td>10.28↓</td><td>12.6↑</td><td>9.44↓</td></tr><tr><td>DE</td><td>9.33</td><td>7.52↓</td><td>6.57↓</td><td>6.84↓</td><td>10.75↑</td><td>9.75↑</td></tr><tr><td>NL</td><td>17.66</td><td>13.96↓</td><td>15.14↓</td><td>16.54↓</td><td>16.84↓</td><td>17.40↓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.143,
+                0.489,
+                0.187
+            ],
+            "angle": 0,
+            "content": "Table 1: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in English."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.212,
+                0.313,
+                0.226
+            ],
+            "angle": 0,
+            "content": "and evaluating in German."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.228,
+                0.489,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Is cross-lingual transferability of debiasing techniques possible? Table 1 shows that cross-lingual transfer is possible using English as debiasing language. Figure 2 confirms this, depicting the bias scores averaged over all debiasing techniques. As discussed, for English, these techniques increase the bias contained in the model due to its already close to optimal performance. For the other evaluation languages, we find better performance after debiasing. Therefore, we conclude that for these four languages, it is possible to debias the mBERT model to some extent using a different debiasing language, except when the bias contained in the model is already relatively low."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.453,
+                0.489,
+                0.852
+            ],
+            "angle": 0,
+            "content": "To shed some light on the insights that can be gathered from Figure 2, Table 2 offers an overview of the best- and worst-performing techniques per evaluation language. As shown, Dutch is found to be the best debiasing language for English. This is because this debiasing language has shown to overcompensate the gender bias category the least, therefore, resulting in the best performance. In general, we find that using the same debiasing language as evaluation language often results in an overcompensation of the bias, therefore turning around the bias direction. This means that the best-performing debiasing language is often not the same as the evaluation language. However, German is the exception. As this language already has the highest bias score for gender before debiasing, strong debiasing is beneficial and therefore does not result in overcompensation. Besides German being the best-performing debiasing language for German, it also shows the best performance for French because it achieves the best performance on all different evaluation sets. Moreover, it also shows less overcompensation for the gender bias present in the model than other languages such as Dutch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.855,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "French is the worst-performing debiasing language for all evaluation languages except for Dutch, where it is the best-performing one. We find that when evaluating in French, the gender bias is over"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.524,
+                0.082,
+                0.87,
+                0.128
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Evaluation language</td><td>Best debiasing language</td><td>worst debiasing language</td></tr><tr><td>English</td><td>Dutch</td><td>French</td></tr><tr><td>French</td><td>German</td><td>French</td></tr><tr><td>German</td><td>German</td><td>French</td></tr><tr><td>Dutch</td><td>French</td><td>English</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.509,
+                0.138,
+                0.884,
+                0.166
+            ],
+            "angle": 0,
+            "content": "Table 2: Overview best- and worst-performing debiasing languages per evaluation language."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.543,
+                0.18,
+                0.85,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.509,
+                0.334,
+                0.884,
+                0.363
+            ],
+            "angle": 0,
+            "content": "Figure 2: Average bias scores per evaluation and debi-aising language."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.388,
+                0.884,
+                0.565
+            ],
+            "angle": 0,
+            "content": "compensated. For English, both racial and gender bias are overcompensated. The German evaluation shows lower overall performance due to already two ineffective methods (INLP and CDA), which were also due to overcompensating racial bias. Finally, for Dutch, we find that debiasing with French overcompensates gender bias less than Dutch and, therefore, is the best-performing method. As Dutch has the second highest gender bias score before debiasing, it also benefits from strong debiasing and therefore both French and Dutch perform well."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.566,
+                0.884,
+                0.709
+            ],
+            "angle": 0,
+            "content": "We believe that these results are influenced by the fact that both German and French have a grammatical gender distinction, which may impact debiasing gender to a greater extent. This grammatical gender distinction is not embedded in English and Dutch. Moreover, as the religion category regularly shows limited bias decrease, we find that the performance in the gender and race category often determines whether a technique works well or not."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.71,
+                0.885,
+                0.919
+            ],
+            "angle": 0,
+            "content": "How are the different techniques affected by cross-lingual debiasing? Table 3 shows the overall percentage increase of the bias score per technique. From this, we conclude that SenDeb is the best-performing technique and reduces bias in mBERT on average by \\(13\\%\\). DO is the second best-performing method reducing bias on average by \\(10\\%\\). However, Figure 3 shows that DO performs well for all debiasing languages except English, while SenDeb performs consistently well for all languages. The other techniques perform worse overall. Hence, we suggest using SenDeb as cross-lingual debiasing technique for these languages."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2890"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.159,
+                0.081,
+                0.444,
+                0.11
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>Dropout</td></tr><tr><td>1.11</td><td>13.21</td><td>7.1</td><td>-0.16</td><td>10.21</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.12,
+                0.489,
+                0.149
+            ],
+            "angle": 0,
+            "content": "Table 3: Average percentage difference in bias scores of each technique compared to the base model."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.149,
+                0.163,
+                0.456,
+                0.295
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.306,
+                0.487,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Figure 3: Average bias score per technique per debiasing language."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.362,
+                0.489,
+                0.571
+            ],
+            "angle": 0,
+            "content": "When zooming in on the projection-based techniques, i.e. INLP, SenDeb, and DR, a high performance variation is shown in Table 3 and Figure 3. While SenDeb offers consistent performance for all different debiasing languages, we see more variation and a lower bias decrease for INLP. This is due to the high variation in performance, resulting in a higher overall average. As INLP uses multiple linear classifiers to define the projection matrix, high variability is introduced. Since DR was only implemented for gender, no performance gains can be obtained from the other bias types, therefore resulting in a lower overall performance increase."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.573,
+                0.49,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Techniques using an additional pretraining step obtain the best results when debiasing in Dutch, as illustrated in Figure 4. Notably, Dutch is the lowest resource language out of these four languages during pretraining (Wu and Dredze, 2020). This additional pretraining step lets the model learn unbiased associations between words while becoming familiar with the lower-resource language resulting in lower overall bias. Therefore, we conclude that, for our set of languages, these techniques are most effective when applied to low-resource languages."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.78,
+                0.266,
+                0.794
+            ],
+            "angle": 0,
+            "content": "4 Related work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.807,
+                0.489,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Significant research focuses on the cross-lingual performance of mBERT (Wu and Dredze, 2020; Pires et al., 2019; Libovický et al., 2019). Limited research focuses on the cross-lingual transferability of debiasing techniques in mBERT (Stanczak and Augenstein, 2021; Sun et al., 2019). Liang et al. (2020b) use DensRay in English to debias Chinese"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.545,
+                0.083,
+                0.85,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.509,
+                0.205,
+                0.882,
+                0.233
+            ],
+            "angle": 0,
+            "content": "Figure 4: Average bias score per debiasing languages for both CDA and DO."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.26,
+                0.884,
+                0.469
+            ],
+            "angle": 0,
+            "content": "in mBERT for gender. Similarly, Zhao et al. (2020) analyze the cross-lingual transfer of gender bias mitigation using one method. Lauscher et al. (2021) also find that their proposed technique, ADELE, can transfer debiasing across six languages. Other studies analyze biases contained in multilingual language models. Kaneko et al. (2022) evaluate bias across multiple languages in masked language models using a new metric. Ahn and Oh (2021) study ethnic bias and its variability over languages proposing mBERT as debiasing technique. Finally, some studies also explore the cross-lingual transferability of downstream tasks (Levy et al., 2023)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.483,
+                0.642,
+                0.497
+            ],
+            "angle": 0,
+            "content": "5 Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.51,
+                0.884,
+                0.799
+            ],
+            "angle": 0,
+            "content": "Most studies focus on debiasing techniques for large language models, but rarely explore their cross-lingual transferability. Therefore, we offer a benchmark for SOTA debiasing techniques on mBERT across multiple languages (EN, FR, DE, NL) and show that debiasing is transferable across languages, yielding promising results. We provide guidance for cross-lingual debiasing, highlighting SenDeb as the best-performing method, reducing bias in mBERT by \\(13\\%\\). Additionally, we find that, for the studied languages, debiasing with the lowest resource language is effective for techniques involving an additional training step (CDA and DO). This research is a first step into the cross-lingual transferability of debiasing techniques. Further studies should include languages from different cultures and other multilingual large language models to assess generalizability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.813,
+                0.615,
+                0.828
+            ],
+            "angle": 0,
+            "content": "Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.84,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "A first limitation concerns the analysis focused on four closely related languages from a similar culture. A broader range of languages should be explored to ensure the generalizability of the findings. Our research was conducted employing a"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.519,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2891"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.492,
+                0.697
+            ],
+            "angle": 0,
+            "content": "single multilingual model, mBERT. Extending this to other multilingual language models would provide valuable insights into the wider applicability of the results. Moreover, the evaluation of outcomes relied primarily on the CrowS-Pairs metric, although efforts were made to enhance the understanding by examining the absolute difference compared to the optimal model. Next, the consideration of gender was limited to binary classification, overlooking non-binary gender identities. This should be further addressed in future research. Furthermore, a comprehensive multilingual dataset to assess stereotypes across different languages is not available, and thus, the English CrowS-Pairs dataset was translated and corresponding sentences of the French dataset were used. Nevertheless, typical stereotypes for other languages were not adequately represented. Furthermore, the dataset used in the study exhibited certain flaws highlighted by Blodgett et al. (2021), such as the influence of selected names on predictions, which was observed to have a significant impact. This needs to be investigated further. Additionally, attribute lists for languages other than English were not available to the same extent. We tried to compile lists for French, Dutch, and German, excluding words with multiple meanings to minimize noise. However, our lists were not exhaustive, and therefore the omission of relevant attributes is possible. It is also worth noting that, in certain cases, the generic masculine form was considered the preferred answer, despite it being included in the attribute lists. Finally, the applicability of downstream tasks should be investigated (e.g. (Levy et al., 2023)). Hence, future research should encompass a wider language scope, include multiple models, address existing dataset flaws, and develop more comprehensive attribute lists for various languages."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.714,
+                0.267,
+                0.729
+            ],
+            "angle": 0,
+            "content": "Ethics Statement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.743,
+                0.491,
+                0.92
+            ],
+            "angle": 0,
+            "content": "We would like to address three key ethical considerations in this study that highlight ongoing challenges and complexities associated with mitigating bias in large language models. First, it is important to acknowledge that the gender bias examined in this paper is approached from a binary perspective. However, this does not capture the full range of gender identities present in reality. While we recognize this limitation, it was necessary to simplify the analysis for experimental purposes. In future research, we hope to address this limitation. Second, despite"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.887,
+                0.263
+            ],
+            "angle": 0,
+            "content": "efforts to debias the multilingual large language model, it is important to note that not all forms of bias are completely mitigated. The applied debiasing techniques do lower the bias present in the model, however, there is still bias present in the model both within and outside the targeted bias types. Finally, we recognize that our evaluation datasets do not encompass all the different biases that might be present in the model. Therefore, even if a model would obtain a perfect score, it is still possible that other forms of bias persist."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.275,
+                0.682,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.301,
+                0.886,
+                0.382
+            ],
+            "angle": 0,
+            "content": "This research was funded by the Statistics Flanders research cooperation agreement on Data Science for Official Statistics. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.511,
+                0.408,
+                0.61,
+                0.423
+            ],
+            "angle": 0,
+            "content": "References"
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+        },
+        {
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+        },
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+        },
+        {
+            "type": "list",
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+            "angle": 0,
+            "content": null
+        },
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+        },
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+            "bbox": [
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+        },
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+        },
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+            ],
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+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.512,
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+            ],
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+            "content": "Kellie Webster, Xuezhi Wang, Ian Tenney, Alex Beutel, Emily Pittler, Ellie Pavlick, Jilin Chen, Ed Chi, and Slav Petrov. 2020. Measuring and reducing gendered correlations in pre-trained models. arXiv preprint arXiv:2010.06032."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.512,
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+            ],
+            "angle": 0,
+            "content": "Shijie Wu and Mark Dredze. 2020. Are all languages created equal in multilingual BERT? In Proceedings of the 5th Workshop on Representation Learning for NLP, pages 120-130, Online. Association for Computational Linguistics."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.512,
+                0.596,
+                0.883,
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+            ],
+            "angle": 0,
+            "content": "Jieyu Zhao, Subhabrata Mukherjee, Saghar Hosseini, Kai-Wei Chang, and Ahmed Hassan Awadallah. 2020. Gender bias in multilingual embeddings and crosslingual transfer. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 2896-2907, Online. Association for Computational Linguistics."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.512,
+                0.698,
+                0.883,
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+            ],
+            "angle": 0,
+            "content": "Jieyu Zhao, Tianlu Wang, Mark Yatskar, Ryan Cotterell, Vicente Ordonez, and Kai-Wei Chang. 2019. Gender bias in contextualized word embeddings. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 629-634, Minneapolis, Minnesota. Association for Computational Linguistics."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.512,
+                0.826,
+                0.883,
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+            ],
+            "angle": 0,
+            "content": "Jieyu Zhao, Tianlu Wang, Mark Yatskar, Vicente Ordonez, and Kai-Wei Chang. 2018a. Gender bias in coreference resolution: Evaluation and debiasing methods. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pages 15-20, New"
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "2893"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.133,
+                0.086,
+                0.486,
+                0.113
+            ],
+            "angle": 0,
+            "content": "Orleans, Louisiana. Association for Computational Linguistics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.123,
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+            ],
+            "angle": 0,
+            "content": "Jieyu Zhao, Yichao Zhou, Zeyu Li, Wei Wang, and Kai-Wei Chang. 2018b. Learning gender-neutral word embeddings. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 4847–4853, Brussels, Belgium. Association for Computational Linguistics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.213,
+                0.49,
+                0.306
+            ],
+            "angle": 0,
+            "content": "Ran Zmigrod, Sabrina J. Mielke, Hanna Wallach, and Ryan Cotterell. 2019. Counterfactual data augmentation for mitigating gender stereotypes in languages with rich morphology. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 1651-1661, Florence, Italy. Association for Computational Linguistics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.319,
+                0.466,
+                0.334
+            ],
+            "angle": 0,
+            "content": "A Correlation samples and full dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.344,
+                0.489,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Table 4 shows the overall correlation between the performance of the respective model on the full dataset and on the sample over three random seeds. Full represents that we looked at all different bias types in the CrowS-Pairs dataset and (3) refers to the three bias types used in this study (gender, religion, and race). We used a threshold of \\(75\\%\\) to decide on the sample size."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.127,
+                0.484,
+                0.48,
+                0.539
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT full</td><td>mBERT (3)</td><td>BERT full</td><td>BERT (3)</td></tr><tr><td>size 20</td><td>85.71</td><td>66.58</td><td>74.40</td><td>70.58</td></tr><tr><td>size 30</td><td>88.54</td><td>66.80</td><td>80.14</td><td>70.66</td></tr><tr><td>size 40</td><td>93.11</td><td>86.02</td><td>83.78</td><td>75.88</td></tr><tr><td>size 50</td><td>94.21</td><td>86.82</td><td>90.52</td><td>87.32</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.548,
+                0.49,
+                0.592
+            ],
+            "angle": 0,
+            "content": "Table 4: Correlation between the sample and full respective model's performance over three random seeds before debiasing."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.62,
+                0.28,
+                0.635
+            ],
+            "angle": 0,
+            "content": "B Attribute Lists"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.646,
+                0.49,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The different lists of attribute words per language used for CDA, SenDeb, INLP, and DR are listed below. We started from the lists in (Meade et al., 2022; Zhao et al., 2018a; Liang et al., 2020a) and extended these to other languages. For the non-English lists, we first translated the words in the English attribute list if a similar relation is contained in the translated words. Subsequently, we asked a native speaker of the respective language whether there are extra words that contain similar relations which do not exist in English. We added these to the list. However, note that these lists are not exhaustive, as many other words still exist that express the same relationship. Nevertheless, this list already provides a more extensive attribute list than by only translating the English attribute list."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.134,
+                0.905,
+                0.197,
+                0.919
+            ],
+            "angle": 0,
+            "content": "English"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.085,
+                0.886,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Gender: (Zhao et al., 2018a) actor, actress, actors, actresses, airman, airwoman, airmen, airwomen, uncle, aunt, uncles, aunts, boy, girl, boys, girls, groom, bride, grooms, brides, brother, sister, brothers, sisters, businessman, businesswoman, businessmen, businesswomen, chairman, chairwoman, chairmen, chairwomen, dude, chick, dudes, chicks, dad, mom, dads, moms, daddy, mommy, daddies, mommies, son, daughter, sons, daughters, father, mother, fathers, mothers, male, female, males, females, guy, gal, guys, gals, gentleman, lady, gentlemen, ladies, grandson, granddaughter, granddaughters, grandsons, granddaughters, guy, girl, guys, girls, he, she, himself, herself, him, her, his, her, husband, wife, husbands, wives, king, queen, kings, queens, lord, lady, lords, ladies, sir, ma'am, man, woman, men, women, sir miss mr. mrs. ms. policeman, policeman woman, prince princess princes princesses spokeseman spokeswoman spokesmen spokeswomen."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.407,
+                0.884,
+                0.47
+            ],
+            "angle": 0,
+            "content": "Race: (Meade et al., 2022) black, caucasian, asian, african, caucasian, asian, black, white, asian, africa, america, asia, africa, america, china, africa, europe, asia."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.472,
+                0.884,
+                0.535
+            ],
+            "angle": 0,
+            "content": "Religion: (Liang et al., 2020a) Jewish, christian, muslim, jews, christians, muslims, torah, bible, quran, synagogue, church, mosque, rabbi, priest, imam, judaism, christianity, islam."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.529,
+                0.543,
+                0.589,
+                0.557
+            ],
+            "angle": 0,
+            "content": "French"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.567,
+                0.886,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Gender: acteur, actrice, actuurs, actrices, aviateur, aviatrice, aviateurs, aviatrices, oncle, tante, oncle, tantine, tonton, tata, tontons, tatas, oncles, tantes, oncles, tantines, garcon, fille, garcons, filles, marié, mariée, époux, épouse, mariés, mariées, époux, épouses, brother, sister, frère, soeur, frères, soeurs, entrepreneur, entrepriseuse, entrepreneur, entrepriseure, entrepreneurs, entreprisesures, entrepreneurs, entreprisesuses, président, présidente, prêsidents, prêsentes, mec, meuf, gamin, gamine, mecs, meufs, père, mère, pères, mères, papa, maman, papas, mamans, fils, fille, fils, filles, abbe, abbesse, abbés, abbesses, masculin, féminin, malé, femelle, malés, femelles, gars, fille, gars, filles, monsieur, dame, messieurs, dames, petit-fils, petite-fille, petit-fils, petites-filles, il, elle, lui-même, elle-même, lui, elle, mari, femme, maris, femmes, roi, reine, rois, reines, seigneur, seigneuresse, seigneurs, seigneuresses, monsieur, m'dame, monsieur, madame, homme, femme, hommes, femmes, monsieur, mademoiselle, mr, mme, mr, mLle, policier, policière, prince"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2894"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.086,
+                0.49,
+                0.261
+            ],
+            "angle": 0,
+            "content": "princesse, princes, princesses, copain, copine, copains, copines, ami, amie, amis, amies, voisin, voisine, docteur, doctoresse, docteur, docteure, boulanger, boulangere, héros, héroîne, employé, employeee, employés, employées, chef, cheffe, chefs, cheffes, cousin, cousine, grand-père, grand-mère, expert, experte, pompier, pompère, pompiers, pompières, agricultrice, agriculteurs, agricultrices, travaillerur, travailluse, infirmier, infirmière, infirmiers, infirmières, patron, patronne, patrons, patronnes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.262,
+                0.49,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Race: noir, blanc, asiatique, black, blanc, asiatique, noir, caucasien, asiatique, africain, europeen, asienne, african, americain, asiatique, afrique, amerique, asie, afrique, amerique, chine, afrique, europe, asie."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.343,
+                0.49,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Religion: juif, chretien, musulman, juifs, chretiens, musulmans, torah, bible, coran, synagogue, église, mosquee, rabbin, prétre, imam, judaïisme, christianisme, islam."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.133,
+                0.411,
+                0.204,
+                0.424
+            ],
+            "angle": 0,
+            "content": "German"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.112,
+                0.43,
+                0.49,
+                0.767
+            ],
+            "angle": 0,
+            "content": "Gender: schauspieler, schauspielerin, koch, kochin, Lehrer, Lehrerin, schüler, schülerin, student, studentin, pilot, pilotin, onkel, tante, jungge, madchen, brautigam, braut, bruder, schwester, geschäftsmann, geschäftsfrau, vorsitzender, vorsitzende, vater, mutter, papa, mama, sohn, tochter, mann, Frau, kerl, madel, herr, dame, enkel, enkelin, großvater, großmutter, cousin, cousine, er, sie, ihm, ihr, sein, ihr, seine, ihre, ehemann, ehefrau, feuerwehrmann, feuerwehrfrau, konig, konigin, fürst, fürstin, herzog, herzogin, mann, Frau, Männer, femmes, hr., fr., polizist, polizistin, prinz, prinzessin, sprecher, sprecherin, kollege, kollegin, mitarbeiter, mitarbeiterin, helfer, helferin, anwalt, anwältin, bauarbeiter, bauarbeiterin, krankenpfleger, krankenpflegerin, chef, chefsin, vorgesetzter, vorgesetzte, sönger, söngerin, kunde, kundin, besucher, besucherin, freund, freundin, arzt, ärtzin, verkäufer, verkäuferin, kanzler, kanzlerin, geschäftsleiter, geschäftsleiterin, pfleger, pflegerin, kellner, kellnerin."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.769,
+                0.489,
+                0.815
+            ],
+            "angle": 0,
+            "content": "Race: dunkelhautig, hellhautig, asiatisch, afrikaner, europäer, asiate, amerikaner, afrika, amerika, asien, china."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.817,
+                0.49,
+                0.88
+            ],
+            "angle": 0,
+            "content": "Religion: jiudisch, christlich, muslimisch, Jude, christ, muslim, torah, bibel, koran, synagogue, kirche, moschee, rabbiner, pfarrer, imam, judentum, christentum, islam."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.133,
+                0.884,
+                0.186,
+                0.898
+            ],
+            "angle": 0,
+            "content": "Dutch"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.133,
+                0.904,
+                0.489,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Gender: acteur, actrice, actuers, actrices,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.086,
+                0.886,
+                0.6
+            ],
+            "angle": 0,
+            "content": "oom, tante, ooms, tantes, nonkel, tante, nonkels, tantes,jongen,meisje,jongens,meisjes,bruidgem, bruid, bruidegommen, bruiden, broer, zus, broers,zussen,zakenman,zakenvrouw,zakenmannen,zakenvrouwen,kerel,griet,kerels,grieten,vader,moeder,vaders,moeders,papa,mama,papa's,mama's,zoon, dochter;zonen,dochters,man,vrouw,mannen,vrouwen,gast,wijf,gasten,wijven,heer,dame,heren,dames,kleinzoon,kleindochter,kleinzonen,kleindochters,vent,vrouw,venten,vrouwen,hij,zij,hemzelf,haarzelf,hem,haar,zijn,haar,mannelijk,vrouwelijk,vriend,vriendin,vrienden,vriendinnen,koning,koningin,koningen,koninginnen,heer,dame,heren,dames,meneer,mevrouw,jongeheer,jongedame,jongeheren,jongedames,jongeheer,juffrouw,jongeheren,juffrouwen,politieagent,politieagente,prins,prinses,prinsen,prinsessen,woordvoerder,wordvoerster,wordvoerders,wordvoersters,brandweerman,brandweervrouw,brandweermannen,brandweervrouwen,timmerman,timmervrouw,timmermannen,timmervrouwen,meester,juf,meesters,juffen,verpleger,verpleegster,verplegers,verpleegsters,bestuurder,bestuurster,bestuurders,bestuursters,kuisman,kuisvrouw,kuismannen,kuisvrouwen,kok,kokkin,kokken,kokkinen,leraar,lerares,directeur,directrice,directeurs,directrices,secretaris,secretaresse,secretaris-SEN,secretaressen,boer,boerin,boeren,boerinnen,held,heldin,gastheer,gastvrouw,gastheren,gastvrouwen,opa,oma,opa's,oma's,grootvader,grootmoeder,grootvaders,grootmoeders."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.601,
+                0.885,
+                0.663
+            ],
+            "angle": 0,
+            "content": "Race: afrikaans, amerikaans, aziatisch, afrikaans, europees, aziatisch, zwart, blank, aziatisch, afrika, amerika, aziè, afrika, amerika, china, afrika, europa, aziè."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.665,
+                0.885,
+                0.728
+            ],
+            "angle": 0,
+            "content": "Religion: joods, christen, moslim, joden, christenen, moslims, thorabijbel, koran, synagogue, kerk, moskee, rabbijn, priester, imam, jodendom, christendom, islam."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.742,
+                0.692,
+                0.758
+            ],
+            "angle": 0,
+            "content": "C Averaged results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.768,
+                0.885,
+                0.816
+            ],
+            "angle": 0,
+            "content": "Tables 5, 6, and 7 show the different averaged results are the debiasing languages other than English, namely French, German, and Dutch."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.829,
+                0.712,
+                0.844
+            ],
+            "angle": 0,
+            "content": "D Breakdown results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.855,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "In this section, a breakdown of the different scores per category is shown in terms of the bias metric established in (Nangia et al., 2020) in Tables 8, 9, 10, 11. For brevity, we employ the following"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2895"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.126,
+                0.082,
+                0.48,
+                0.133
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>10.93↑</td><td>6.94↑</td><td>7.50↑</td><td>9.44↑</td><td>9.07↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.91↓</td><td>12.22↑</td><td>11.67↑</td><td>10.00↓</td><td>10.74↓</td></tr><tr><td>DE</td><td>9.33</td><td>11.11↑</td><td>6.29↓</td><td>6.55↓</td><td>9.45↑</td><td>6.09↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.96↓</td><td>14.86↓</td><td>16.26↓</td><td>15.05↓</td><td>12.94↓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.143,
+                0.489,
+                0.187
+            ],
+            "angle": 0,
+            "content": "Table 5: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.126,
+                0.199,
+                0.481,
+                0.251
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>9.44↑</td><td>6.94↑</td><td>7.22↑</td><td>10.19↑</td><td>8.43↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.17↓</td><td>7.5↓</td><td>10.28↓</td><td>8.43↓</td><td>7.13↓</td></tr><tr><td>DE</td><td>9.33</td><td>10.20↑</td><td>4.89↓</td><td>6.27↓</td><td>6.38↓</td><td>6.01↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.31↓</td><td>14.59↓</td><td>16.25↓</td><td>17.10↓</td><td>16.65↓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.261,
+                0.489,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Table 6: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.126,
+                0.317,
+                0.481,
+                0.369
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.80↑</td><td>6.94↑</td><td>7.22↑</td><td>7.69↑</td><td>7.50↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.30↑</td><td>10.28↓</td><td>10.56↓</td><td>9.07↓</td><td>9.17↓</td></tr><tr><td>DE</td><td>9.33</td><td>8.71↓</td><td>6.83↓</td><td>7.39↓</td><td>6.04↓</td><td>5.37↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.68↓</td><td>15.71↓</td><td>16.54↓</td><td>14.69↓</td><td>14.41↓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.379,
+                0.489,
+                0.422
+            ],
+            "angle": 0,
+            "content": "Table 7: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.448,
+                0.486,
+                0.479
+            ],
+            "angle": 0,
+            "content": "abbreviations: Gender (G), Race (Ra), and Religion (Re)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.14,
+                0.49,
+                0.465,
+                0.636
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>51.30</td><td>51.11</td><td>50.28*</td><td>55.28</td><td>50.37</td></tr><tr><td>G</td><td>49.17</td><td>49.17</td><td>49.17</td><td>46.67</td><td>50.83</td><td>51.11</td></tr><tr><td>Ra</td><td>44.17</td><td>41.94</td><td>45.00</td><td>-</td><td>39.72</td><td>39.17</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>59.17</td><td>-</td><td>75.28</td><td>60.83</td></tr><tr><td>FR</td><td>60.56</td><td>57.50</td><td>60.00</td><td>60.28*</td><td>62.59</td><td>58.52</td></tr><tr><td>G</td><td>50.83</td><td>45.56</td><td>50.00</td><td>50.00</td><td>59.72</td><td>60.83</td></tr><tr><td>Ra</td><td>59.17</td><td>56.67</td><td>57.50</td><td>-</td><td>56.39</td><td>50.83</td></tr><tr><td>Re</td><td>71.67</td><td>70.28</td><td>72.50</td><td>-</td><td>71.67</td><td>63.89</td></tr><tr><td>DE</td><td>59.05</td><td>55.93</td><td>54.86</td><td>56.55*</td><td>57.06</td><td>55.50</td></tr><tr><td>G</td><td>60.90</td><td>54.50</td><td>51.71</td><td>53.42</td><td>53.29</td><td>56.70</td></tr><tr><td>Ra</td><td>57.07</td><td>61.35</td><td>57.05</td><td>-</td><td>51.51</td><td>48.42</td></tr><tr><td>Re</td><td>59.17</td><td>51.94</td><td>55.83</td><td>-</td><td>66.39</td><td>61.39</td></tr><tr><td>NL</td><td>67.66</td><td>63.96</td><td>64.59</td><td>65.98*</td><td>66.65</td><td>67.22</td></tr><tr><td>G</td><td>56.32</td><td>54.10</td><td>49.59</td><td>51.28</td><td>56.62</td><td>57.48</td></tr><tr><td>Ra</td><td>65.83</td><td>59.17</td><td>65.00</td><td>-</td><td>66.39</td><td>65.56</td></tr><tr><td>Re</td><td>80.83</td><td>78.61</td><td>79.17</td><td>-</td><td>76.94</td><td>78.61</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.646,
+                0.489,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Table 8: Overall performance score per evaluation language, debiasing technique, and category averaged over the three random seeds after debiasing in English."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.139,
+                0.717,
+                0.465,
+                0.862
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>55.74</td><td>50.28</td><td>50.28*</td><td>54.26</td><td>51.67</td></tr><tr><td>G</td><td>49.17</td><td>52.78</td><td>47.50</td><td>46.67</td><td>49.72</td><td>53.06</td></tr><tr><td>Ra</td><td>44.17</td><td>45.83</td><td>43.33</td><td>-</td><td>46.11</td><td>38.89</td></tr><tr><td>Re</td><td>60.00</td><td>68.61</td><td>60.00</td><td>-</td><td>66.94</td><td>63.06</td></tr><tr><td>FR</td><td>60.56</td><td>54.54</td><td>60.00</td><td>58.89*</td><td>58.15</td><td>57.59</td></tr><tr><td>G</td><td>50.83</td><td>47.22</td><td>46.67</td><td>45.83</td><td>52.22</td><td>55.28</td></tr><tr><td>Ra</td><td>59.17</td><td>47.22</td><td>60.83</td><td>-</td><td>57.50</td><td>51.67</td></tr><tr><td>Re</td><td>71.67</td><td>69.17</td><td>72.50</td><td>-</td><td>64.72</td><td>65.83</td></tr><tr><td>DE</td><td>59.05</td><td>59.68</td><td>55.43</td><td>55.98*</td><td>55.95</td><td>53.09</td></tr><tr><td>G</td><td>60.90</td><td>52.47</td><td>50.85</td><td>51.71</td><td>55.24</td><td>55.83</td></tr><tr><td>Ra</td><td>57.07</td><td>59.91</td><td>58.78</td><td>-</td><td>52.05</td><td>47.04</td></tr><tr><td>Re</td><td>59.17</td><td>66.67</td><td>56.67</td><td>-</td><td>60.56</td><td>56.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>64.31</td><td>65.71*</td><td>65.05</td><td>62.94</td></tr><tr><td>G</td><td>56.32</td><td>49.59</td><td>49.59</td><td>50.45</td><td>54.32</td><td>55.76</td></tr><tr><td>Ra</td><td>65.83</td><td>62.22</td><td>65.00</td><td>-</td><td>62.50</td><td>58.33</td></tr><tr><td>Re</td><td>80.83</td><td>80.83</td><td>78.33</td><td>-</td><td>78.33</td><td>74.72</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.872,
+                0.489,
+                0.915
+            ],
+            "angle": 0,
+            "content": "Table 9: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.534,
+                0.081,
+                0.858,
+                0.226
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.44</td><td>50.28</td><td>50.00*</td><td>52.59</td><td>52.13</td></tr><tr><td>G</td><td>49.17</td><td>46.67</td><td>45.83</td><td>45.83</td><td>45.28</td><td>49.17</td></tr><tr><td>Ra</td><td>44.17</td><td>53.06</td><td>45.00</td><td>-</td><td>44.17</td><td>43.06</td></tr><tr><td>Re</td><td>60.00</td><td>63.61</td><td>60.00</td><td>-</td><td>68.33</td><td>64.17</td></tr><tr><td>FR</td><td>60.56</td><td>56.57</td><td>57.5</td><td>60.28*</td><td>53.80</td><td>53.61</td></tr><tr><td>G</td><td>50.83</td><td>47.48</td><td>50.00</td><td>50.00</td><td>53.89</td><td>55.83</td></tr><tr><td>Ra</td><td>59.17</td><td>60.56</td><td>58.33</td><td>-</td><td>44.44</td><td>45.83</td></tr><tr><td>Re</td><td>71.67</td><td>61.39</td><td>64.17</td><td>-</td><td>63.06</td><td>59.17</td></tr><tr><td>DE</td><td>59.05</td><td>57.64</td><td>53.75</td><td>55.70*</td><td>55.72</td><td>55.35</td></tr><tr><td>G</td><td>60.90</td><td>47.69</td><td>50.00</td><td>50.86</td><td>54.46</td><td>58.41</td></tr><tr><td>Ra</td><td>57.07</td><td>64.38</td><td>57.07</td><td>-</td><td>57.69</td><td>53.47</td></tr><tr><td>Re</td><td>59.17</td><td>60.83</td><td>54.17</td><td>-</td><td>55.00</td><td>54.17</td></tr><tr><td>NL</td><td>67.66</td><td>61.16</td><td>63.48</td><td>65.14*</td><td>67.10</td><td>66.65</td></tr><tr><td>G</td><td>56.32</td><td>49.88</td><td>48.76</td><td>48.76</td><td>56.30</td><td>56.60</td></tr><tr><td>Ra</td><td>65.83</td><td>53.89</td><td>64.17</td><td>-</td><td>69.44</td><td>67.78</td></tr><tr><td>Re</td><td>80.83</td><td>79.72</td><td>77.50</td><td>-</td><td>75.56</td><td>75.56</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.508,
+                0.236,
+                0.882,
+                0.28
+            ],
+            "angle": 0,
+            "content": "Table 10: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.534,
+                0.313,
+                0.858,
+                0.458
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.91</td><td>50.83</td><td>50.56*</td><td>47.69</td><td>51.20</td></tr><tr><td>G</td><td>49.17</td><td>51.94</td><td>48.33</td><td>47.50</td><td>45.56</td><td>52.22</td></tr><tr><td>Ra</td><td>44.17</td><td>50.00</td><td>44.17</td><td>-</td><td>40</td><td>40.83</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>60.00</td><td>-</td><td>57.5</td><td>60.56</td></tr><tr><td>FR</td><td>60.56</td><td>60.37</td><td>60.28</td><td>60.56*</td><td>55.37</td><td>52.50</td></tr><tr><td>G</td><td>50.83</td><td>50.28</td><td>50.83</td><td>50.83</td><td>55.83</td><td>53.89</td></tr><tr><td>Ra</td><td>59.17</td><td>61.94</td><td>61.67</td><td>-</td><td>44.44</td><td>41.11</td></tr><tr><td>Re</td><td>71.67</td><td>68.89</td><td>68.33</td><td>-</td><td>65.83</td><td>62.50</td></tr><tr><td>DE</td><td>59.05</td><td>55.67</td><td>56.55</td><td>56.25*</td><td>48.53</td><td>50.86</td></tr><tr><td>G</td><td>60.90</td><td>47.71</td><td>53.38</td><td>52.52</td><td>53.04</td><td>54.73</td></tr><tr><td>Ra</td><td>57.07</td><td>58.20</td><td>59.59</td><td>-</td><td>45.89</td><td>46.47</td></tr><tr><td>Re</td><td>59.17</td><td>61.11</td><td>56.67</td><td>-</td><td>46.67</td><td>51.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>63.74</td><td>64.57*</td><td>64.51</td><td>63.67</td></tr><tr><td>G</td><td>56.32</td><td>52.92</td><td>47.05</td><td>47.05</td><td>52.97</td><td>53.22</td></tr><tr><td>Ra</td><td>65.83</td><td>59.72</td><td>67.50</td><td>-</td><td>61.67</td><td>57.78</td></tr><tr><td>Re</td><td>80.83</td><td>80.00</td><td>76.67</td><td>-</td><td>78.89</td><td>80.00</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.508,
+                0.468,
+                0.882,
+                0.511
+            ],
+            "angle": 0,
+            "content": "Table 11: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "2896"
+        }
+    ]
+]

2023/Investigating Bias in Multilingual Language Models_ Cross-Lingual Transfer of Debiasing Techniques/ac884595-2bc6-45c5-8d3c-8fe9015e5586_origin.pdf

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2023/Investigating Bias in Multilingual Language Models_ Cross-Lingual Transfer of Debiasing Techniques/full.md

@@ -0,0 +1,262 @@
+# Investigating Bias in Multilingual Language Models: Cross-Lingual Transfer of Debiasing Techniques
+
+Manon Reusens<sup>1</sup>, Philipp Borchert<sup>1,2</sup>, Margot Mieskes<sup>3</sup>, Jochen De Weerdt<sup>1</sup>, Bart Baesens<sup>1,4</sup>
+
+<sup>1</sup>Research Centre for Information Systems Engineering (LIRIS), KU Leuven
+
+$^{2}$ IESEG School of Management, 3 Rue de la Digue, 59000 Lille, France
+
+<sup>3</sup>University of Applied Sciences Darmstadt
+
+$^{4}$ Department of Decision Analytics and Risk, University of Southampton {manon.reusens, philipp.borchert, jochen.deweerdt, bart.daesens} @kuleuven.be margot.mieskes@h-da.de
+
+DISCLAIMER: This paper contains explicit statements that are potentially offensive.
+
+# Abstract
+
+This paper investigates the transferability of debiasing techniques across different languages within multilingual models. We examine the applicability of these techniques in English, French, German, and Dutch. Using multilingual BERT (mBERT), we demonstrate that cross-lingual transfer of debiasing techniques is not only feasible but also yields promising results. Surprisingly, our findings reveal no performance disadvantages when applying these techniques to non-English languages. Using translations of the CrowS-Pairs dataset, our analysis identifies SentenceDebias as the best technique across different languages, reducing bias in mBERT by an average of  $13\%$ . We also find that debiasing techniques with additional pretraining exhibit enhanced cross-lingual effectiveness for the languages included in the analyses, particularly in lower-resource languages. These novel insights contribute to a deeper understanding of bias mitigation in multilingual language models and provide practical guidance for debiasing techniques in different language contexts.
+
+# 1 Introduction
+
+There has been a growing interest in addressing bias detection and mitigation in Natural Language Processing (NLP) due to their societal implications. Initially, research focused on debiasing word embeddings (Bolukbasi et al., 2016; Zhao et al., 2018b), but recent studies found that pretrained language models also capture social biases present in training data (Meade et al., 2022). Hence, attention has shifted towards debiasing techniques that target sentence representations. These techniques include additional pretraining steps (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019)
+
+![](images/ccbe36bc7cf718d0565ea636470abe47965474edc31478ceb635fccb2d995619.jpg)  
+Figure 1: The example of the English CrowS-Pairs dataset illustrates sentence probabilities after debiasing mBERT with SentenceDebias in English, French, German, and Dutch.
+
+and projection-based methods that assume a bias direction (Liang et al., 2020a; Ravfogel et al., 2020; Liang et al., 2020b).
+
+While debiasing techniques have been developed and evaluated for monolingual, and mostly English models, the effectiveness and transferability of these techniques to diverse languages within multilingual models remain largely unexplored (Stanczak and Augenstein, 2021; Sun et al., 2019). Our research aims to bridge this gap by examining the potential of debiasing techniques applied to one language to effectively mitigate bias in other languages within multilingual large language models. We examine English (EN), French (FR), German (DE), and Dutch (NL). Figure 1 illustrates an example sentence pair included in the English CrowS-Pairs dataset<sup>1</sup>, where the unmodified and modified parts are highlighted in blue and yellow respectively. It shows the predicted probabilities of
+
+the modified part occurring given the unmodified part across different debiasing languages.
+
+This study examines the cross-lingual transferability of debiasing techniques using mBERT. mBERT, trained on Wikipedia data from diverse languages, possesses the capability to process and generate text in various linguistic contexts. Despite balancing efforts, it still performs worse on low-resource languages (Wu and Dredze, 2020; Devlin, 2018). We investigate whether this performance disparity extends to gender, religious, and racial biases. Related studies demonstrate the effectiveness of cross-lingual debiasing for individual techniques and selected bias scopes (Liang et al., 2020b; Lauscher et al., 2021). We show how to reduce bias in mBERT across different languages by conducting a benchmark of state-of-the-art (SOTA) debiasing techniques and providing guidance on its implementation. To facilitate further research and reproducibility, we make the code and additional data available to the research community $^{2}$ .
+
+Our contributions can be summarized as follows: 1) We provide a benchmark of different SOTA debiasing techniques across multiple languages in a multilingual large language model. 2) We find that SentenceDebias is the most effective for cross-lingual debiasing, reducing the bias in mBERT by  $13\%$ . 3) We provide implementation guidelines for debiasing multilingual models and highlight the differences in the cross-lingual transferability of different debiasing techniques. We find that most projection-based techniques applied to one language yield similar predictions across evaluation languages. We also recommend performing the techniques with an additional pretraining step on the lowest resource language within the multilingual model for optimal results.
+
+# 2 Methodology
+
+This section introduces the data, debiasing techniques, and experimental setup respectively.
+
+# 2.1 CrowS-Pairs
+
+CrowS-Pairs is a benchmark dataset comprising 1508 examples that address stereotypes associated with historically disadvantaged groups in the US, encompassing various types of bias, such as age and religion (Nangia et al., 2020). Following Meade et al. (2022), where different debiasing tech
+
+niques were benchmarked and their effectiveness demonstrated on BERT for gender, race, and religion, we focus on these three types of bias. Néveol et al. (2022) translated the dataset in French. To the best of our knowledge, there are currently no peer-reviewed variants of CrowS-Pairs available in other languages. Therefore, we used three samples of the full dataset and translated them into the respective language to evaluate our experiments.
+
+To create an evaluation set for our experiments, we started from the English CrowS-Pairs dataset (Nangia et al., 2020). We randomly sampled  $N$  instances, where  $N \in \{20,30,40,50\}$ , and measured the performance differences on mBERT and BERT. Through three random seeds, we found that a sample size of 40 resulted in an average performance correlation of more than  $75\%$  with the full dataset for both models. Thus, we conclude that using 40 instances with three random seeds provides a representative dataset for our evaluation. Further details are shown in Appendix A. Subsequently, we included the translated samples from each language into our dataset, either the corresponding sentences from the French CrowS-Pairs or a translation.
+
+# 2.2 Debiasing techniques
+
+Next, the different debiasing techniques are explained. For more information on the attribute lists used, we refer to Appendix B.
+
+Counterfactual Data Augmentation (CDA) is a debiasing technique that trains the model on an augmented training set (Zhao et al., 2019; Webster et al., 2020; Zmigrod et al., 2019). First, the corpus is augmented by duplicating sentences that include words from a predefined attribute list. Next, counterfactual sentences are generated by swapping these attribute words with other variants in the list, for example, swapping  $he$  by  $she$ . We augment  $10\%$  of the Wikipedia corpus of the respective language and use an additional pretraining step to debias the model for three random seeds and average the results.
+
+Dropout Regularization (DO) is introduced by Webster et al. (2020) as a debiasing technique by implementing an additional pretraining step. We execute this pretraining step while training on  $10\%$  of the Wikipedia corpus of the respective language using three random seeds and averaging the results.
+
+SentenceDebias (SenDeb) introduced by Liang et al. (2020a) is a projection-based debiasing technique extending debiasing word embeddings
+
+(Bolukbasi et al., 2016) to sentence representations. Attribute words from a predefined list are contextualized by retrieving their occurrences from a corpus and augmented with CDA. Next, the bias subspace is computed using the representations of these sentences through principal component analysis (PCA). The first  $K$  dimensions of PCA are assumed to define the bias subspace as they capture the principle directions of variation of the representations. We debias the last hidden state of the mBERT model and implement SenDeb using  $2.5\%$  of the Wikipedia text in the respective language.
+
+Iterative Nullspace Projection (INLP) is a projection-based debiasing technique in which multiple linear classifiers are trained to predict biases, such as gender, that are to be removed from the sentence representations (Ravfogel et al., 2020). After training a single classifier, the representations are debiased by projecting them onto the learned linear classifier's weight matrix to gather the rowspace projection. We implement this technique using the  $2.5\%$  of the Wikipedia text in each language.
+
+DensRay (DR) is a projection-based debiasing technique first implemented by (Duftner and Schütze, 2019) and adapted for contextualized word embeddings by (Liang et al., 2020b). This technique is similar to SenDeb, but the bias direction is calculated differently. This method aims to find an optimal orthogonal matrix so that the first  $K$  dimensions correlate well with the linguistic features in the rotated space. The second dimension is assumed to be orthogonal to the first one. The bias direction is considered to correspond to the eigenvector of the highest eigenvalue of the matrix. DR is only implemented for a binary bias type and using it for multiclass bias types requires modifying the technique. Therefore, we only apply it to the gender bias type. We implement DR debiasing the last hidden state of mBERT and using  $2.5\%$  of the Wikipedia text in the respective language.
+
+# 2.3 Experimental setup
+
+We debias mBERT using language  $X$  and evaluating it on language  $Y$  with  $X, Y \in \{EN, FR, DE, NL\}$ . In essence, we debiased the model using one language and evaluated it on another, covering all language combinations in our experiments. We implement mBERT in its base configuration (uncased, 12 layers, 768 hidden size) and utilize the bias score as implemented in Meade et al. (2022). This metric evaluates the percentage
+
+of sentences where the model prefers the more biased sentence over the less biased sentence, with an optimal performance of  $50\%$ . All experiments are performed on P100 GPUs.
+
+# 3 Results
+
+Table 1 shows the performance of the different debiasing techniques when debiasing in English in terms of the absolute deviation of the ideal unbiased model. This is an average score for all bias types and models trained for the respective evaluation language. Base represents the score that is achieved by mBERT on the respective evaluation language dataset before debiasing. More results are shown in Appendices C and D.
+
+As shown in Table 1, English is relatively unbiased compared to the other languages and shows a small bias increase after debiasing. This observation aligns with the findings of Ahn and Oh (2021), who propose mBERT as a debiasing technique. In cases where the initial bias score is already close to the optimal level, further debiasing can lead to overcompensation, consequently amplifying the total bias. We assume that an unbiased model should equally prioritize both biased and unbiased sentences. However, when debiasing techniques tend to overcorrect, they skew the balance towards favoring the prediction of unbiased sentences over biased ones. Addressing this challenge necessitates the adoption of specialized techniques to effectively mitigate any residual bias.
+
+This phenomenon of overcompensation occurs in several underperforming techniques, as illustrated in Table 1. Notably, we find instances of overcompensation for gender when debiasing using INLP for French and using CDA for German, as well as for race when debiasing using DO for German. Another contributing factor to the poor performance of certain techniques within specific debiasing and evaluation language combinations lies in the inherent ineffectiveness of the debiasing method itself, exemplified by the cases of gender debiasing using CDA for French and religion debiasing using CDA for German. In Tables 5, 6, and 7, we find overcompensation for gender when debiasing with INLP in German and French, evaluating in German, debiasing with Sendeb and DR in French, and evaluating in French, as well as when debiasing in Dutch with INLP and evaluating in French. Moreover, overcompensation for race is also observed when debiasing with CDA in French
+
+<table><tr><td></td><td>Base</td><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.70↑</td><td>7.78↑</td><td>6.94↑</td><td>13.43↑</td><td>8.70↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.20↑</td><td>10↓</td><td>10.28↓</td><td>12.6↑</td><td>9.44↓</td></tr><tr><td>DE</td><td>9.33</td><td>7.52↓</td><td>6.57↓</td><td>6.84↓</td><td>10.75↑</td><td>9.75↑</td></tr><tr><td>NL</td><td>17.66</td><td>13.96↓</td><td>15.14↓</td><td>16.54↓</td><td>16.84↓</td><td>17.40↓</td></tr></table>
+
+and evaluating in German.
+
+Is cross-lingual transferability of debiasing techniques possible? Table 1 shows that cross-lingual transfer is possible using English as debiasing language. Figure 2 confirms this, depicting the bias scores averaged over all debiasing techniques. As discussed, for English, these techniques increase the bias contained in the model due to its already close to optimal performance. For the other evaluation languages, we find better performance after debiasing. Therefore, we conclude that for these four languages, it is possible to debias the mBERT model to some extent using a different debiasing language, except when the bias contained in the model is already relatively low.
+
+To shed some light on the insights that can be gathered from Figure 2, Table 2 offers an overview of the best- and worst-performing techniques per evaluation language. As shown, Dutch is found to be the best debiasing language for English. This is because this debiasing language has shown to overcompensate the gender bias category the least, therefore, resulting in the best performance. In general, we find that using the same debiasing language as evaluation language often results in an overcompensation of the bias, therefore turning around the bias direction. This means that the best-performing debiasing language is often not the same as the evaluation language. However, German is the exception. As this language already has the highest bias score for gender before debiasing, strong debiasing is beneficial and therefore does not result in overcompensation. Besides German being the best-performing debiasing language for German, it also shows the best performance for French because it achieves the best performance on all different evaluation sets. Moreover, it also shows less overcompensation for the gender bias present in the model than other languages such as Dutch.
+
+French is the worst-performing debiasing language for all evaluation languages except for Dutch, where it is the best-performing one. We find that when evaluating in French, the gender bias is over
+
+Table 1: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in English.  
+
+<table><tr><td>Evaluation language</td><td>Best debiasing language</td><td>worst debiasing language</td></tr><tr><td>English</td><td>Dutch</td><td>French</td></tr><tr><td>French</td><td>German</td><td>French</td></tr><tr><td>German</td><td>German</td><td>French</td></tr><tr><td>Dutch</td><td>French</td><td>English</td></tr></table>
+
+Table 2: Overview best- and worst-performing debiasing languages per evaluation language.
+
+![](images/9730fd8a88c0edb9da23f7d55bcdfa07c9f51f298fea8ebc259d0563075d7d42.jpg)  
+Figure 2: Average bias scores per evaluation and debi-aising language.
+
+compensated. For English, both racial and gender bias are overcompensated. The German evaluation shows lower overall performance due to already two ineffective methods (INLP and CDA), which were also due to overcompensating racial bias. Finally, for Dutch, we find that debiasing with French overcompensates gender bias less than Dutch and, therefore, is the best-performing method. As Dutch has the second highest gender bias score before debiasing, it also benefits from strong debiasing and therefore both French and Dutch perform well.
+
+We believe that these results are influenced by the fact that both German and French have a grammatical gender distinction, which may impact debiasing gender to a greater extent. This grammatical gender distinction is not embedded in English and Dutch. Moreover, as the religion category regularly shows limited bias decrease, we find that the performance in the gender and race category often determines whether a technique works well or not.
+
+How are the different techniques affected by cross-lingual debiasing? Table 3 shows the overall percentage increase of the bias score per technique. From this, we conclude that SenDeb is the best-performing technique and reduces bias in mBERT on average by  $13\%$ . DO is the second best-performing method reducing bias on average by  $10\%$ . However, Figure 3 shows that DO performs well for all debiasing languages except English, while SenDeb performs consistently well for all languages. The other techniques perform worse overall. Hence, we suggest using SenDeb as cross-lingual debiasing technique for these languages.
+
+<table><tr><td>INLP</td><td>Sendeb</td><td>DR</td><td>CDA</td><td>Dropout</td></tr><tr><td>1.11</td><td>13.21</td><td>7.1</td><td>-0.16</td><td>10.21</td></tr></table>
+
+Table 3: Average percentage difference in bias scores of each technique compared to the base model.
+
+![](images/e95201d19415bb36863f645c9b70e4055bc0d942a37c68f83da930823f45e0ce.jpg)  
+Figure 3: Average bias score per technique per debiasing language.
+
+When zooming in on the projection-based techniques, i.e. INLP, SenDeb, and DR, a high performance variation is shown in Table 3 and Figure 3. While SenDeb offers consistent performance for all different debiasing languages, we see more variation and a lower bias decrease for INLP. This is due to the high variation in performance, resulting in a higher overall average. As INLP uses multiple linear classifiers to define the projection matrix, high variability is introduced. Since DR was only implemented for gender, no performance gains can be obtained from the other bias types, therefore resulting in a lower overall performance increase.
+
+Techniques using an additional pretraining step obtain the best results when debiasing in Dutch, as illustrated in Figure 4. Notably, Dutch is the lowest resource language out of these four languages during pretraining (Wu and Dredze, 2020). This additional pretraining step lets the model learn unbiased associations between words while becoming familiar with the lower-resource language resulting in lower overall bias. Therefore, we conclude that, for our set of languages, these techniques are most effective when applied to low-resource languages.
+
+# 4 Related work
+
+Significant research focuses on the cross-lingual performance of mBERT (Wu and Dredze, 2020; Pires et al., 2019; Libovický et al., 2019). Limited research focuses on the cross-lingual transferability of debiasing techniques in mBERT (Stanczak and Augenstein, 2021; Sun et al., 2019). Liang et al. (2020b) use DensRay in English to debias Chinese
+
+![](images/3b20bcb64277e02f2f9e6a3ba214f4a93af3f37c1dc0b1696a7b1f9913379497.jpg)  
+Figure 4: Average bias score per debiasing languages for both CDA and DO.
+
+in mBERT for gender. Similarly, Zhao et al. (2020) analyze the cross-lingual transfer of gender bias mitigation using one method. Lauscher et al. (2021) also find that their proposed technique, ADELE, can transfer debiasing across six languages. Other studies analyze biases contained in multilingual language models. Kaneko et al. (2022) evaluate bias across multiple languages in masked language models using a new metric. Ahn and Oh (2021) study ethnic bias and its variability over languages proposing mBERT as debiasing technique. Finally, some studies also explore the cross-lingual transferability of downstream tasks (Levy et al., 2023).
+
+# 5 Conclusion
+
+Most studies focus on debiasing techniques for large language models, but rarely explore their cross-lingual transferability. Therefore, we offer a benchmark for SOTA debiasing techniques on mBERT across multiple languages (EN, FR, DE, NL) and show that debiasing is transferable across languages, yielding promising results. We provide guidance for cross-lingual debiasing, highlighting SenDeb as the best-performing method, reducing bias in mBERT by  $13\%$ . Additionally, we find that, for the studied languages, debiasing with the lowest resource language is effective for techniques involving an additional training step (CDA and DO). This research is a first step into the cross-lingual transferability of debiasing techniques. Further studies should include languages from different cultures and other multilingual large language models to assess generalizability.
+
+# Limitations
+
+A first limitation concerns the analysis focused on four closely related languages from a similar culture. A broader range of languages should be explored to ensure the generalizability of the findings. Our research was conducted employing a
+
+single multilingual model, mBERT. Extending this to other multilingual language models would provide valuable insights into the wider applicability of the results. Moreover, the evaluation of outcomes relied primarily on the CrowS-Pairs metric, although efforts were made to enhance the understanding by examining the absolute difference compared to the optimal model. Next, the consideration of gender was limited to binary classification, overlooking non-binary gender identities. This should be further addressed in future research. Furthermore, a comprehensive multilingual dataset to assess stereotypes across different languages is not available, and thus, the English CrowS-Pairs dataset was translated and corresponding sentences of the French dataset were used. Nevertheless, typical stereotypes for other languages were not adequately represented. Furthermore, the dataset used in the study exhibited certain flaws highlighted by Blodgett et al. (2021), such as the influence of selected names on predictions, which was observed to have a significant impact. This needs to be investigated further. Additionally, attribute lists for languages other than English were not available to the same extent. We tried to compile lists for French, Dutch, and German, excluding words with multiple meanings to minimize noise. However, our lists were not exhaustive, and therefore the omission of relevant attributes is possible. It is also worth noting that, in certain cases, the generic masculine form was considered the preferred answer, despite it being included in the attribute lists. Finally, the applicability of downstream tasks should be investigated (e.g. (Levy et al., 2023)). Hence, future research should encompass a wider language scope, include multiple models, address existing dataset flaws, and develop more comprehensive attribute lists for various languages.
+
+# Ethics Statement
+
+We would like to address three key ethical considerations in this study that highlight ongoing challenges and complexities associated with mitigating bias in large language models. First, it is important to acknowledge that the gender bias examined in this paper is approached from a binary perspective. However, this does not capture the full range of gender identities present in reality. While we recognize this limitation, it was necessary to simplify the analysis for experimental purposes. In future research, we hope to address this limitation. Second, despite
+
+efforts to debias the multilingual large language model, it is important to note that not all forms of bias are completely mitigated. The applied debiasing techniques do lower the bias present in the model, however, there is still bias present in the model both within and outside the targeted bias types. Finally, we recognize that our evaluation datasets do not encompass all the different biases that might be present in the model. Therefore, even if a model would obtain a perfect score, it is still possible that other forms of bias persist.
+
+# Acknowledgements
+
+This research was funded by the Statistics Flanders research cooperation agreement on Data Science for Official Statistics. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center).
+
+# References
+
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+Jacob Devlin. 2018. Multilingual bert readme document.  
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+Jindrich Libovický, Rudolf Rosa, and Alexander Fraser. 2019. How language-neutral is multilingual bert? arXiv preprint arXiv:1911.03310.  
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+Nikita Nangia, Clara Vania, Rasika Bhalerao, and Samuel R. Bowman. 2020. CrowS-pairs: A challenge dataset for measuring social biases in masked language models. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 1953-1967, Online. Association for Computational Linguistics.  
+Aurelie Néveol, Yoann Dupont, Julien Bezànçon, and Karen Fort. 2022. French CrowS-pairs: Extending a challenge dataset for measuring social bias in masked language models to a language other than English. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 8521-8531, Dublin, Ireland. Association for Computational Linguistics.
+
+Telmo Pires, Eva Schlinger, and Dan Garrette. 2019. How multilingual is multilingual BERT? In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 4996-5001, Florence, Italy. Association for Computational Linguistics.  
+Shauli Ravfogel, Yanai Elazar, Hila Gonen, Michael Twiton, and Yoav Goldberg. 2020. Null it out: Guarding protected attributes by iterative nullspace projection. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 7237-7256, Online. Association for Computational Linguistics.  
+Karolina Stanczak and Isabelle Augenstein. 2021. A survey on gender bias in natural language processing. arXiv preprint arXiv:2112.14168.  
+Tony Sun, Andrew Gaut, Shirlyn Tang, Yuxin Huang, Mai ElSherief, Jieyu Zhao, Diba Mirza, Elizabeth Belding, Kai-Wei Chang, and William Yang Wang. 2019. Mitigating gender bias in natural language processing: Literature review. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 1630–1640, Florence, Italy. Association for Computational Linguistics.  
+Kellie Webster, Xuezhi Wang, Ian Tenney, Alex Beutel, Emily Pittler, Ellie Pavlick, Jilin Chen, Ed Chi, and Slav Petrov. 2020. Measuring and reducing gendered correlations in pre-trained models. arXiv preprint arXiv:2010.06032.  
+Shijie Wu and Mark Dredze. 2020. Are all languages created equal in multilingual BERT? In Proceedings of the 5th Workshop on Representation Learning for NLP, pages 120-130, Online. Association for Computational Linguistics.  
+Jieyu Zhao, Subhabrata Mukherjee, Saghar Hosseini, Kai-Wei Chang, and Ahmed Hassan Awadallah. 2020. Gender bias in multilingual embeddings and crosslingual transfer. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 2896-2907, Online. Association for Computational Linguistics.  
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+
+Orleans, Louisiana. Association for Computational Linguistics.
+
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+
+Ran Zmigrod, Sabrina J. Mielke, Hanna Wallach, and Ryan Cotterell. 2019. Counterfactual data augmentation for mitigating gender stereotypes in languages with rich morphology. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 1651-1661, Florence, Italy. Association for Computational Linguistics.
+
+# A Correlation samples and full dataset
+
+Table 4 shows the overall correlation between the performance of the respective model on the full dataset and on the sample over three random seeds. Full represents that we looked at all different bias types in the CrowS-Pairs dataset and (3) refers to the three bias types used in this study (gender, religion, and race). We used a threshold of  $75\%$  to decide on the sample size.
+
+<table><tr><td></td><td>mBERT full</td><td>mBERT (3)</td><td>BERT full</td><td>BERT (3)</td></tr><tr><td>size 20</td><td>85.71</td><td>66.58</td><td>74.40</td><td>70.58</td></tr><tr><td>size 30</td><td>88.54</td><td>66.80</td><td>80.14</td><td>70.66</td></tr><tr><td>size 40</td><td>93.11</td><td>86.02</td><td>83.78</td><td>75.88</td></tr><tr><td>size 50</td><td>94.21</td><td>86.82</td><td>90.52</td><td>87.32</td></tr></table>
+
+Table 4: Correlation between the sample and full respective model's performance over three random seeds before debiasing.
+
+# B Attribute Lists
+
+The different lists of attribute words per language used for CDA, SenDeb, INLP, and DR are listed below. We started from the lists in (Meade et al., 2022; Zhao et al., 2018a; Liang et al., 2020a) and extended these to other languages. For the non-English lists, we first translated the words in the English attribute list if a similar relation is contained in the translated words. Subsequently, we asked a native speaker of the respective language whether there are extra words that contain similar relations which do not exist in English. We added these to the list. However, note that these lists are not exhaustive, as many other words still exist that express the same relationship. Nevertheless, this list already provides a more extensive attribute list than by only translating the English attribute list.
+
+English
+
+Gender: (Zhao et al., 2018a) actor, actress, actors, actresses, airman, airwoman, airmen, airwomen, uncle, aunt, uncles, aunts, boy, girl, boys, girls, groom, bride, grooms, brides, brother, sister, brothers, sisters, businessman, businesswoman, businessmen, businesswomen, chairman, chairwoman, chairmen, chairwomen, dude, chick, dudes, chicks, dad, mom, dads, moms, daddy, mommy, daddies, mommies, son, daughter, sons, daughters, father, mother, fathers, mothers, male, female, males, females, guy, gal, guys, gals, gentleman, lady, gentlemen, ladies, grandson, granddaughter, granddaughters, grandsons, granddaughters, guy, girl, guys, girls, he, she, himself, herself, him, her, his, her, husband, wife, husbands, wives, king, queen, kings, queens, lord, lady, lords, ladies, sir, ma'am, man, woman, men, women, sir miss mr. mrs. ms. policeman, policeman woman, prince princess princes princesses spokeseman spokeswoman spokesmen spokeswomen.
+
+Race: (Meade et al., 2022) black, caucasian, asian, african, caucasian, asian, black, white, asian, africa, america, asia, africa, america, china, africa, europe, asia.
+
+Religion: (Liang et al., 2020a) Jewish, christian, muslim, jews, christians, muslims, torah, bible, quran, synagogue, church, mosque, rabbi, priest, imam, judaism, christianity, islam.
+
+# French
+
+Gender: acteur, actrice, actuurs, actrices, aviateur, aviatrice, aviateurs, aviatrices, oncle, tante, oncle, tantine, tonton, tata, tontons, tatas, oncles, tantes, oncles, tantines, garcon, fille, garcons, filles, marié, mariée, époux, épouse, mariés, mariées, époux, épouses, brother, sister, frère, soeur, frères, soeurs, entrepreneur, entrepriseuse, entrepreneur, entrepriseure, entrepreneurs, entreprisesures, entrepreneurs, entreprisesuses, président, présidente, prêsidents, prêsentes, mec, meuf, gamin, gamine, mecs, meufs, père, mère, pères, mères, papa, maman, papas, mamans, fils, fille, fils, filles, abbe, abbesse, abbés, abbesses, masculin, féminin, malé, femelle, malés, femelles, gars, fille, gars, filles, monsieur, dame, messieurs, dames, petit-fils, petite-fille, petit-fils, petites-filles, il, elle, lui-même, elle-même, lui, elle, mari, femme, maris, femmes, roi, reine, rois, reines, seigneur, seigneuresse, seigneurs, seigneuresses, monsieur, m'dame, monsieur, madame, homme, femme, hommes, femmes, monsieur, mademoiselle, mr, mme, mr, mLle, policier, policière, prince
+
+princesse, princes, princesses, copain, copine, copains, copines, ami, amie, amis, amies, voisin, voisine, docteur, doctoresse, docteur, docteure, boulanger, boulangere, héros, héroîne, employé, employeee, employés, employées, chef, cheffe, chefs, cheffes, cousin, cousine, grand-père, grand-mère, expert, experte, pompier, pompère, pompiers, pompières, agricultrice, agriculteurs, agricultrices, travaillerur, travailluse, infirmier, infirmière, infirmiers, infirmières, patron, patronne, patrons, patronnes.
+
+Race: noir, blanc, asiatique, black, blanc, asiatique, noir, caucasien, asiatique, africain, europeen, asienne, african, americain, asiatique, afrique, amerique, asie, afrique, amerique, chine, afrique, europe, asie.
+
+Religion: juif, chretien, musulman, juifs, chretiens, musulmans, torah, bible, coran, synagogue, église, mosquee, rabbin, prétre, imam, judaïisme, christianisme, islam.
+
+# German
+
+Gender: schauspieler, schauspielerin, koch, kochin, Lehrer, Lehrerin, schüler, schülerin, student, studentin, pilot, pilotin, onkel, tante, jungge, madchen, brautigam, braut, bruder, schwester, geschäftsmann, geschäftsfrau, vorsitzender, vorsitzende, vater, mutter, papa, mama, sohn, tochter, mann, Frau, kerl, madel, herr, dame, enkel, enkelin, großvater, großmutter, cousin, cousine, er, sie, ihm, ihr, sein, ihr, seine, ihre, ehemann, ehefrau, feuerwehrmann, feuerwehrfrau, konig, konigin, fürst, fürstin, herzog, herzogin, mann, Frau, Männer, femmes, hr., fr., polizist, polizistin, prinz, prinzessin, sprecher, sprecherin, kollege, kollegin, mitarbeiter, mitarbeiterin, helfer, helferin, anwalt, anwältin, bauarbeiter, bauarbeiterin, krankenpfleger, krankenpflegerin, chef, chefsin, vorgesetzter, vorgesetzte, sönger, söngerin, kunde, kundin, besucher, besucherin, freund, freundin, arzt, ärtzin, verkäufer, verkäuferin, kanzler, kanzlerin, geschäftsleiter, geschäftsleiterin, pfleger, pflegerin, kellner, kellnerin.
+
+Race: dunkelhautig, hellhautig, asiatisch, afrikaner, europäer, asiate, amerikaner, afrika, amerika, asien, china.
+
+Religion: jiudisch, christlich, muslimisch, Jude, christ, muslim, torah, bibel, koran, synagogue, kirche, moschee, rabbiner, pfarrer, imam, judentum, christentum, islam.
+
+# Dutch
+
+Gender: acteur, actrice, actuers, actrices,
+
+oom, tante, ooms, tantes, nonkel, tante, nonkels, tantes,jongen,meisje,jongens,meisjes,bruidgem, bruid, bruidegommen, bruiden, broer, zus, broers,zussen,zakenman,zakenvrouw,zakenmannen,zakenvrouwen,kerel,griet,kerels,grieten,vader,moeder,vaders,moeders,papa,mama,papa's,mama's,zoon, dochter;zonen,dochters,man,vrouw,mannen,vrouwen,gast,wijf,gasten,wijven,heer,dame,heren,dames,kleinzoon,kleindochter,kleinzonen,kleindochters,vent,vrouw,venten,vrouwen,hij,zij,hemzelf,haarzelf,hem,haar,zijn,haar,mannelijk,vrouwelijk,vriend,vriendin,vrienden,vriendinnen,koning,koningin,koningen,koninginnen,heer,dame,heren,dames,meneer,mevrouw,jongeheer,jongedame,jongeheren,jongedames,jongeheer,juffrouw,jongeheren,juffrouwen,politieagent,politieagente,prins,prinses,prinsen,prinsessen,woordvoerder,wordvoerster,wordvoerders,wordvoersters,brandweerman,brandweervrouw,brandweermannen,brandweervrouwen,timmerman,timmervrouw,timmermannen,timmervrouwen,meester,juf,meesters,juffen,verpleger,verpleegster,verplegers,verpleegsters,bestuurder,bestuurster,bestuurders,bestuursters,kuisman,kuisvrouw,kuismannen,kuisvrouwen,kok,kokkin,kokken,kokkinen,leraar,lerares,directeur,directrice,directeurs,directrices,secretaris,secretaresse,secretaris-SEN,secretaressen,boer,boerin,boeren,boerinnen,held,heldin,gastheer,gastvrouw,gastheren,gastvrouwen,opa,oma,opa's,oma's,grootvader,grootmoeder,grootvaders,grootmoeders.
+
+Race: afrikaans, amerikaans, aziatisch, afrikaans, europees, aziatisch, zwart, blank, aziatisch, afrika, amerika, aziè, afrika, amerika, china, afrika, europa, aziè.
+
+Religion: joods, christen, moslim, joden, christenen, moslims, thorabijbel, koran, synagogue, kerk, moskee, rabbijn, priester, imam, jodendom, christendom, islam.
+
+# C Averaged results
+
+Tables 5, 6, and 7 show the different averaged results are the debiasing languages other than English, namely French, German, and Dutch.
+
+# D Breakdown results
+
+In this section, a breakdown of the different scores per category is shown in terms of the bias metric established in (Nangia et al., 2020) in Tables 8, 9, 10, 11. For brevity, we employ the following
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>10.93↑</td><td>6.94↑</td><td>7.50↑</td><td>9.44↑</td><td>9.07↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.91↓</td><td>12.22↑</td><td>11.67↑</td><td>10.00↓</td><td>10.74↓</td></tr><tr><td>DE</td><td>9.33</td><td>11.11↑</td><td>6.29↓</td><td>6.55↓</td><td>9.45↑</td><td>6.09↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.96↓</td><td>14.86↓</td><td>16.26↓</td><td>15.05↓</td><td>12.94↓</td></tr></table>
+
+Table 5: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>9.44↑</td><td>6.94↑</td><td>7.22↑</td><td>10.19↑</td><td>8.43↑</td></tr><tr><td>FR</td><td>11.11</td><td>9.17↓</td><td>7.5↓</td><td>10.28↓</td><td>8.43↓</td><td>7.13↓</td></tr><tr><td>DE</td><td>9.33</td><td>10.20↑</td><td>4.89↓</td><td>6.27↓</td><td>6.38↓</td><td>6.01↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.31↓</td><td>14.59↓</td><td>16.25↓</td><td>17.10↓</td><td>16.65↓</td></tr></table>
+
+Table 6: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>6.11</td><td>8.80↑</td><td>6.94↑</td><td>7.22↑</td><td>7.69↑</td><td>7.50↑</td></tr><tr><td>FR</td><td>11.11</td><td>11.30↑</td><td>10.28↓</td><td>10.56↓</td><td>9.07↓</td><td>9.17↓</td></tr><tr><td>DE</td><td>9.33</td><td>8.71↓</td><td>6.83↓</td><td>7.39↓</td><td>6.04↓</td><td>5.37↓</td></tr><tr><td>NL</td><td>17.66</td><td>14.68↓</td><td>15.71↓</td><td>16.54↓</td><td>14.69↓</td><td>14.41↓</td></tr></table>
+
+abbreviations: Gender (G), Race (Ra), and Religion (Re).
+
+Table 7: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>51.30</td><td>51.11</td><td>50.28*</td><td>55.28</td><td>50.37</td></tr><tr><td>G</td><td>49.17</td><td>49.17</td><td>49.17</td><td>46.67</td><td>50.83</td><td>51.11</td></tr><tr><td>Ra</td><td>44.17</td><td>41.94</td><td>45.00</td><td>-</td><td>39.72</td><td>39.17</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>59.17</td><td>-</td><td>75.28</td><td>60.83</td></tr><tr><td>FR</td><td>60.56</td><td>57.50</td><td>60.00</td><td>60.28*</td><td>62.59</td><td>58.52</td></tr><tr><td>G</td><td>50.83</td><td>45.56</td><td>50.00</td><td>50.00</td><td>59.72</td><td>60.83</td></tr><tr><td>Ra</td><td>59.17</td><td>56.67</td><td>57.50</td><td>-</td><td>56.39</td><td>50.83</td></tr><tr><td>Re</td><td>71.67</td><td>70.28</td><td>72.50</td><td>-</td><td>71.67</td><td>63.89</td></tr><tr><td>DE</td><td>59.05</td><td>55.93</td><td>54.86</td><td>56.55*</td><td>57.06</td><td>55.50</td></tr><tr><td>G</td><td>60.90</td><td>54.50</td><td>51.71</td><td>53.42</td><td>53.29</td><td>56.70</td></tr><tr><td>Ra</td><td>57.07</td><td>61.35</td><td>57.05</td><td>-</td><td>51.51</td><td>48.42</td></tr><tr><td>Re</td><td>59.17</td><td>51.94</td><td>55.83</td><td>-</td><td>66.39</td><td>61.39</td></tr><tr><td>NL</td><td>67.66</td><td>63.96</td><td>64.59</td><td>65.98*</td><td>66.65</td><td>67.22</td></tr><tr><td>G</td><td>56.32</td><td>54.10</td><td>49.59</td><td>51.28</td><td>56.62</td><td>57.48</td></tr><tr><td>Ra</td><td>65.83</td><td>59.17</td><td>65.00</td><td>-</td><td>66.39</td><td>65.56</td></tr><tr><td>Re</td><td>80.83</td><td>78.61</td><td>79.17</td><td>-</td><td>76.94</td><td>78.61</td></tr></table>
+
+Table 8: Overall performance score per evaluation language, debiasing technique, and category averaged over the three random seeds after debiasing in English.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>55.74</td><td>50.28</td><td>50.28*</td><td>54.26</td><td>51.67</td></tr><tr><td>G</td><td>49.17</td><td>52.78</td><td>47.50</td><td>46.67</td><td>49.72</td><td>53.06</td></tr><tr><td>Ra</td><td>44.17</td><td>45.83</td><td>43.33</td><td>-</td><td>46.11</td><td>38.89</td></tr><tr><td>Re</td><td>60.00</td><td>68.61</td><td>60.00</td><td>-</td><td>66.94</td><td>63.06</td></tr><tr><td>FR</td><td>60.56</td><td>54.54</td><td>60.00</td><td>58.89*</td><td>58.15</td><td>57.59</td></tr><tr><td>G</td><td>50.83</td><td>47.22</td><td>46.67</td><td>45.83</td><td>52.22</td><td>55.28</td></tr><tr><td>Ra</td><td>59.17</td><td>47.22</td><td>60.83</td><td>-</td><td>57.50</td><td>51.67</td></tr><tr><td>Re</td><td>71.67</td><td>69.17</td><td>72.50</td><td>-</td><td>64.72</td><td>65.83</td></tr><tr><td>DE</td><td>59.05</td><td>59.68</td><td>55.43</td><td>55.98*</td><td>55.95</td><td>53.09</td></tr><tr><td>G</td><td>60.90</td><td>52.47</td><td>50.85</td><td>51.71</td><td>55.24</td><td>55.83</td></tr><tr><td>Ra</td><td>57.07</td><td>59.91</td><td>58.78</td><td>-</td><td>52.05</td><td>47.04</td></tr><tr><td>Re</td><td>59.17</td><td>66.67</td><td>56.67</td><td>-</td><td>60.56</td><td>56.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>64.31</td><td>65.71*</td><td>65.05</td><td>62.94</td></tr><tr><td>G</td><td>56.32</td><td>49.59</td><td>49.59</td><td>50.45</td><td>54.32</td><td>55.76</td></tr><tr><td>Ra</td><td>65.83</td><td>62.22</td><td>65.00</td><td>-</td><td>62.50</td><td>58.33</td></tr><tr><td>Re</td><td>80.83</td><td>80.83</td><td>78.33</td><td>-</td><td>78.33</td><td>74.72</td></tr></table>
+
+Table 9: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in French.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.44</td><td>50.28</td><td>50.00*</td><td>52.59</td><td>52.13</td></tr><tr><td>G</td><td>49.17</td><td>46.67</td><td>45.83</td><td>45.83</td><td>45.28</td><td>49.17</td></tr><tr><td>Ra</td><td>44.17</td><td>53.06</td><td>45.00</td><td>-</td><td>44.17</td><td>43.06</td></tr><tr><td>Re</td><td>60.00</td><td>63.61</td><td>60.00</td><td>-</td><td>68.33</td><td>64.17</td></tr><tr><td>FR</td><td>60.56</td><td>56.57</td><td>57.5</td><td>60.28*</td><td>53.80</td><td>53.61</td></tr><tr><td>G</td><td>50.83</td><td>47.48</td><td>50.00</td><td>50.00</td><td>53.89</td><td>55.83</td></tr><tr><td>Ra</td><td>59.17</td><td>60.56</td><td>58.33</td><td>-</td><td>44.44</td><td>45.83</td></tr><tr><td>Re</td><td>71.67</td><td>61.39</td><td>64.17</td><td>-</td><td>63.06</td><td>59.17</td></tr><tr><td>DE</td><td>59.05</td><td>57.64</td><td>53.75</td><td>55.70*</td><td>55.72</td><td>55.35</td></tr><tr><td>G</td><td>60.90</td><td>47.69</td><td>50.00</td><td>50.86</td><td>54.46</td><td>58.41</td></tr><tr><td>Ra</td><td>57.07</td><td>64.38</td><td>57.07</td><td>-</td><td>57.69</td><td>53.47</td></tr><tr><td>Re</td><td>59.17</td><td>60.83</td><td>54.17</td><td>-</td><td>55.00</td><td>54.17</td></tr><tr><td>NL</td><td>67.66</td><td>61.16</td><td>63.48</td><td>65.14*</td><td>67.10</td><td>66.65</td></tr><tr><td>G</td><td>56.32</td><td>49.88</td><td>48.76</td><td>48.76</td><td>56.30</td><td>56.60</td></tr><tr><td>Ra</td><td>65.83</td><td>53.89</td><td>64.17</td><td>-</td><td>69.44</td><td>67.78</td></tr><tr><td>Re</td><td>80.83</td><td>79.72</td><td>77.50</td><td>-</td><td>75.56</td><td>75.56</td></tr></table>
+
+Table 10: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in German.  
+
+<table><tr><td></td><td>mBERT</td><td>INLP</td><td>SenDeb</td><td>DR*</td><td>CDA</td><td>DO</td></tr><tr><td>EN</td><td>51.11</td><td>54.91</td><td>50.83</td><td>50.56*</td><td>47.69</td><td>51.20</td></tr><tr><td>G</td><td>49.17</td><td>51.94</td><td>48.33</td><td>47.50</td><td>45.56</td><td>52.22</td></tr><tr><td>Ra</td><td>44.17</td><td>50.00</td><td>44.17</td><td>-</td><td>40</td><td>40.83</td></tr><tr><td>Re</td><td>60.00</td><td>62.78</td><td>60.00</td><td>-</td><td>57.5</td><td>60.56</td></tr><tr><td>FR</td><td>60.56</td><td>60.37</td><td>60.28</td><td>60.56*</td><td>55.37</td><td>52.50</td></tr><tr><td>G</td><td>50.83</td><td>50.28</td><td>50.83</td><td>50.83</td><td>55.83</td><td>53.89</td></tr><tr><td>Ra</td><td>59.17</td><td>61.94</td><td>61.67</td><td>-</td><td>44.44</td><td>41.11</td></tr><tr><td>Re</td><td>71.67</td><td>68.89</td><td>68.33</td><td>-</td><td>65.83</td><td>62.50</td></tr><tr><td>DE</td><td>59.05</td><td>55.67</td><td>56.55</td><td>56.25*</td><td>48.53</td><td>50.86</td></tr><tr><td>G</td><td>60.90</td><td>47.71</td><td>53.38</td><td>52.52</td><td>53.04</td><td>54.73</td></tr><tr><td>Ra</td><td>57.07</td><td>58.20</td><td>59.59</td><td>-</td><td>45.89</td><td>46.47</td></tr><tr><td>Re</td><td>59.17</td><td>61.11</td><td>56.67</td><td>-</td><td>46.67</td><td>51.39</td></tr><tr><td>NL</td><td>67.66</td><td>64.21</td><td>63.74</td><td>64.57*</td><td>64.51</td><td>63.67</td></tr><tr><td>G</td><td>56.32</td><td>52.92</td><td>47.05</td><td>47.05</td><td>52.97</td><td>53.22</td></tr><tr><td>Ra</td><td>65.83</td><td>59.72</td><td>67.50</td><td>-</td><td>61.67</td><td>57.78</td></tr><tr><td>Re</td><td>80.83</td><td>80.00</td><td>76.67</td><td>-</td><td>78.89</td><td>80.00</td></tr></table>
+
+Table 11: Overall performance score per evaluation language and debiasing technique averaged over the three random seeds after debiasing in Dutch.

2023/Investigating Bias in Multilingual Language Models_ Cross-Lingual Transfer of Debiasing Techniques/images.zip

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2023/Investigating Efficiently Extending Transformers for Long Input Summarization/a422d190-1a1c-47cc-8b2f-d5bf8bb5cbbc_origin.pdf

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2023/Investigating Efficiently Extending Transformers for Long Input Summarization/full.md

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+# Investigating Efficiently Extending Transformers for Long Input Summarization
+
+Jason Phang  $^{1*}$  Yao Zhao $^{2}$  Peter J. Liu $^{2}$
+
+1New York University, 2Google Research, Brain Team
+
+jasonphang@nyu.edu
+
+{yaozhaoyz, peterjliu}@google.com
+
+# Abstract
+
+While large pretrained Transformer models have proven highly capable at tackling natural language tasks, handling long sequence inputs still poses a significant challenge. One such task is long input summarization, where inputs are longer than the maximum input context of most models. Through an extensive set of experiments, we investigate what model architectural changes and pretraining paradigms most efficiently adapt a pretrained Transformer for long input summarization. We find that a staggered, block-local Transformer with global encoder tokens strikes a good balance of performance and efficiency, and that an additional pretraining phase on long sequences meaningfully improves downstream summarization performance. Based on our findings, we introduce PEGASUS-X, an extension of the PE-GASUS model with additional long input pretraining to handle inputs of up to 16K tokens, which achieves strong performance on long input summarization tasks comparable with much larger models.
+
+# 1 Introduction
+
+Large pretrained Transformer models have proven to be extremely capable at tackling natural language tasks (Devlin et al., 2018; Brown et al., 2020). However, handling long textual sequences continues to be a significant challenge for these models. Training models to handle long sequences is expensive in both computation and memory, and moreover requires training and evaluating on long sequence data, which is rarer and more costly to collect. Given the broad success of Transformer models on short-sequence language tasks, our goal is to investigate the best way to extend these models to handle longer input sequences.
+
+In this work, we focus on the task of long input summarization: summarizing long input documents into shorter text sequences. The inputs
+
+![](images/ec0752a7f21f7f1e569544b5ac7b5f5cb5b2fcb751b38c923ddcd025dc1b20d9.jpg)  
+Figure 1: Performance on SCROLLS (Shaham et al., 2022) summarization tasks. All models evaluated on up to 16K input tokens. PEGASUS-X outperforms other models at comparable model sizes. Scores (as of 08/08/22) shown are the average of the geometric mean of ROUGE-1/2/L.
+
+of such tasks are often significantly longer than the maximum input lengths of most standard Transformer models, and hence warrant both architecture modifications as well as new training regimes. For instance, to avoid the quadratic growth in memory consumption of attention in Transformers, many memory-efficient Transformer variants have been proposed (Tay et al., 2020, 2021). However, the manner in which these changes are incorporated into models has been inconsistent and ad-hoc, and there are few established best practices. For instance, some works directly fine-tune on long-input summarization tasks (Zaheer et al., 2020; Pang et al., 2022), while others first perform additional pretraining (Beltagy et al., 2020). Because of the high cost of training these models, there has yet to be a systematic study of how best to adapt models for long input sequences. Hence, it has been difficult to establish which model and training changes are necessary or complementary.
+
+To answer these questions, we conduct an extensive empirical investigation into the architectural changes, model configurations and pretraining
+
+schemes to identify better approaches to training Transformer models for long input summarization. We evaluate a set of efficient Transformer variants, and propose a simple block-wise local Transformer architecture with staggered blocks and global tokens that strikes a good balance of performance and memory efficiency. We show that given a fixed token budget, pretraining on short sequences and then pre-adapting the model to an efficient Transformer architecture by training on longer sequences leads to better performance than only long input pretraining or no adaptation at all. We also investigate model design choices such as position encoding schemes, encoder-decoder layer distributions, and the impact of discrepancies between pretraining and fine-tuning architecture hyperparameters.
+
+Based on the findings from our empirical investigation, we adapt the pretrained PEGASUSLarge model (Zhang et al., 2020) to tackle long input summarization on up to 16K input tokens. The resulting model, which we call PEGASUS-X, attains top scores on long summarization tasks, outperforming much larger models like LongT5 (Guo et al., 2021). Moreover, impact on short input summarization performance is minimal. A smaller version which we call PEGASUS-XBase attains similar scores with much fewer parameters. Beyond summarization, we believe that many of our findings will be useful to the community for efficiently adapting Transformer models to handle ever longer input sequences for other tasks.
+
+In summary, our contributions are:
+
+1. We evaluate a series of proposed efficient Transformer architectures as well as other model modifications, and report their efficacy and computational trade-offs when applied to long input summarization tasks.  
+2. Based on our findings, we propose a recipe for adapting a short-context, pretrained Transformer encoder-decoder to longer inputs, and apply it to PEGASUS to greatly improve its long-document summarization performance, with comparable short-input performance.
+
+# 2 Experimental Setup
+
+Similar to Zhang et al. (2020), we perform the majority of our experiments with a PEGASUS<sub>Base-sized</sub> model, before applying our findings to PEGASUS<sub>Large-sized</sub> model.
+
+# 2.1 Pretraining
+
+We generally follow the recipe from PEGASUS (Zhang et al., 2020) for pretraining PEGASUS<sup>Base-sized</sup> models. All experiments in our ablation study performed pretraining with C4 (Raffel et al., 2020) for 500k steps with 512 input tokens and 256 output tokens and a masking ratio of  $45\%$ , unless otherwise stated. For long input pretraining we extend the input length to 4096 tokens, and adjust the masking ratio from  $45\%$  to  $5.625\%$ , reducing the ratio by a factor of 8 to account for the 8x increase in input sequence length. We also filter for only documents longer than 10000 characters.
+
+# 2.2 Fine-tuning
+
+We evaluate models by fine-tuning on the arXiv (Cohan et al., 2018) and GovReport (Huang et al., 2021) long input summarization tasks. Where relevant, we also fine-tune on the shorter-context XSUM and CNN/DailyMail tasks. For each experiment, we report the best validation set scores based on the geometric average (RG) of ROUGE-1, ROUGE-2 and ROUGE-L scores (Lin, 2004) based on the rouge-score package. Fine-tuning hyperparameters can be found in Appendix E. Unless otherwise stated, we directly switch to the efficient Transformer architectures between pretraining (on shorter context) and fine-tuning (on longer contexts), with no adaptation phase in between.
+
+# 3 Ablation Experiments
+
+# 3.1 Encoder architectures
+
+We first investigate whether using an efficient Transformer encoder allows models to incorporate longer input sequences while consuming reasonable amounts of device memory. We consider two encoder architectures that exemplify different approaches to efficient attention. Big Bird (Zaheer et al., 2020) uses sparse attention computation, combining sliding-window and random attention, and a set of global-attention tokens. Conversely, Performer (Choromanski et al., 2021) factorizes attention matrices via orthogonal random features. Both model also performed well on the LRA tasks (Tay et al., 2021). For this experiment, we perform both pretraining and fine-tuning with the same encoder architecture to avoid the issue of mismatch between pretraining and fine-tuning architectures.
+
+<table><tr><td rowspan="2">Encoder</td><td colspan="2">XSUM</td><td colspan="2">CNN/DM</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td><td rowspan="2">Steps/s</td><td rowspan="2">Mem</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td>Transformer</td><td>40.0 / 16.9 / 32.0</td><td>27.9</td><td>39.5 / 19.0 / 28.6</td><td>27.8</td><td>- / - / -</td><td>-</td><td>- / - / -</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BigBird</td><td>39.6 / 16.7 / 31.7</td><td>27.6</td><td>39.3 / 18.2 / 28.1</td><td>27.2</td><td>46.8 / 19.6 / 28.0</td><td>29.5</td><td>60.5 / 28.5 / 30.1</td><td>37.3</td><td>0.31</td><td>1.88</td></tr><tr><td>Performer</td><td>36.5 / 14.0 / 28.7</td><td>24.5</td><td>37.4 / 17.4 / 26.9</td><td>26.0</td><td>39.0 / 13.2 / 23.8</td><td>23.1</td><td>55.8 / 20.2 / 24.7</td><td>30.3</td><td>0.96</td><td>1.12</td></tr><tr><td>Local</td><td>38.5 / 15.7 / 30.6</td><td>26.4</td><td>39.0 / 18.4 / 28.1</td><td>27.2</td><td>46.5 / 19.7 / 27.9</td><td>29.5</td><td>60.2 / 28.3 / 30.0</td><td>37.1</td><td>1.00</td><td>1.00</td></tr><tr><td>Global-Local</td><td>38.7 / 16.2 / 31.2</td><td>26.9</td><td>39.0 / 18.6 / 28.2</td><td>27.3</td><td>47.6 / 20.2 / 28.5</td><td>30.1</td><td>61.4 / 29.3 / 30.6</td><td>38.0</td><td>0.87</td><td>1.08</td></tr></table>
+
+Table 1: Comparison of different encoder architectures on short (XSUM, CNN/DM) and long (arXiv, GovReport) summarization tasks. Training steps per second and memory are computed based on arXiv, and normalized to Local Transformer performance.  
+
+<table><tr><td rowspan="2">Encoder</td><td rowspan="2">Stagger Local Blocks</td><td rowspan="2">Use Global In Decoder</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td>Global-Local</td><td>✓</td><td>✓</td><td>48.1/20.3/28.5</td><td>30.3</td><td>60.5/28.8/30.5</td><td>37.6</td></tr><tr><td>Global-Local</td><td></td><td>✓</td><td>47.0/19.5/27.9</td><td>29.5</td><td>60.9/28.9/30.2</td><td>37.6</td></tr><tr><td>Global-Local</td><td>✓</td><td></td><td>47.7/20.4/28.6</td><td>30.3</td><td>61.3/29.4/30.8</td><td>38.1</td></tr><tr><td>Global-Local</td><td></td><td></td><td>46.7/19.5/27.9</td><td>29.4</td><td>59.5/27.8/29.4</td><td>36.5</td></tr><tr><td>Local</td><td>✓</td><td>-</td><td>46.8/19.7/28.0</td><td>29.6</td><td>59.2/27.9/30.0</td><td>36.7</td></tr><tr><td>Local</td><td></td><td>-</td><td>46.5/19.2/27.5</td><td>29.1</td><td>58.8/27.5/28.9</td><td>36.0</td></tr></table>
+
+Table 2: Comparison of architectural tweaks to Local and GlobalLocal encoder. Staggering local blocks uses different blocks boundaries for different layers in block-local attention. Global information is incorporated in the decoder via an additional cross-attention before cross-attention over the encoded input.
+
+In addition, we also introduce two simple variants of local attention Transformer encoders. First, we use a simple block-local Transformer (Local), where encoder input tokens are divided into non-overlapping blocks, and tokens can only attend to other tokens within the block. Second, we extend the local Transformer by adding a set of global tokens with learned embeddings, that can attend to and be attended from every encoder token (Global-Local). These components are similar to the sliding window attention and global token attention of Big Bird, ETC (Ainslie et al., 2020) and Longformer (Beltagy et al., 2020). However, we opt for the simpler block-local attention rather than sliding window attention, and compensate for the lack of overlapping blocks by staggering the local attention blocks, which we elaborate on in Section 3.2. As we show below, the performance is highly competitive despite its simplicity.
+
+Results on short and long summarization tasks are shown in Table 1, with the relative training steps per second and memory consumed per device for fine-tuning on arXiv shown in the right-most columns. Among the short tasks, the full-attention Transformer performs best, followed by BigBird. On the long tasks, Big Bird and Global-Local models perform best, but Big Bird consumes significantly more memory and trains much more slowly than the other architectures. Conversely, although
+
+Performer has relatively low memory consumption and trains efficiently, it performs worst among the architectures tested by a noticeable margin.
+
+On the other hand, Local and Global-Local encoders strike a good balance of performance and efficiency. The simple local attention encoder, which uses block-local attention, attains performance close to that of Big Bird while being much faster and using much less memory. Global-Local trades off a small amount of speed and memory for better performance, outperforming Big Bird.
+
+Takeaways: Local attention is a strong baseline, and adding global tokens significantly improves performance. Both models are resource-efficient.
+
+# 3.2 Local and Global-Local configurations
+
+Given the good performance of both Local and Global-Local encoder variants, we next consider further architectural tweaks to these models.
+
+First, we introduce staggering of local attention blocks. In block-local attention, tokens can only attend to other tokens within the same block. If the input tokens are divided up into the same blocks in every layer, this means that no information is exchanged across blocks through the entire encoder. To address this pitfall, we stagger attention blocks by shifting the block boundaries by half a block every other layer. We show an example of this in Figure 2. In practice, we implement this by padding
+
+![](images/1c565547e5ca2b39d429adbc629d2ed634186a723560666a353a919e2f5f3df1.jpg)  
+(a) Block-local attention
+
+![](images/7876522647f580a4dcbb9a9b0afa300c07d6d30c04ee80ad0d3e320d7691669c.jpg)  
+(b) Block-local attention with staggered blocks  
+Figure 2: In block-local attention (a), the same block boundaries are used across all layers, preventing information from being shared across blocks. Staggering the block boundaries (b) be shifting the boundaries every other layer allows for cross-block interactions with minimal additional computational cost or complexity.
+
+the hidden representations on either side by half a block and masking accordingly.
+
+Secondly, in the Global-Local model, the decoder only attends to the encoded token representations, and not the global token representations. We consider a variant where we supply the global token representations to the decoder and introduce a second cross-attention layer that attends only to the global tokens. Our goal is to allow the decoder to incorporate global information before performing cross-attention over the encoded sequence.
+
+Results are shown in Table 2. We find that staggering local blocks noticeably improves performance in both Local and Global-Local models. Performance improves even with Global-Local models, which already allow for cross-block interactions via global tokens, indicating that both model improvements are complementary. Conversely, incorporating global token information in the decoder did not lead to much performance improvement, particularly once staggered local blocks were used.
+
+Takeaways: Staggering local attention blocks significantly improves performance, and is complementary to global tokens.
+
+# 3.3 Global-Local: Block Size and Number of Global Tokens
+
+Next, we vary the block size and number of global tokens for the Global-Local encoder, with results shown in Table 3.2 Broadly, we find that increasing either block size or global tokens leads to improved performance, with a corresponding increase in memory consumption and computation time. However, the effect size from going to larger block sizes is not large, and saturates with larger block sizes or number of global tokens. As such, increasing either of these hyperparameters is ideal if
+
+resources allow, but is not a high priority compared to other model improvements. For the remainder of the ablation experiments, we use a block size of 64 and 32 global tokens for consistency.
+
+Takeaways: Larger block sizes and/or number of global tokens leads to improved performance, although the effect saturates.
+
+# 3.4 Other Architecture Modifications
+
+We further investigate a series of architectural modifications to the encoder-decoder model, including the position encoding scheme (Table 8), scaling the encoder and decoder layers (Table 10) and using cross-attention in only a fraction of the decoder layers (Table 12). We find that the sinusoidal position encoding provides a good balance of performance and efficiency, and that a balanced encoder-decoder with full cross-attention generally performs the best. More details are provided in Appendix B.
+
+# 3.5 Pretraining vs Fine-tuning Architectures
+
+Previous works using efficient Transformer encoders have generally taken the parameters of a full-attention Transformer pretrained on a shorter sequences and adapted them to efficient architectures, either directly during fine-tuning (Zaheer et al., 2020) or with an intermediate stage of additional pretraining (Beltagy et al., 2020). In this section, we investigate if such an approach is optimal, or if models benefit from being pretrained with efficient encoders from the beginning. Note that we still perform pretraining on a short sequences (512 tokens), even with an efficient encoder.
+
+We consider both pretraining with a Transformer and pretraining with the efficient architecture for both Local and Global-Local models. We also vary the block size, as the main difference between a Transformer and Local Transformer is the block size (aside from staggering, a Local model with block size 512 is equivalent to a dense
+
+<table><tr><td rowspan="2">Block Size</td><td rowspan="2">Global Tokens</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td><td rowspan="2">Steps/s</td><td rowspan="2">Mem</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td rowspan="3">16</td><td>32</td><td>47.1/20.0/28.3</td><td>29.9</td><td>59.7/27.8/29.2</td><td>36.5</td><td>0.92</td><td>1.15</td></tr><tr><td>64</td><td>46.8/19.7/28.0</td><td>29.6</td><td>60.8/28.6/30.0</td><td>37.4</td><td>0.75</td><td>1.54</td></tr><tr><td>128</td><td>47.7/20.0/28.2</td><td>30.0</td><td>60.7/28.8/30.2</td><td>37.5</td><td>0.58</td><td>1.70</td></tr><tr><td rowspan="3">64</td><td>32</td><td>47.7/20.3/28.5</td><td>30.2</td><td>61.0/29.3/30.8</td><td>38.0</td><td>0.47</td><td>1.07</td></tr><tr><td>64</td><td>47.4/20.2/28.5</td><td>30.1</td><td>60.9/29.1/30.7</td><td>37.9</td><td>0.94</td><td>1.10</td></tr><tr><td>128</td><td>47.8/20.4/28.6</td><td>30.3</td><td>60.9/29.0/30.3</td><td>37.7</td><td>0.85</td><td>1.26</td></tr><tr><td rowspan="3">128</td><td>32</td><td>46.9/19.7/28.0</td><td>29.6</td><td>60.9/28.7/30.1</td><td>37.5</td><td>1.00</td><td>1.00</td></tr><tr><td>64</td><td>47.4/20.2/28.4</td><td>30.1</td><td>60.9/28.9/30.8</td><td>37.8</td><td>0.96</td><td>1.05</td></tr><tr><td>128</td><td>47.1/20.0/28.3</td><td>29.9</td><td>61.0/28.9/30.6</td><td>37.8</td><td>0.90</td><td>1.15</td></tr><tr><td rowspan="3">256</td><td>32</td><td>47.3/20.2/28.3</td><td>30.0</td><td>61.6/29.4/30.7</td><td>38.2</td><td>0.92</td><td>1.11</td></tr><tr><td>64</td><td>47.2/20.2/28.4</td><td>30.0</td><td>59.2/28.6/30.5</td><td>37.2</td><td>0.88</td><td>1.16</td></tr><tr><td>128</td><td>48.1/20.5/28.6</td><td>30.4</td><td>61.7/29.3/30.8</td><td>38.2</td><td>0.83</td><td>1.26</td></tr></table>
+
+Table 3: Varying the block size and number of global tokens in Global-Local encoders. Training steps per second and memory are computed based on arXiv, and normalized to the run with Block Size=128 and Global Tokens=32.
+
+Transformer), and hence the difference in block size also corresponds to the extent to which the model needs to adapt between architectures. When adapting from a pretrained Transformer encoder to a Global-Local architecture, because the Global-Local model relies on newly introduced global token embeddings, we initialize them by randomly sampling tokens from the vocabulary embeddings.
+
+Results are shown in Table 11. For Local models, pretraining with local attention using small block sizes tends to hurt performance, but at moderate block sizes (e.g. 64) there is little difference between the two approaches. In contrast, for Global-Local pretraining with the efficient architecture tends to perform better. We hypothesize that this difference arises because of the learned global embedding tokens, which are randomly initialized when adapting from a pretrained Transformer and hence may benefit from pretraining and being jointly trained with the local attention.
+
+Takeaways: For moderate block sizes, either pretraining or adapting to a Local encoder performs about equally well, but pretraining with a Global-Local encoder performs slightly better.
+
+# 3.6 Pretraining Schemes
+
+Up to this point, we have only considered pretraining with short sequences. We might expect that pretraining with longer sequences ought to improve performance on downstream long input summarization. However, pretraining only on long sequences is computationally expensive and requires a large collection of long input documents, which are relatively rarer. Long documents may also contain
+
+different information from short documents, hence limiting training to only long inputs may reduce the diversity of training data. Different long context Transformers have taken different approaches to pretraining on long inputs. For instance, Longformer (Beltagy et al., 2020) performed several additional stages of increasingly longer-sequence pretraining to adapt the initial RoBERTa to long sequence inputs. On the other hand, LongT5 (Guo et al., 2021) is pretrained exclusively with long input sequences. Others (Zaheer et al., 2020; Ivgi et al., 2022) perform no long input pretraining at all. In this section, we investigate how the balance of short and long pretraining impact downstream performance, and try to find the best trade-off between pretraining cost and downstream performance.
+
+We consider two setups for pretraining: short-input pretraining, with 512 input tokens and 256 output tokens, and long-input pretraining, with 4096 input tokens and 256 output tokens. We describe the corresponding differences in data preprocessing in Section 2.1. We fix the number of input tokens seen during training, and vary configurations subject to this constraint. This constraint roughly proxies for the amount of compute consumed and corresponds to the number of input tokens seen during pretraining.
+
+We set our total input token budget at 131 billion tokens, which corresponds to 1 million steps with 512 input tokens, compared to the  $500\mathrm{k}$  steps in the above experiments. This larger budget ensures that when we only do long-input pretraining, the model
+
+<table><tr><td rowspan="2">Pretraining Scheme</td><td rowspan="2">Encoder</td><td colspan="2">XSUM</td><td colspan="2">CNN/DM</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td rowspan="2">Short (50%)</td><td>Local</td><td>38.4/15.8/30.6</td><td>26.5</td><td>39.2/18.1/27.9</td><td>27.1</td><td>46.8/19.7/28.0</td><td>29.6</td><td>60.1/28.3/29.8</td><td>37.0</td></tr><tr><td>Global-Local</td><td>39.4/16.5/31.5</td><td>27.4</td><td>39.1/18.6/28.3</td><td>27.4</td><td>47.7/20.4/28.6</td><td>30.3</td><td>61.9/29.6/30.8</td><td>38.4</td></tr><tr><td rowspan="2">Short (100%)</td><td>Local</td><td>39.2/16.3/31.3</td><td>27.1</td><td>39.2/18.6/28.3</td><td>27.4</td><td>46.9/19.7/28.0</td><td>29.6</td><td>60.1/28.3/29.8</td><td>37.0</td></tr><tr><td>Global-Local</td><td>39.9/17.0/31.9</td><td>27.9</td><td>39.8/18.6/28.3</td><td>27.6</td><td>48.1/20.5/28.7</td><td>30.5</td><td>61.9/29.6/30.8</td><td>38.4</td></tr><tr><td rowspan="2">Short (75%)→Long (25%)</td><td>Local</td><td>38.8/15.9/30.7</td><td>26.7</td><td>39.1/18.2/28.0</td><td>27.1</td><td>47.5/20.1/28.2</td><td>30.0</td><td>60.6/28.9/30.6</td><td>37.7</td></tr><tr><td>Global-Local</td><td>39.6/16.8/31.7</td><td>27.6</td><td>39.8/18.8/28.5</td><td>27.7</td><td>48.4/20.7/28.8</td><td>30.7</td><td>61.8/29.8/31.1</td><td>38.5</td></tr><tr><td rowspan="2">Short (50%)→Long (50%)</td><td>Local</td><td>38.4/15.7/30.5</td><td>26.4</td><td>39.4/18.1/27.9</td><td>27.1</td><td>47.7/20.2/28.3</td><td>30.1</td><td>60.9/29.1/30.7</td><td>37.9</td></tr><tr><td>Global-Local</td><td>39.3/16.4/31.4</td><td>27.3</td><td>39.4/18.3/28.1</td><td>27.3</td><td>48.4/20.9/29.1</td><td>30.9</td><td>61.7/30.0/31.2</td><td>38.7</td></tr><tr><td rowspan="2">Long (100%)</td><td>Local</td><td>36.0/14.0/28.6</td><td>24.3</td><td>38.4/17.7/27.4</td><td>26.5</td><td>46.7/19.5/27.7</td><td>29.3</td><td>59.8/28.0/29.5</td><td>36.7</td></tr><tr><td>Global-Local</td><td>36.4/14.3/28.9</td><td>24.7</td><td>38.5/17.8/27.5</td><td>26.6</td><td>47.3/19.9/28.1</td><td>29.8</td><td>61.1/29.1/30.7</td><td>37.9</td></tr></table>
+
+Table 4: Comparison of different pretraining formats, given a input token budget of 131B tokens, which corresponds to 1M steps with 512 input tokens. Short pretraining uses 512 input tokens, whereas long pretraining uses 4096 input tokens.
+
+is still pretrained for a reasonable number of steps. We consider four pretraining configurations:
+
+- Short-input for  $100\%$  of tokens (1M steps)  
+- Short-input for  $75\%$  of tokens (98.3B, 750k steps), then long-input for  $25\%$  of tokens (32.8B, 31.25k steps)  
+- Short-input for  $50\%$  of tokens (62.5B, 500k steps), then long-input for  $50\%$  of tokens (62.5B, 62.5k steps)  
+- Long-input for  $100\%$  of tokens (125k steps)
+
+We compare the performance of the different pretraining schemes in Table 4. We also include short-input pretraining for  $500\mathrm{k}$  steps for comparison. First, comparing short-input pretraining for  $500\mathrm{k}$  and 1M steps, we find that more pretraining still improves performance, indicating that our base models may still be undertrained at  $500\mathrm{k}$  steps. Second, long-input pretraining performs consistently worse than the other variants, which we attribute having fewer training steps, again highlighting the issue of potential undertraining. For the middle three configurations, on the long tasks, all three non-long-only variants attain similar scores, with more long-input pretraining having slightly better performance, particularly on the ROUGE-2 and ROUGE-L scores. While the small absolute differences in scores make it hard to draw strong conclusions, we lean towards the conclusion that adding a short phase of long input pretraining can improve performance on long input summarization tasks.
+
+Takeaways: Given a fixed compute budget, allocating some training steps to long-input training can improve performance, although the optimal allocation is difficult to determine. Exclusively long pretraining results in worse performance.
+
+# 4 PEGASUS-X
+
+Based on our findings, we settle on the following recipe for adapting PEGASUS models (Zhang et al., 2020) to long sequence summarization.
+
+- We use a Global-Local architecture with block staggering, a large number of global tokens, and large block sizes during pretraining.  
+- We perform additional long input pretraining on 4096 token inputs for  $300\mathrm{k}$  steps.  
+- We extend input sequences up to 16384 input tokens in fine-tuning, depending on the task.
+
+We experiment with two model sizes: PEGASUS-X (PEGASUS eXtended) based on PEGASUSLarge, and PEGASUS-  $\mathbf{X}_{\mathrm{Base}}$  based on a newly trained PEGASUSBase model which we call PEGASUSBase+.
+
+We initialize the weights of PEGASUS-X and PEGASUS-  $\mathrm{X_{Base}}$  with the pretrained weights of PEGASUSLarge and PEGASUS  $\mathrm{Bases + }$  respectively. Only two new sets of parameters are introduced: global token embeddings, and a new LayerNorm for the global input representations in each Transformer layer. This is  $\sim 1\mathrm{M}$  more parameters for PEGASUS-  $\mathbf{X}_{\mathrm{Base}}$  and 2M more for PEGASUS-X. We initialize the global token embeddings by randomly sampling tokens from the input embeddings, and we initialize the LayerNorm weights with the regular input LayerNorm weights.
+
+The task- and model-specific hyperparameters for fine-tuning can be found in Appendix 15. For this section, we report ROUGE-Lsum $^{5}$  rather than ROUGE-L for consistency with the metrics reported in other papers and leaderboards.
+
+<table><tr><td></td><td>PEGASUS-XBase</td><td>PEGASUS-X</td></tr><tr><td># Parameters</td><td>272M</td><td>568M</td></tr><tr><td># Global Tokens</td><td>128</td><td>128</td></tr><tr><td>Block Size</td><td>512</td><td>512</td></tr><tr><td>Batch Size</td><td>512</td><td>1024</td></tr><tr><td>Additional 
+Pretraining</td><td>300K steps</td><td>300K steps</td></tr></table>
+
+Table 5: Hyperparameters of PEGASUS-X Models
+
+# 4.1 Results on Summarization Tasks
+
+Long summarization tasks In Table 6, we compare the performance of PEGASUS models to those of PEGASUS-X on three long-input summarization tasks: arXiv, Big Patent and PubMed. In all three tasks, we see significant improvements in performance of PEGASUS- $\mathrm{X_{Base}}$  over PEGASUS $_{\text{Base+}}$ , and PEGASUS-X over PEGASUS $_{\text{Large}}$ . To isolate the impact of additional long input pretraining compared to only switching the architecture during fine-tuning, we also include evaluation on the PEGASUS models using the Global-Local architecture with no further pretraining, which we list in the table as PEGASUS $_{\text{Base+}}$  + Global-Local.
+
+We also compare to reported results of Big Bird-PEGASUS $^{6}$  (Zaheer et al., 2020), LED (Beltagy et al., 2020), Top-Down Transformer (Pang et al., 2022) with both Average-Pool (AvgP) and Adaptive-Pool (AdaP) variants, BART-LS (Xiong et al., 2022a), LongT5-Large and XL, and SLED (Ivgi et al., 2022). LED, Top-Down and SLED are initialized with  $\mathrm{BART}_{\mathrm{Large}}$  weights with no additional pretraining on long input sequences. BART-LS is concurrent work that also incorporates staggered block-local attention and addition long-sequence pretraining, in addition to pooling layers and different pretraining data.
+
+PEGASUS-X outperforms Big Bird-PEGASUS on all tasks, and Top-Down-AvgP on both compared tasks. Although Top-Down-AdaP outperforms PEGASUS-X, it uses a much more complex fine-tuning setup, using an importance tagger on reference summaries to construct token pooling weights, whereas PEGASUS-X only uses standard fine-tuning. Even so, PEGASUS-X still outperforms Top-Down-AdaP on PubMed. PEGASUS-X outperforms BART-LS on PubMed and slightly underperforms on arXiv; as mentioned above,
+
+PEGASUS-X and BART-LS share many similarities, and we see the strong performance of BART-LS as confirmation of the efficacy of parts of our recipe for longer sequence models. PEGASUS-X also outperforms LongT5 on both arXiv and PubMed, despite both compared LongT5 models having more parameters. However, we find that LongT5 performs much better on BigPatent, which is a largely extractive summarization task. We hypothesize that a larger hidden size may improve extraction over very long sequences.
+
+Short summarization tasks We show in Table 14 the performance of PEGASUS and PEGASUS-X models on shorter summarization tasks, where there is a slight regression in performance of both PEGASUS-X models compared to their PEGASUS equivalents. We hypothesize that long input pretraining might negatively impact the performance on shorter input tasks because of the data filtering for long documents, resulting in a potentially less diverse training data distribution.
+
+# 4.2 SCROLLS Summarization Tasks
+
+We report the performance of the PEGASUS-X models on the summarization tasks in the recently introduced SCROLLS benchmark in Table 7. This includes GovReport (Huang et al., 2021), the ForeverDreaming subset of SummScreen (Chen et al., 2022), and QMSum (Zhong et al., 2021).
+
+PEGASUS-X outperforms all other models on GovReport, setting the state of the art on the dataset. It also performs comparably to both LongT5Large and Top-Down-AvgP on SummScreen/FD, although it underperforms LongT5 models and BART-LS on QMSum. Moreover, PEGASUS-XBase also performs competitively, outperforming both LongT5 models on GovReport, and only a small margin behind PEGASUS-X on all three tasks. PEGASUS-XBase also outperforms BARTLarge-SLED, a larger model with a similar 16K input length.
+
+# 5 Pertinent Related Work
+
+Many works such as Zaheer et al. (2020), Beltagy et al. (2020), Ivgi et al. (2022) have investigated extending short input models to longer sequences using efficient attention mechanisms. In closely comparable work, Guo et al. (2021) pretrained a T5 model on long sequences from scratch, incor
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">#Params</td><td colspan="2">arXiv</td><td colspan="2">Big Patent</td><td colspan="2">PubMed</td></tr><tr><td>R1 / R2 / RLs</td><td>RG</td><td>R1 / R2 / RLs</td><td>RG</td><td>R1 / R2 / RLs</td><td>RG</td></tr><tr><td>PEGASUSBase</td><td>271M</td><td>34.8 / 10.2 / 22.5*</td><td>20.0*</td><td>43.5 / 20.4 / 31.8*</td><td>30.5*</td><td>40.0 / 15.2 / 25.2*</td><td>24.8*</td></tr><tr><td>PEGASUSBase+</td><td>271M</td><td>42.2 / 15.8 / 37.3</td><td>29.2</td><td>51.2 / 32.6 / 41.0</td><td>40.9</td><td>44.1 / 18.3 / 40.1</td><td>31.9</td></tr><tr><td>PEGASUSBase+ + Global-Local</td><td>272M</td><td>47.6 / 20.2 / 42.4</td><td>34.4</td><td>58.1 / 39.5 / 47.2</td><td>47.7</td><td>47.3 / 21.4 / 43.0</td><td>35.2</td></tr><tr><td>PEGASUS-XBase</td><td>272M</td><td>49.4 / 21.6 / 44.0</td><td>36.1</td><td>61.3 / 42.6 / 50.1</td><td>50.8</td><td>49.6 / 23.6 / 45.2</td><td>37.5</td></tr><tr><td>PEGASUSLarge</td><td>567M</td><td>44.7 / 17.2 / 25.7*</td><td>27.0*</td><td>53.4 / 32.9 / 42.1*</td><td>42.0*</td><td>45.1 / 19.6 / 27.4*</td><td>28.9*</td></tr><tr><td>PEGASUS-X</td><td>568M</td><td>50.0 / 21.8 / 44.6</td><td>36.5</td><td>64.8 / 47.5 / 54.3</td><td>55.1</td><td>51.0 / 24.7 / 46.6</td><td>38.9</td></tr><tr><td>BART-LS</td><td>460M</td><td>50.2 / 22.1 / 45.4</td><td>36.9</td><td>-- / -- / --</td><td>--</td><td>50.3 / 24.3 / 46.3</td><td>38.4</td></tr><tr><td>Longformer Encoder-Decoder</td><td>464M</td><td>46.6 / 19.6 / 41.8</td><td>33.7</td><td>-- / -- / --</td><td>--</td><td>-- / -- / --</td><td>--</td></tr><tr><td>Top-Down (AvgP)</td><td>464M</td><td>48.7 / 20.7 / 43.9</td><td>35.4</td><td>-- / -- / --</td><td>--</td><td>48.3 / 21.4 / 44.2</td><td>35.7</td></tr><tr><td>Top-Down (AdaP)</td><td>464M</td><td>51.0 / 21.9 / 45.6</td><td>37.1</td><td>-- / -- / --</td><td>--</td><td>51.1 / 23.3 / 46.5</td><td>38.1</td></tr><tr><td>Big Bird-Pegasus</td><td>567M</td><td>46.6 / 19.0 / 41.8</td><td>33.3</td><td>60.6 / 42.5 / 50.1</td><td>50.5</td><td>46.3 / 20.7 / 42.3</td><td>34.4</td></tr><tr><td>LongT5Large</td><td>770M</td><td>48.3 / 21.6 / 44.1</td><td>35.8</td><td>70.4 / 56.8 / 62.7</td><td>63.1</td><td>50.0 / 24.7 / 46.5</td><td>38.6</td></tr><tr><td>LongT5XL</td><td>3B</td><td>48.4 / 21.9 / 44.3</td><td>36.1</td><td>76.9 / 66.1 / 70.8</td><td>71.1</td><td>50.2 / 24.8 / 46.7</td><td>38.7</td></tr></table>
+
+Table 6: Comparison on long summarization tasks (Test sets). Results for other models are taken from their respective papers. *: PEGASUS (Zhang et al., 2020) only reports ROUGE-L and not ROUGE-LSum.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">#Params</td><td colspan="3">GovReport</td><td colspan="3">SummScreen/FD</td><td colspan="3">QMSum</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td></td></tr><tr><td>PEGASUS-XBase</td><td>272M</td><td>59.3 / 29.3 / 30.9</td><td>37.7</td><td>35.0 / 8.9 / 20.4</td><td>18.5</td><td>32.9 / 9.8 / 21.4</td><td>19.0</td><td></td><td></td><td></td></tr><tr><td>PEGASUS-X</td><td>568M</td><td>60.3 / 30.0 / 31.5</td><td>38.5</td><td>35.7 / 9.1 / 20.6</td><td>18.8</td><td>33.2 / 9.6 / 21.6</td><td>19.0</td><td></td><td></td><td></td></tr><tr><td>BARTLarge-SLED</td><td>406M</td><td>58.0 / 26.9 / 27.6</td><td>35.1</td><td>33.8 / 8.0 / 18.5</td><td>17.1</td><td>32.1 / 10.2 / 21.0</td><td>19.0</td><td></td><td></td><td></td></tr><tr><td>BART-LS</td><td>460M</td><td>59.4 / 29.8 / 30.8</td><td>37.9</td><td>37.7 / 10.2 / 21.5</td><td>20.2</td><td>35.1 / 12.0 / 23.3</td><td>21.4</td><td></td><td></td><td></td></tr><tr><td>Top-Down-AvgP</td><td>464M</td><td>-- / -- / --</td><td>--</td><td>35.8 / 8.9 / 30.6*</td><td>21.4*</td><td>-- / -- / --</td><td>--</td><td></td><td></td><td></td></tr><tr><td>Top-Down-AdaP</td><td>464M</td><td>-- / -- / --</td><td>--</td><td>36.8 / 9.2 / 31.1*</td><td>21.9*</td><td>-- / -- / --</td><td>--</td><td></td><td></td><td></td></tr><tr><td>LongT5Large</td><td>770M</td><td>54.2 / 27.8 / 29.8</td><td>35.5</td><td>35.6 / 9.2 / 21.2</td><td>19.1</td><td>35.1 / 12.0 / 23.3</td><td>21.4</td><td></td><td></td><td></td></tr><tr><td>LongT5XL</td><td>3B</td><td>54.7 / 28.2 / 30.2</td><td>36.0</td><td>35.8 / 9.6 / 21.1</td><td>19.4</td><td>34.9 / 11.8 / 23.5</td><td>21.3</td><td></td><td></td><td></td></tr><tr><td>UL2</td><td>20B</td><td>53.6 / 26.1 / 28.8</td><td>34.3</td><td>32.9 / 7.8 / 19.4</td><td>17.1</td><td>31.1 / 8.5 / 20.4</td><td>17.5</td><td></td><td></td><td></td></tr></table>
+
+Table 7: Comparison on SCROLLS benchmark (Summarization tasks, Test sets). Results for SLED, BART-LS, LongT5 and UL2 models are taken from the SCROLLS benchmark leaderboard.*: Top-Down (Pang et al., 2022) reports much higher scores for ROUGE-L on SummScreen/FD than any other model, and may have been computed with a variant of ROUGE-L that involves splitting on sentences rather than newlines.
+
+porating sliding window attention and global representations. However, pretraining only on long sequences significantly increases the pretraining time, and as we show in Section 3.6, pretraining first on short inputs and then subsequently on long inputs is much more cost efficient.
+
+In concurrent work released shortly before this submission deadline, Xiong et al. (2022a) also investigated extending short input Transformer models for long input tasks. While they focus on BART rather than PEGASUS, they similarly find that global tokens, staggered block-local attention, and extended pretraining greatly improve performance, lending further support to our findings. Their final model also incorporates pooling layers and is trained on different data.
+
+A broader treatment of related work can be found in Appendix A.
+
+# 6 Conclusion
+
+In this work, we investigate a range of proposed improvements to Transformer models to effectively and economically handle long inputs in summarization tasks. Through extensive ablation experiments, we find a simple but effective recipe for extending short-input models to tackle long-input summarization. Based on our findings, we introduce PEGASUS-X, an extended version of PEGASUS with a modified architecture and additional long-sequence pretraining. We show that PEGASUS-X sets the state of the art on two long input summarization tasks (GovReport and PubMed) and performs competitively on many others, even despite being much smaller than some compared models. Our findings can be extended to models in other domains beyond summarization, both for pretraining long input models from scratch as well as extending already pretrained short sequence models.
+
+# Limitations
+
+# Challenges of Evaluating Long-Document Summarization Models
+
+One limitation of our work is that evaluation of long-document summarization models is challenging, and while we evaluate on the widely used benchmarks for long-document summarization models, we highlight here the difficulties of measuring the capabilities of such models. In addition to the widely accepted issues with automatic evaluation of model-generated summaries with metrics such as ROUGE, long-document summarization brings about new challenges. In particular, there are relatively fewer long-document summarization tasks available to evaluate models on, and many of them (e.g. arXiv, Pub Med, SummScreen) are constructed by repurposing existing data and proxies for summaries (e.g. abstracts) rather than explicitly written summaries. As such, the available datasets for summarization reflect the data that is easy to repurpose into summarization rather than practical downstream summarization settings; in other words, the available evaluation datasets may not match the distribution of data or settings where such models are realistically used.
+
+On scoring generations, human evaluation should ideally be conducted to measure the quality of model-generated summaries. However, the much longer input texts also means that human evaluation of summaries becomes much more expensive and onerous, as raters would need to read the whole input before judging the quality of the summary.
+
+More discussion on the challenges of evaluating long-document summarization models can be found in Wang et al. (2022).
+
+# Findings May Not Generalize to Other Tasks
+
+We have confined our study to summarization tasks, as it matches our goal of investigating the ability for models to process large input contexts, with less focus on generating long outputs. We acknowledge that our ablation studies and experiments are focused solely on summarization tasks, and that our findings may not directly apply or extend to other long-input language tasks.
+
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+
+# A Full Related Work
+
+Long Document Summarization Several new long input summarization datasets and benchmarks have been recently introduced, providing better measures of long input summarization capability as well as prompting new interest in this research direction. The BookSum dataset (Kryscinski et al., 2021) consists of paragraph, chapter, and full summaries of books on Project Gutenberg based on web-scraped educational website. (Chen et al., 2022) consists of television show transcripts and episode summaries based on web-scraped fan-written summaries. The SCROLLS benchmark (Shaham et al., 2022) and the MuLD benchmark (Hudson and Al Moubayed, 2022) consist of multiple natural language tasks with long inputs, including long input summarization. The SQuALITY dataset (Wang et al., 2022) consists of question-focused summaries of Project Gutenberg stories, where annotators write summaries based on different questions that cover different aspects of the same story.
+
+Efficient Transformers Many efficient Transformer variants have been introduced in recent years (Tay et al., 2020), and we discuss here the works more relevant to this manuscript. (Beltagy et al., 2020) use global tokens as well as a sliding window local attention, implemented using custom CUDA kernels. The ETC model (Ainslie et al., 2020) uses both global tokens and block-wise sliding window local attention, although the global attention is incorporated based on the first few tokens of a sequence, rather than separately learned global tokens. Zaheer et al. (2020) extend ETC by adding random attention blocks, but we found that this significantly increases code complexity and computational cost. Guo et al. (2021) similarly extend ETC's block-wise sliding window attention, but computes transient "global token" representations by pooling over blocks of tokens. Pang et al. (2022) propose to augment the Longformer encoder-decoder with additional pooling layers to improve long-sequence summarization performance. Ivgi et al. (2022) propose an alternative approach to sparse attention via encoding overlapping chunks and fusing information across chunks int he decoder. We highlight that while the final Global-Local model architecture that we settle on shares similarity with several other proposed efficient Transformer architectures, our key con
+
+ribution lies in our extensive ablation study that identifies architectural tweaks that improve and, just as importantly, do not improve downstream performance.
+
+Among the listed model architectures for long input summarization, LongT5 (Guo et al., 2021) is the most similar to PEGASUS-X, sharing a similar encoder-decoder architecture, a similar training objective in generating masked sentences, and a mix of local attention and global information sharing for the encoder. We briefly highlight the key differences between the two models. Firstly, LongT5 trains from scratch on long sequences, whereas we initialize our model weights with PEGASUS weights (which is trained on short sequences) before doing additional pretraining on long input sequences. This significantly reduces the overall pretraining cost, as short sequence pretraining and be performed much more economically. LongT5 also uses the T5 relative position biases whereas PEGASUS-X uses sinusoidal position embeddings—as shown in Section B.1, T5 relative position biases perform slightly better but are significantly slower. The efficient encoder architecture between the two models is also different: LongT5 uses a transient global representations based on pooling chunks of tokens, whereas PEGASUS-X uses learned global token embeddings. LongT5 also uses a sliding window local attention based on ETC (Ainslie et al., 2020), whereas we use a simpler block-local attention with staggered blocks. Lastly, the largest LongT5 model is 3B parameters, more than  $5 \times$  the size of PEGASUS-X.
+
+More broadly, Tay et al. (2021) compare a variety of efficient Transformer architectures on a set of tasks designed to probe long-sequence processing capability, evaluating the different models on both performance as well as computation requirements. Tay et al. (2022) further evaluate the scaling properties of novel Transformer architectures, finding that deviating from full attention tends to hurt downstream performance. Xiong et al. (2022b) showed that simple local attention variants can be highly competitive with more complex sparse attention schemes, consistent with our findings.
+
+# B Details of Architecture Modification Experiments
+
+# B.1 Position Encoding Schemes
+
+New position encoding schemes encoding schemes such as RoPE (Su et al., 2021) and ALiBi (Press
+
+<table><tr><td rowspan="2">Position Encoding</td><td colspan="2">XSUM</td><td colspan="2">CNN/DM</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td><td rowspan="2">Step/s</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td>None</td><td>34.3 / 12.5 / 26.8</td><td>22.6</td><td>25.6 / 7.8 / 17.7</td><td>15.2</td><td>36.1 / 9.8 / 22.0</td><td>19.8</td><td>38.3 / 13.2 / 18.7</td><td>21.1</td><td>0.96</td></tr><tr><td>Sinusoidal</td><td>39.8 / 16.9 / 31.8</td><td>27.8</td><td>40.0 / 18.6 / 28.4</td><td>27.6</td><td>44.5 / 17.6 / 26.7</td><td>27.6</td><td>40.0 / 18.8 / 22.3</td><td>25.6</td><td>0.96</td></tr><tr><td>T5</td><td>40.1 / 17.1 / 32.0</td><td>28.0</td><td>39.8 / 18.8 / 28.6</td><td>27.8</td><td>44.9 / 17.9 / 26.8</td><td>27.8</td><td>40.2 / 19.5 / 22.9</td><td>26.2</td><td>0.53</td></tr><tr><td>RoPE</td><td>39.8 / 16.9 / 31.8</td><td>27.8</td><td>39.2 / 18.7 / 28.5</td><td>27.5</td><td>43.5 / 17.2 / 26.5</td><td>27.1</td><td>40.0 / 19.1 / 22.6</td><td>25.8</td><td>0.85</td></tr><tr><td>Absolute</td><td>39.1 / 16.4 / 31.3</td><td>27.2</td><td>39.7 / 18.7 / 28.5</td><td>27.7</td><td>44.3 / 17.5 / 26.5</td><td>27.4</td><td>38.6 / 17.5 / 21.1</td><td>24.2</td><td>1.00</td></tr></table>
+
+Table 8: Comparison of position encodings schemes for a Transformer encoder-decoder. Training steps per second are computed based on arXiv summarization. Absolute position embeddings are replicated to longer input sequences, following Beltagy et al. (2020). Training steps per second is computed based on arXiv, and normalized to the run with absolute position embeddings.  
+
+<table><tr><td rowspan="2">Position Encoding</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td>Factor=10000</td><td>48.1 / 20.4 / 28.6</td><td>30.4</td><td>60.9 / 29.3 / 30.8</td><td>38.0</td></tr><tr><td>Factor=50000</td><td>48.1 / 20.4 / 28.6</td><td>30.4</td><td>61.4 / 29.5 / 30.9</td><td>38.3</td></tr></table>
+
+Table 9: Comparison of different scaling constants in sinusoidal position encodings.
+
+et al., 2022) have garnered recent attention, showing improved performance on downstream evaluations. As input sequence lengths have gotten much longer, and in particular longer than the dimensions of hidden representations, previous choices of position encoding may no longer be optimal. Moreover, relative position encodings such as RoPE, T5 and ALiBi may be better suited for adapting models to different input lengths between pretraining and fine-tuning. Hence, this is a good opportunity to revisit the choice of positioning encoding schemes in encoder models.
+
+Because of the more complex interaction between local attention blocks and relative position encoding implementations, we conduct a preliminary investigation with a full-attention Transformer. We pretrain with an input length of 512, and finetune with an input length of 2048 for the long sequence tasks – this experiment also tests the propensity for position encodings to be adapted to longer sequences downstream. In addition to the sinusoidal position encoding used in PEGASUS and Vaswani et al. (2017), we also consider the bucket-based relative position encoding scheme of T5, RoPE, absolute position embeddings, and no position encoding as a baseline. For absolute position embeddings, we follow the recipe of Beltagy et al. (2020) and duplicate the learned position embeddings to handle longer sequences before finetuning. The chosen position encoding scheme is applied to all parts of the model, including both the encoder and the decoder. We do not experiment with ALiBi, as we found no natural way to adapt
+
+ALiBi to cross-attention.
+
+Our results are shown in Table 8. We find that although T5 performs the best, it is also almost twice as slow as the other position encoding schemes, which is consistent with the findings of Press et al. (2022). Sinusoidal position encodings and RoPE perform only slightly worse than T5 with much better efficiency, making them more desirable choices. Given the much simpler implementation of sinusoidal position encodings, we opt to stick with them for the remainder of the experiments.
+
+Takeaways: Sinusoidal position encodings still remain a good choice for long input Transformers.
+
+# B.2 Scaling Encoder and Decoder Layers
+
+Scaling laws (Kaplan et al., 2020; Ghorbani et al., 2021; Zhang et al., 2022) that describe the empirical relationship between model sizes and performance have proven surprisingly consistent and gotten significant attention in recent years. We present in this section a small set of scaling experiments, exploring the distribution of layers between encoder and decoder.
+
+Our results are shown in Table 10. In the top half, we fix the total number of layers to 24, and consider both encoder-heavy and decoder-heavy distributions, for both Local and Global-Local models. We observe that impact of distribution of encoder and decoder layers on performance is relatively small. For Local models, we see a slight boost from decoder-heavy models. For Global-Local models, we observe that a balanced encoder-decoder outperforms encoder- and decoder-heavy models, both of
+
+<table><tr><td rowspan="2">Architecture</td><td rowspan="2">Enc</td><td rowspan="2">Dec</td><td colspan="2">XSUM</td><td colspan="2">CNN/DM</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td rowspan="3">Local</td><td>18</td><td>6</td><td>37.4 / 15.0 / 29.7</td><td>25.5</td><td>39.0 / 18.2 / 27.9</td><td>27.0</td><td>46.0 / 19.4 / 27.6</td><td>29.1</td><td>58.9 / 27.4 / 29.1</td><td>36.1</td></tr><tr><td>12</td><td>12</td><td>37.5 / 14.9 / 29.7</td><td>25.5</td><td>38.5 / 18.0 / 27.6</td><td>26.7</td><td>45.4 / 18.9 / 27.3</td><td>28.6</td><td>59.2 / 27.6 / 29.3</td><td>36.3</td></tr><tr><td>6</td><td>18</td><td>37.7 / 15.1 / 29.9</td><td>25.7</td><td>38.5 / 18.1 / 27.7</td><td>26.9</td><td>46.3 / 19.3 / 27.6</td><td>29.1</td><td>59.4 / 27.8 / 29.5</td><td>36.5</td></tr><tr><td rowspan="3">Global-Local</td><td>18</td><td>6</td><td>38.6 / 15.9 / 30.9</td><td>26.7</td><td>39.2 / 18.5 / 28.2</td><td>27.3</td><td>47.3 / 20.1 / 28.3</td><td>30.0</td><td>60.2 / 28.7 / 30.6</td><td>37.5</td></tr><tr><td>12</td><td>12</td><td>38.6 / 15.9 / 30.7</td><td>26.6</td><td>40.0 / 18.6 / 28.3</td><td>27.6</td><td>47.5 / 20.1 / 28.3</td><td>30.0</td><td>61.1 / 29.3 / 30.7</td><td>38.1</td></tr><tr><td>6</td><td>18</td><td>37.7 / 15.1 / 29.9</td><td>25.7</td><td>38.5 / 18.1 / 27.7</td><td>26.9</td><td>46.4 / 19.5 / 27.9</td><td>29.3</td><td>60.3 / 28.6 / 30.0</td><td>37.2</td></tr><tr><td rowspan="2">Global-Local</td><td>18</td><td>12</td><td>38.5 / 15.7 / 30.6</td><td>26.4</td><td>38.7 / 18.4 / 28.1</td><td>27.1</td><td>47.3 / 20.0 / 28.3</td><td>29.9</td><td>60.2 / 29.2 / 31.0</td><td>37.9</td></tr><tr><td>12</td><td>18</td><td>38.6 / 15.8 / 30.5</td><td>26.5</td><td>38.6 / 18.3 / 28.0</td><td>27.0</td><td>47.5 / 20.3 / 28.5</td><td>30.2</td><td>60.9 / 29.0 / 30.4</td><td>37.7</td></tr></table>
+
+Table 10: Varying the distribution of encoder/decoder layers)
+
+which perform about comparably.
+
+We also consider cases where we further increase the size of either the encoder or decoder to 18 layers, shown in the second half of Table 10. We observe no improvement in performance over the 12/12-layer encoder-decoder, and suspect that other hyperparameters (e.g. hidden size) might be the bottleneck rather than the number of layers.
+
+We highlight here that because of the asymmetry of the input and output lengths, there are different computational trade-offs to different balances of encoder and decoder layers. Encoder-heavy models require more memory because of the long input sequences, whereas decoder-heavy models are relative slower at inference because of the autoregressive nature of decoding. Given the relatively small difference in the margin of performance, memory or computational constraints may outweigh the performance differences in practical scenarios.
+
+Takeaways: A balanced encoder-decoder performs best, but the difference in performance may be outweighed by other resource considerations.
+
+# B.3 Partial Cross Attention
+
+Given the use of an efficient attention architecture, which has memory consumption scale linearly rather than quadratically in input sequence length, another major memory bottleneck is the encoder-decoder cross-attention. Because each decoder layer attends separately to the long encoder representations, and the attention is dense, this is a large contiguous chunk of memory that we could seek to reduce.
+
+Perceiver AR (Hawthorne et al., 2022) demonstrated strong performance by using only a single cross-attention at the bottom layer of an autoregressive language model. Based on these results, we investigate the impact of only having cross-attention on a subset of decoder layers. In Table 12, we show
+
+the results of pretraining and fine-tuning Global-Local models with cross-attention only on specific layers on a variety of configurations. We find that reducing the number of cross-attention layers leads to a drop in performance, but the impact on performance is smaller than expected. For instance, with only cross-attention on the first and sixth layer, the Global-Local model still outperforms a Local model. The reduction of cross-attention layers also leads to a corresponding improvement in training step and reduction in memory consumption.
+
+Given the small drop in performance from using fewer decoder layers with cross-attention, we consider the viability of dropping cross-attention layers after pretraining. In other words, we take a Global-Local model pretrained with full cross-attention, drop the cross-attention for a subset of layers, and fine-tune directly. Our results are shown in Table 13. We find that dropping the cross-attention after pretraining again only leads to a small (additional) dip in performance. This indicates that dropping cross-attention may be a viable strategy for further reducing memory requirements for an existing pretrained model with a small performance trade-off, and pretraining a separate model from scratch is not necessary.
+
+Takeaways: Dropping cross-attention for a fraction of decoder layers can reduce memory consumption at the cost of slight performance regression. Cross-attention can be dropped after pretraining, with an associated performance trade-off.
+
+# B.4 Comparison on short summarization tasks
+
+# C PEGASUSBase+
+
+In a similar finding as Hoffmann et al. (2022), we found that PEGASUS<sub>Base</sub> benefits from training on significantly more tokens. As such, we trained a PEGASUS<sub>Base</sub> for a much larger number of to-
+
+<table><tr><td rowspan="2">Pretraining → Fine-tuning</td><td rowspan="2">Block Size</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td rowspan="3">Transformer → Local</td><td>16</td><td>46.4 / 19.6 / 27.9</td><td>29.4</td><td>59.6 / 28.2 / 29.9</td><td>36.9</td></tr><tr><td>64</td><td>46.5 / 19.5 / 27.8</td><td>29.3</td><td>59.5 / 28.0 / 29.6</td><td>36.7</td></tr><tr><td>256</td><td>46.8 / 19.7 / 28.0</td><td>29.6</td><td>59.8 / 28.0 / 29.8</td><td>36.8</td></tr><tr><td rowspan="3">Local → Local</td><td>16</td><td>45.9 / 19.1 / 27.5</td><td>28.9</td><td>59.0 / 27.5 / 29.3</td><td>36.2</td></tr><tr><td>64</td><td>46.5 / 19.5 / 27.8</td><td>29.3</td><td>59.7 / 28.1 / 29.8</td><td>36.8</td></tr><tr><td>256</td><td>47.1 / 19.9 / 28.1</td><td>29.8</td><td>59.7 / 28.5 / 30.3</td><td>37.2</td></tr><tr><td rowspan="3">Transformer → Global-Local</td><td>16</td><td>46.0 / 19.2 / 27.5</td><td>29.0</td><td>60.3 / 28.2 / 29.8</td><td>37.0</td></tr><tr><td>64</td><td>47.0 / 20.0 / 28.2</td><td>29.8</td><td>60.8 / 28.7 / 30.1</td><td>37.4</td></tr><tr><td>256</td><td>47.6 / 20.3 / 28.4</td><td>30.2</td><td>60.8 / 28.7 / 30.0</td><td>37.4</td></tr><tr><td rowspan="3">Global-Local → Global-Local</td><td>16</td><td>47.1 / 20.0 / 28.3</td><td>29.9</td><td>59.7 / 27.8 / 29.2</td><td>36.5</td></tr><tr><td>64</td><td>47.7 / 20.3 / 28.5</td><td>30.2</td><td>61.0 / 29.3 / 30.8</td><td>38.0</td></tr><tr><td>256</td><td>47.3 / 20.2 / 28.3</td><td>30.0</td><td>61.6 / 29.4 / 30.7</td><td>38.2</td></tr></table>
+
+Table 11: Comparison of adapting models architectures between pretraining and fine-tuning.  
+
+<table><tr><td rowspan="2">Cross-Attention</td><td colspan="2">XSUM</td><td colspan="2">CNN/DM</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td><td rowspan="2">Step/s</td><td rowspan="2">Mem</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td>Full</td><td>38.8 / 16.0 / 31.0</td><td>26.8</td><td>39.5 / 18.6 / 28.4</td><td>27.5</td><td>47.7 / 20.4 / 28.6</td><td>30.3</td><td>61.3 / 29.4 / 30.8</td><td>38.1</td><td>1.00</td><td>1.00</td></tr><tr><td>Cross[0,2,4,6,8,10]</td><td>38.3 / 15.6 / 30.5</td><td>26.3</td><td>39.8 / 18.8 / 28.5</td><td>27.7</td><td>48.1 / 20.4 / 28.6</td><td>30.4</td><td>61.0 / 29.0 / 30.7</td><td>37.9</td><td>1.10</td><td>0.90</td></tr><tr><td>Cross[0,3,6,9,11]</td><td>38.0 / 15.3 / 30.2</td><td>26.0</td><td>38.8 / 18.4 / 28.1</td><td>27.2</td><td>46.9 / 19.9 / 28.2</td><td>29.7</td><td>60.1 / 28.6 / 30.2</td><td>37.3</td><td>1.15</td><td>0.88</td></tr><tr><td>Cross[0,4,8,11]</td><td>37.8 / 15.3 / 30.1</td><td>25.9</td><td>38.5 / 18.1 / 27.9</td><td>26.9</td><td>47.6 / 20.2 / 28.4</td><td>30.1</td><td>60.9 / 28.9 / 30.3</td><td>37.6</td><td>1.15</td><td>0.86</td></tr><tr><td>Cross[0,6,11]</td><td>37.4 / 14.8 / 29.7</td><td>25.4</td><td>38.8 / 18.1 / 27.9</td><td>27.0</td><td>46.9 / 19.7 / 28.1</td><td>29.6</td><td>60.3 / 28.5 / 30.2</td><td>37.3</td><td>1.18</td><td>0.87</td></tr><tr><td>Cross[0,6]</td><td>37.5 / 14.9 / 29.7</td><td>25.5</td><td>38.3 / 18.0 / 27.8</td><td>26.8</td><td>47.1 / 19.8 / 28.1</td><td>29.7</td><td>60.4 / 28.1 / 29.7</td><td>36.9</td><td>1.21</td><td>0.85</td></tr></table>
+
+Table 12: Comparison of models with cross-attention only in a subset of the 12 decoder layers. Training steps per second and memory are computed based on arXiv, and normalized to the Cross[0,6] run.
+
+kens (the same as PEGASUSLarge), which achieves much better performance than the previously released PEGASUSBase model.
+
+# D Encoder Architecture Hyperparameters
+
+For experiments in Section 3.1, BigBird, Local and Global-Local all use a block size of 64. BigBird and Global-Local also use 32 global tokens. Performer uses 256 random features.
+
+# E Fine-tuning Hyperparameters
+
+For arXiv, we fine-tune with an input length of up to 16384 tokens and 256 output tokens, while for GovReport we use an input length of 10240 input tokens and 1024 output tokens given the longer summaries for the task. For XSUM and CNN/Daily Mail, with use an input length of 512, and output lengths of 64 and 128 respectively, following PE-GASUS hyperparameters. The full set of hyperparameters for fine-tuning models are shown in Table 15.
+
+# F Engineering Details
+
+The original PEGASUS model was trained using a codebase based on TensorFlow. The experiments in this paper were run using a new codebase written
+
+with JAX (Bradbury et al., 2018) and Flax (Heek et al., 2020). PEGASUS-XBase and PEGASUS-Xwere trained by converting the weights from the TensorFlow checkpoint to a Flax checkpoint format, and then continuing with long input training.
+
+<table><tr><td rowspan="2">Cross-Attention</td><td rowspan="2">Model</td><td colspan="2">arXiv</td><td colspan="2">GovReport</td></tr><tr><td>R1 / R2 / RL</td><td>RG</td><td>R1 / R2 / RL</td><td>RG</td></tr><tr><td rowspan="3">Pretrained</td><td>Full</td><td>47.7 / 20.4 / 28.6</td><td>30.3</td><td>61.3 / 29.4 / 30.8</td><td>38.1</td></tr><tr><td>Cross[0,2,4,6,8,10]</td><td>48.1 / 20.4 / 28.6</td><td>30.4</td><td>61.0 / 29.0 / 30.7</td><td>37.9</td></tr><tr><td>Cross[0,6]</td><td>47.1 / 19.8 / 28.1</td><td>29.7</td><td>60.4 / 28.1 / 29.7</td><td>36.9</td></tr><tr><td rowspan="2">Converted</td><td>Cross[0,2,4,6,8,10]</td><td>46.4 / 19.7 / 28.1</td><td>29.5</td><td>60.2 / 28.8 / 30.3</td><td>37.4</td></tr><tr><td>Cross[0,6]</td><td>46.2 / 19.7 / 28.1</td><td>29.5</td><td>60.2 / 28.1 / 29.8</td><td>36.9</td></tr></table>
+
+Table 13: Comparison of models pretrained with cross-attention for a subset of layers, and adapting a pretrained model by dropping cross-attention layers only during fine-tuning  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">CNN/DailyMail</td><td colspan="2">XSum</td></tr><tr><td>R1 / R2 / RLs</td><td>RG</td><td>R1 / R2 / RLs</td><td>RG</td></tr><tr><td>PEGASUSBase</td><td>41.8 / 18.8 / 38.9</td><td>31.3</td><td>39.8 / 16.6 / 31.7</td><td>27.6</td></tr><tr><td>PEGASUSBase+</td><td>42.5 / 20.1 / 39.6</td><td>32.4</td><td>43.8 / 21.2 / 36.0</td><td>32.2</td></tr><tr><td>PEGASUS-XBase</td><td>42.5 / 20.1 / 39.6</td><td>32.4</td><td>42.9 / 20.1 / 35.0</td><td>31.2</td></tr><tr><td>PEGASUSLarge</td><td>44.2 / 21.5 / 41.1</td><td>33.9</td><td>47.2 / 24.6 / 39.2</td><td>35.7</td></tr><tr><td>PEGASUS-X</td><td>43.4 / 21.2 / 40.6</td><td>33.5</td><td>45.8 / 22.8 / 37.6</td><td>34.0</td></tr></table>
+
+Table 14: Comparison on short summarization tasks (Test sets)  
+
+<table><tr><td>Dataset</td><td>Batch Size</td><td>Learning Rate</td><td>Num Steps</td><td>Max Input Tokens</td><td>Max Output Tokens</td><td>Beam Size</td><td>Beam Alpha</td></tr><tr><td colspan="8">PEGASUS-XBase</td></tr><tr><td>XSum</td><td>64</td><td>8e-4</td><td>97.5K</td><td>1024</td><td>128</td><td>4</td><td>0.8</td></tr><tr><td>CNN/DailyMail</td><td>64</td><td>8e-4</td><td>410K</td><td>1024</td><td>128</td><td>4</td><td>0.8</td></tr><tr><td>arXiv</td><td>64</td><td>8e-4</td><td>92.5K</td><td>16384</td><td>256</td><td>1</td><td>1</td></tr><tr><td>Big Patent</td><td>64</td><td>8e-4</td><td>272.5K</td><td>16384</td><td>256</td><td>1</td><td>1</td></tr><tr><td>PubMed</td><td>64</td><td>8e-4</td><td>85K</td><td>8096</td><td>256</td><td>1</td><td>1</td></tr><tr><td>GovReport</td><td>64</td><td>8e-4</td><td>40K</td><td>12288</td><td>1024</td><td>2</td><td>1</td></tr><tr><td>SummScreen</td><td>64</td><td>8e-4</td><td>90K</td><td>16384</td><td>256</td><td>1</td><td>1</td></tr><tr><td>QMSum</td><td>64</td><td>8e-4</td><td>7.5K</td><td>16384</td><td>256</td><td>1</td><td>1</td></tr><tr><td colspan="8">PEGASUS-X</td></tr><tr><td>XSum</td><td>64</td><td>8e-4</td><td>5k</td><td>1024</td><td>128</td><td>4</td><td>0.8</td></tr><tr><td>CNN/DailyMail</td><td>64</td><td>8e-4</td><td>7.5k</td><td>1024</td><td>128</td><td>4</td><td>0.8</td></tr><tr><td>arXiv</td><td>64</td><td>8e-4</td><td>85k</td><td>16384</td><td>256</td><td>1</td><td>1</td></tr><tr><td>Big Patent</td><td>64</td><td>8e-4</td><td>390k</td><td>12192</td><td>256</td><td>1</td><td>1</td></tr><tr><td>PubMed</td><td>64</td><td>8e-4</td><td>47.5k</td><td>12192</td><td>256</td><td>1</td><td>1</td></tr><tr><td>GovReport</td><td>64</td><td>8e-4</td><td>75K</td><td>12288</td><td>1024</td><td>1</td><td>1</td></tr><tr><td>SummScreen</td><td>64</td><td>8e-4</td><td>40K</td><td>12192</td><td>256</td><td>1</td><td>1</td></tr><tr><td>QMSum</td><td>64</td><td>8e-4</td><td>35K</td><td>12192</td><td>256</td><td>1</td><td>1</td></tr></table>
+
+Table 15: Hyperparameters for fine-tuning models

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2023/Is ChatGPT Good at Search_ Investigating Large Language Models as Re-Ranking Agents/889a8053-d0b1-4931-8523-fb8eab29a9bc_origin.pdf

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2023/Is ChatGPT Good at Search_ Investigating Large Language Models as Re-Ranking Agents/full.md

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+# Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents
+
+Weiwei Sun $^{1*}$  Lingyong Yan $^{2}$  Xinyu Ma $^{2}$  Shuaiqiang Wang $^{2}$  Pengjie Ren $^{1}$  Zhumin Chen $^{1}$  Dawei Yin $^{2\dagger}$  Zhaochun Ren $^{3\dagger}$
+
+<sup>1</sup>Shandong University, Qingdao, China <sup>2</sup>Baidu Inc., Beijing, China <sup>3</sup>Leiden University, Leiden, The Netherlands
+
+{sunnweiwei,lingyongy,xinyuma2016,shqiang.wang}@gmail.com
+
+{renpengjie, chenzhumin}@sdu.edu.cn yindawei@acm.org
+
+z. ren@liacs.leidenuniv.nl
+
+# Abstract
+
+Large Language Models (LLMs) have demonstrated remarkable zero-shot generalization across various language-related tasks, including search engines. However, existing work utilizes the generative ability of LLMs for Information Retrieval (IR) rather than direct passage ranking. The discrepancy between the pretraining objectives of LLMs and the ranking objective poses another challenge. In this paper, we first investigate generative LLMs such as ChatGPT and GPT-4 for relevance ranking in IR. Surprisingly, our experiments reveal that properly instructed LLMs can deliver competitive, even superior results to state-of-the-art supervised methods on popular IR benchmarks. Furthermore, to address concerns about data contamination of LLMs, we collect a new test set called NovelEval, based on the latest knowledge and aiming to verify the model's ability to rank unknown knowledge. Finally, to improve efficiency in real-world applications, we delve into the potential for distilling the ranking capabilities of ChatGPT into small specialized models using a permutation distillation scheme. Our evaluation results turn out that a distilled 440M model outperforms a 3B supervised model on the BEIR benchmark. The code to reproduce our results is available at www.github.com/sunnweiwei/RankGPT.
+
+# 1 Introduction
+
+Large Language Models (LLMs), such as ChatGPT and GPT-4 (OpenAI, 2022, 2023), are revolutionizing natural language processing with strong zero-shot and few-shot generalization. By pretraining on large-scale text corpora and alignment fine-tuning to follow human instructions, LLMs have demonstrated their superior capabilities in language understanding, generation, interaction, and reasoning (Ouyang et al., 2022).
+
+![](images/296d1fc973ea75e5d4d2a67727da8db91d784a3fa200382946668527084e5ffe.jpg)  
+Figure 1: Average results of ChatGPT and GPT-4 (zero-shot) on passage re-ranking benchmarks (TREC, BEIR, and Mr.TyDi), compared with BM25 and previous best-supervised systems (SOTA sup., e.g., monoT5 (Nogueira et al., 2020)).
+
+As one of the most successful AI applications, Information Retrieval (IR) systems satisfy user requirements through several pipelined sub-modules, such as passage retrieval and re-ranking (Lin et al., 2020). Most previous methods heavily rely on manual supervision signals, which require significant human effort and demonstrate weak generalizability (Campos et al., 2016; Izacard et al., 2022). Therefore, there is a growing interest in leveraging the zero-shot language understanding and reasoning capabilities of LLMs in the IR area. However, most existing approaches primarily focus on exploiting LLMs for content generation (e.g., query or passage) rather than relevance ranking for groups of passages (Yu et al., 2023; Microsoft, 2023).
+
+Compared to the common generation settings, the objectives of relevance re-ranking vary significantly from those of LLMs: the re-ranking agents need to comprehend user requirements, globally compare, and rank the passages based on their relevance to queries. Therefore, leveraging the LLMs' capabilities for passage re-ranking remains a challenging and unanswered task.
+
+To this end, we focus on the following questions:
+
+(RQ1) How does ChatGPT perform on passage re-ranking tasks?  
+(RQ2) How can we imitate the ranking capabilities of ChatGPT in a smaller, specialized model?
+
+To answer the first question, we investigate prompting ChatGPT with two existing strategies (Sachan et al., 2022; Liang et al., 2022). However, we observe that they have limited performance and heavily rely on the availability of the log-probability of model output. Thus, we propose an alternative instructional permutation generation approach, instructing the LLMs to directly output the permutations of a group of passages. In addition, we propose an effective sliding window strategy to address context length limitations. For a comprehensive evaluation of LLMs, we employ three well-established IR benchmarks: TREC (Craswell et al., 2020), BEIR (Thakur et al., 2021), and My.TyDi (Zhang et al., 2021). Furthermore, to assess the LLMs on unknown knowledge and address concerns of data contamination, we suggest collecting a continuously updated evaluation testbed and propose NovelEval, a new test set with 21 novel questions.
+
+To answer the second question, we introduce a permutation distillation technique to imitate the passage ranking capabilities of ChatGPT in a smaller, specialized ranking model. Specifically, we randomly sample 10K queries from the MS MARCO training set, and each query is retrieved by BM25 with 20 candidate passages. On this basis, we distill the permutation predicted by ChatGPT into a student model using a RankNet-based distillation objective (Burges et al., 2005).
+
+Our evaluation results demonstrate that GPT-4, equipped with zero-shot instructional permutation generation, surpasses supervised systems across nearly all datasets. Figure 1 illustrates that GPT-4 outperforms the previous state-of-the-art models by an average nDCG improvement of 2.7, 2.3, and 2.7 on TREC, BEIR, and My.TyDi, respectively. Furthermore, GPT-4 achieves state-of-the-art performance on the new NovelEval test set. Through our permutation distillation experiments, we observe that a 435M student model outperforms the previous state-of-the-art monoT5 (3B) model by an average nDCG improvement of 1.67 on BEIR. Additionally, the proposed distillation method demonstrates cost-efficiency benefits.
+
+In summary, our contributions are tri-fold:
+
+- We examine instructional methods for LLMs on passage re-ranking tasks and introduce a novel permutation generation approach; See Section 3 for details.  
+- We comprehensively evaluate ChatGPT and GPT-4 on various passage re-ranking benchmarks, including a newly proposed NovelEval test set; See Section 5 for details.  
+- We propose a distillation approach for learning specialized models with the permutation generated by ChatGPT; See Section 4 for details.
+
+# 2 Related Work
+
+# 2.1 Information Retrieval with LLMs
+
+Recently, large language models (LLMs) have found increasing applications in information retrieval (Zhu et al., 2023). Several approaches have been proposed to utilize LLMs for passage retrieval. For example, SGPT (Muennighoff, 2022) generates text embeddings using GPT, generative document retrieval explores a differentiable search index (Tay et al., 2022; Cao et al., 2021; Sun et al., 2023), and HyDE (Gao et al., 2023; Wang et al., 2023a) generates pseudo-documents using GPT-3. In addition, LLMs have also been used for passage re-ranking tasks. UPR (Sachan et al., 2022) and SGPT-CE (Muennighoff, 2022) introduce instructional query generation methods, while HELM (Liang et al., 2022) utilizes instructional relevance generation. LLMs are also employed for training data generation. InPars (Bonifacio et al., 2022) generates pseudo-queries using GPT-3, and Promptagator (Dai et al., 2023) proposes a few-shot dense retrieval to leverage a few demonstrations from the target domain for pseudo-query generation. Furthermore, LLMs have been used for content generation (Yu et al., 2023) and web browsing (Nakano et al., 2021; Izacard et al., 2023; Microsoft, 2023). In this paper, we explore using ChatGPT and GPT-4 in passage re-ranking tasks, propose an instructional permutation generation method, and conduct a comprehensive evaluation of benchmarks from various domains, tasks, and languages. Recent work (Ma et al., 2023) concurrently investigated listwise passage re-ranking using LLMs. In comparison, our study provides a more comprehensive evaluation, incorporating a newly annotated dataset, and validates the proposed permutation distillation technique.
+
+![](images/1ee2562e728cedc9f8886b016d394845bab4ffca8719af4b6335984969a8c44e.jpg)  
+Figure 2: Three types of instructions for zero-shot passage re-ranking with LLMs. The gray and yellow blocks indicate the inputs and outputs of the model. (a) Query generation relies on the log probability of LLMs to generate the query based on the passage. (b) Relevance generation instructs LLMs to output relevance judgments. (c) Permutation generation generates a ranked list of a group of passages. See Appendix A for details.
+
+# 2.2 LLMs Specialization
+
+Despite their impressive capabilities, LLMs such as GPT-4 often come with high costs and lack of source availability. As a result, considerable research has explored ways to distill the capabilities of LLMs into specialized, custom models. For instance, Fu et al. (2023) and Magister et al. (2023) have successfully distilled the reasoning ability of LLMs into smaller models. Self-instruct (Wang et al., 2023b; Taori et al., 2023) propose iterative approaches to distill GPT-3 using their outputs. Additionally, Sachan et al. (2023) and Shi et al. (2023) utilize the generation probability of LLMs to improve retrieval systems. This paper presents a permutation distillation method that leverages ChatGPT as a teacher to obtain specialized re-ranking models. Our experiments demonstrate that even with a small amount of ChatGPT-generated data, the specialized model can outperform strong supervised systems.
+
+# 3 Passage Re-Ranking with LLMs
+
+Ranking is the core task in information retrieval applications, such as ad-hoc search (Lin et al., 2020; Fan et al., 2022), Web search (Zou et al., 2021), and open-domain question answering (Karpukhin et al., 2020). Modern IR systems generally employ a multi-stage pipeline where the retrieval stage focuses on retrieving a set of candidates from a large
+
+![](images/29f8ff5c76e816e77647e6595489e942d957e015455969f18277af53ca624362.jpg)  
+Figure 3: Illustration of re-ranking 8 passages using sliding windows with a window size of 4 and a step size of 2. The blue color represents the first two windows, while the yellow color represents the last window. The sliding windows are applied in back-to-first order, meaning that the first 2 passages in the previous window will participate in re-ranking the next window.
+
+corpus, and the re-ranking stage aims to re-rank this set to output a more precise list. Recent studies have explored LLMs for zero-shot re-ranking, such as instructional query generation or relevance generation (Sachan et al., 2022; Liang et al., 2022). However, existing methods have limited performance in re-ranking and heavily rely on the availability of the log probability of model output and thus cannot be applied to the latest LLMs such as GPT-4. Since ChatGPT and GPT-4 have a strong capacity for text understanding, instruction following, and reasoning, we introduce a novel instructional permutation generation method with a sliding window strategy to directly output a ranked list given a set of candidate passages. Figure 2 illustrates examples of three types of instructions; all the detailed instructions are included in Appendix A.
+
+# 3.1 Instructional Permutation Generation
+
+As illustrated in Figure 2 (c), our approach involves inputting a group of passages into the LLMs, each identified by a unique identifier (e.g., [1], [2], etc.). We then ask the LLMs to generate the permutation of passages in descending order based on their relevance to the query. The passages are ranked using the identifiers, in a format such as [2]  $> [3] > [1] > \text{etc}$ . The proposed method ranks passages directly without producing an intermediate relevance score.
+
+# 3.2 Sliding Window Strategy
+
+Due to the token limitations of LLMs, we can only rank a limited number of passages using the permutation generation approach. To overcome this constraint, we propose a sliding window strategy. Figure 3 illustrates an example of re-ranking 8 pas
+
+sages using a sliding window. Suppose the first-stage retrieval model returns  $M$  passages. We rerank these passages in a back-to-first order using a sliding window. This strategy involves two hyperparameters: window size  $(w)$  and step size  $(s)$ . We first use the LLMs to rank the passages from the  $(M - w)$ -th to the  $M$ -th. Then, we slide the window in steps of  $s$  and re-rank the passages within the range from the  $(M - w - s)$ -th to the  $(M - s)$ -th. This process is repeated until all passages have been re-ranked.
+
+# 4 Specialization by Permutation Distillation
+
+Although ChatGPT and GPT-4 are highly capable, they are also too expensive to deploy in commercial search systems. Using GPT-4 to re-rank passages will greatly increase the latency of the search system. In addition, large language models suffer from the problem of unstable generation. Therefore, we argue that the capabilities of large language models are redundant for the re-ranking task. Thus, we can distill the re-ranking capability of large language models into a small model by specialization.
+
+# 4.1 Permutation Distillation
+
+In this paper, we present a novel permutation distillation method that aims to distill the passage reranking capability of ChatGPT into a specialized model. The key difference between our approach and previous distillation methods is that we directly use the model-generated permutation as the target, without introducing any inductive bias such as consistency-checking or log-probability manipulation (Bonifacio et al., 2022; Sachan et al., 2023). To achieve this, we sample 10,000 queries from MS MARCO and retrieve 20 candidate passages using BM25 for each query. The objective of distillation aims to reduce the differences between the permutation outputs of the student and ChatGPT.
+
+# 4.2 Training Objective
+
+Formally, suppose we have a query  $q$  and  $M$  passages  $(p_1, \ldots, p_M)$  retrieved by BM25 ( $M = 20$  in our implementation). ChatGPT with instructional permutation generation could produce the ranking results of the  $M$  passages, denoted as  $R = (r_1, \ldots, r_M)$ , where  $r_i \in [1, 2, \ldots, M]$  is the rank of the passage  $p_i$ . For example,  $r_i = 3$  means  $p_i$  ranks third among the  $M$  passages. Now we have a specialized model  $s_i = f_\theta(q, p_i)$  with
+
+parameters  $\theta$  to calculate the relevance score  $s_i$  of paired  $(q, p_i)$  using a cross-encoder. Using the permutation  $R$  generated by ChatGPT, we consider RankNet loss (Burges et al., 2005) to optimize the student model:
+
+$$
+\mathcal {L} _ {\mathrm {R a n k N e t}} = \sum_ {i = 1} ^ {M} \sum_ {j = 1} ^ {M} \mathbb {1} _ {r _ {i} <   r _ {j}} \log \left(1 + \exp \left(s _ {i} - s _ {j}\right)\right)
+$$
+
+RankNet is a pairwise loss that measures the correctness of relative passage orders. When using permutations generated by ChatGPT, we can construct  $M(M - 1) / 2$  pairs.
+
+# 4.3 Specialized Model Architecture
+
+Regarding the architecture of the specialized model, we consider two model structures: the BERT-like model and the GPT-like model.
+
+# 4.3.1 BERT-like model.
+
+We utilize a cross-encoder model (Nogueira and Cho, 2019) based on DeBERTa-large. It concatenates the query and passage with a [SEP] token and estimates relevance using the representation of the [CLS] token.
+
+# 4.3.2 GPT-like model.
+
+We utilize the LLaMA-7B (Touvron et al., 2023) with a zero-shot relevance generation instruction (see Appendix A). It classifies the query and passage as relevance or irrelevance by generating a relevance token. The relevance score is then defined as the generation probability of the relevance token.
+
+Figure 5 illustrates the structure of the two types of specialized models.
+
+# 5 Datasets
+
+Our experiments are conducted on three benchmark datasets and one newly collected test set NovelEval.
+
+# 5.1 Benchmark Datasets
+
+The benchmark datasets include, TREC-DL (Craswell et al., 2020), BEIR (Thakur et al., 2021), and Mr.TyDi (Zhang et al., 2021).
+
+TREC is a widely used benchmark dataset in IR research. We use the test sets of the 2019 and 2020 competitions: (i) TREC-DL19 contains 43 queries, (ii) TREC-DL20 contains 54 queries.
+
+BEIR consists of diverse retrieval tasks and domains. We choose eight tasks in BEIR to evaluate the models: (i) Covid: retrieves scientific articles
+
+for COVID-19 related questions. (ii) NFCorpus is a bio-medical IR data. (iii) Touche is an argument retrieval datasets. (iv) DBPedia retrieves entities from DBpedia corpus. (v) SciFact retrieves evidence for claims verification. (vi) Signal retrieves relevant tweets for a given news title. (vii) News retrieves relevant news articles for news headlines. (viii) Robust04 evaluates poorly performing topics.
+
+Mr.TyDi is a multilingual passages retrieval dataset of ten low-resource languages: Arabic, Bengali, Finnish, Indonesian, Japanese, Korean, Russian, Swahili, Telugu, and Thai. We use the first 100 samples in the test set of each language.
+
+# 5.2 A New Test Set - NovelEval
+
+The questions in the current benchmark dataset are typically gathered years ago, which raises the issue that existing LLMs already possess knowledge of these questions (Yu et al., 2023). Furthermore, since many LLMs do not disclose information about their training data, there is a potential risk of contamination of the existing benchmark test set (OpenAI, 2023). However, re-ranking models are expected to possess the capability to comprehend, deduce, and rank knowledge that is inherently unknown to them. Therefore, we suggest constructing continuously updated IR test sets to ensure that the questions, passages to be ranked, and relevance annotations have not been learned by the latest LLMs for a fair evaluation.
+
+As an initial effort, we built NovelEval-2306, a novel test set with 21 novel questions. This test set is constructed by gathering questions and passages from 4 domains that were published after the release of GPT-4. To ensure that GPT-4 did not possess prior knowledge of these questions, we presented them to both gpt-4-0314 and gpt-4-0613. For instance, question "Which film was the 2023 Palme d'Or winner?" pertains to the Cannes Film Festival that took place on May 27, 2023, rendering its answer inaccessible to most existing LLMs. Next, we searched 20 candidate passages for each question using Google search. The relevance of these passages was manually labeled as: 0 for not relevant, 1 for partially relevant, and 2 for relevant. See Appendix C for more details.
+
+# 6 Experimental Results of LLMs
+
+# 6.1 Implementation and Metrics
+
+In benchmark datasets, we re-rank the top-100 passages retrieved by BM25 using pyserini<sup>1</sup> and use nDCG@{1, 5,10} as evaluation metrics. Since ChatGPT cannot manage 100 passages at a time, we use the sliding window strategy introduced in Section 3.2 with a window size of 20 and step size of 10. In NovelEval, we randomly shuffled the 20 candidate passages searched by Google and re-ranked them using ChatGPT and GPT-4 with permutation generation.
+
+# 6.2 Results on Benchmarks
+
+On benchmarks, we compare ChatGPT and GPT-4 with state-of-the-art supervised and unsupervised passage re-ranking methods. The supervised baselines include: monoBERT (Nogueira and Cho, 2019), monoT5 (Nogueira et al., 2020), mmarcoCE (Bonifacio et al., 2021), and Cohere Rerank  ${}^{2}$  . The unsupervised baselines include: UPR (Sachan et al., 2022), InPars (Bonifacio et al., 2022), and Promptator++ (Dai et al., 2023). See Appendix E for more details on implementing the baseline.
+
+Table 1 presents the evaluation results obtained from the TREC and BEIR datasets. The following observations can be made: (i) GPT-4, when equipped with the permutation generation instruction, demonstrates superior performance on both datasets. Notably, GPT-4 achieves an average improvement of 2.7 and 2.3 in nDCG@10 on TREC and BEIR, respectively, compared to monoT5 (3B). (ii) ChatGPT also exhibits impressive results on the BEIR dataset, surpassing the majority of supervised baselines. (iii) On BEIR, we use only GPT-4 to re-rank the top-30 passages re-ranked by ChatGPT. The method achieves good results, while the cost is only 1/5 of that of only using GPT-4 for re-ranking.
+
+Table 2 illustrates the results on Mr. TyDi of ten low-resource languages. Overall, GPT-4 outperforms the supervised system in most languages, demonstrating an average improvement of 2.65 nDCG over mmarcoCE. However, there are instances where GPT-4 performs worse than mmarcoCE, particularly in low-resource languages like Bengali, Telugu, and Thai. This may be attributed to the weaker language modeling ability of GPT-4
+
+<table><tr><td>Method</td><td>DL19</td><td>DL20</td><td>Covid</td><td>NFCorpus</td><td>Touche</td><td>DBPedia</td><td>SciFact</td><td>Signal</td><td>News</td><td>Robust04</td><td>BEIR (Avg)</td></tr><tr><td>BM25</td><td>50.58</td><td>47.96</td><td>59.47</td><td>30.75</td><td>44.22</td><td>31.80</td><td>67.89</td><td>33.05</td><td>39.52</td><td>40.70</td><td>43.42</td></tr><tr><td colspan="12">Supervised</td></tr><tr><td>monoBERT (340M)</td><td>70.50</td><td>67.28</td><td>70.01</td><td>36.88</td><td>31.75</td><td>41.87</td><td>71.36</td><td>31.44</td><td>44.62</td><td>49.35</td><td>47.16</td></tr><tr><td>monoT5 (220M)</td><td>71.48</td><td>66.99</td><td>78.34</td><td>37.38</td><td>30.82</td><td>42.42</td><td>73.40</td><td>31.67</td><td>46.83</td><td>51.72</td><td>49.07</td></tr><tr><td>monoT5 (3B)</td><td>71.83</td><td>68.89</td><td>80.71</td><td>38.97</td><td>32.41</td><td>44.45</td><td>76.57</td><td>32.55</td><td>48.49</td><td>56.71</td><td>51.36</td></tr><tr><td>Cohere Rerank-v2</td><td>73.22</td><td>67.08</td><td>81.81</td><td>36.36</td><td>32.51</td><td>42.51</td><td>74.44</td><td>29.60</td><td>47.59</td><td>50.78</td><td>49.45</td></tr><tr><td colspan="12">Unsupervised</td></tr><tr><td>UPR (FLAN-T5-XL)</td><td>53.85</td><td>56.02</td><td>68.11</td><td>35.04</td><td>19.69</td><td>30.91</td><td>72.69</td><td>31.91</td><td>43.11</td><td>42.43</td><td>42.99</td></tr><tr><td>InPars (monoT5-3B)</td><td>-</td><td>66.12</td><td>78.35</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Promptagator++ (few-shot)</td><td>-</td><td>-</td><td>76.2</td><td>37.0</td><td>38.1</td><td>43.4</td><td>73.1</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td colspan="12">LLM API (Permutation generation)</td></tr><tr><td>gpt-3.5-turbo</td><td>65.80</td><td>62.91</td><td>76.67</td><td>35.62</td><td>36.18</td><td>44.47</td><td>70.43</td><td>32.12</td><td>48.85</td><td>50.62</td><td>49.37</td></tr><tr><td>gpt-4†</td><td>75.59</td><td>70.56</td><td>85.51</td><td>38.47</td><td>38.57</td><td>47.12</td><td>74.95</td><td>34.40</td><td>52.89</td><td>57.55</td><td>53.68</td></tr></table>
+
+Table 1: Results (nDCG@10) on TREC and BEIR. Best performing unsupervised and overall system(s) are marked bold. All models except InPars and Promptagator++ re-rank the same BM25 top-100 passages. †On BEIR, we use gpt-4 to re-rank the top-30 passages re-ranked by gpt-3.5-turbo to reduce the cost of calling gpt-4 API.  
+
+<table><tr><td>Method</td><td>BM25</td><td>mmarcoCE</td><td>gpt-3.5</td><td>+gpt-4</td></tr><tr><td>Arabic</td><td>39.19</td><td>68.18</td><td>71.00</td><td>72.56</td></tr><tr><td>Bengali</td><td>45.56</td><td>65.98</td><td>53.10</td><td>64.37</td></tr><tr><td>Finnish</td><td>29.91</td><td>54.15</td><td>56.48</td><td>62.29</td></tr><tr><td>Indonesian</td><td>51.79</td><td>69.94</td><td>68.45</td><td>75.47</td></tr><tr><td>Japanese</td><td>27.39</td><td>49.80</td><td>50.70</td><td>58.22</td></tr><tr><td>Korean</td><td>26.29</td><td>44.00</td><td>41.48</td><td>49.63</td></tr><tr><td>Russian</td><td>34.04</td><td>53.16</td><td>48.75</td><td>53.45</td></tr><tr><td>Swahili</td><td>45.15</td><td>60.31</td><td>62.38</td><td>67.67</td></tr><tr><td>Telugu</td><td>37.05</td><td>68.92</td><td>51.69</td><td>62.22</td></tr><tr><td>Thai</td><td>44.62</td><td>68.36</td><td>55.57</td><td>63.41</td></tr><tr><td>Avg</td><td>38.10</td><td>60.28</td><td>55.96</td><td>62.93</td></tr></table>
+
+in these languages and the fact that text in low-resource languages tends to consume more tokens than English text, leading to the over-cropping of passages. Similar trends are observed with ChatGPT, which is on par with the supervised system in most languages, and consistently trails behind GPT-4 in all languages.
+
+# 6.3 Results on NovelEval
+
+Table 3 illustrates the evaluation results on our newly collected NovelEval, a test set containing 21 novel questions and 420 passages that GPT-4 had not learned. The results show that GPT-4 performs well on these questions, significantly outperforming the previous best-supervised method, monoT5 (3B). Additionally, ChatGPT achieves a performance level comparable to that of monoBERT. This outcome implies that LLMs possess the capability to effectively re-rank unfamiliar information.
+
+Table 2: Results (nDCG@10) on Mr.TyDi.  
+
+<table><tr><td>Method</td><td>nDCG@1</td><td>nDCG@5</td><td>nDCG@10</td></tr><tr><td>BM25</td><td>33.33</td><td>45.96</td><td>55.77</td></tr><tr><td>monoBERT (340M)</td><td>78.57</td><td>70.65</td><td>77.27</td></tr><tr><td>monoT5 (220M)</td><td>83.33</td><td>77.46</td><td>81.27</td></tr><tr><td>monoT5 (3B)</td><td>83.33</td><td>78.38</td><td>84.62</td></tr><tr><td>gpt-3.5-turbo</td><td>76.19</td><td>74.15</td><td>75.71</td></tr><tr><td>gpt-4</td><td>85.71</td><td>87.49</td><td>90.45</td></tr></table>
+
+Table 3: Results on NovelEval.  
+
+<table><tr><td>Method</td><td>DL19
+nDCG@1/5/10</td><td>DL20
+nDCG@1/5/10</td></tr><tr><td>curie-001</td><td>RG 39.53 / 40.02 / 41.53</td><td>41.98 / 34.80 / 34.91</td></tr><tr><td>curie-001</td><td>QG 50.78 / 50.77 / 49.76</td><td>50.00 / 48.36 / 48.73</td></tr><tr><td>curie-001</td><td>PG 66.67 / 56.79 / 54.21</td><td>59.57 / 55.20 / 52.17</td></tr><tr><td>davinci-003</td><td>RG 54.26 / 52.78 / 50.58</td><td>64.20 / 58.41 / 56.87</td></tr><tr><td>davinci-003</td><td>QG 37.60 / 44.73 / 45.37</td><td>51.25 / 47.46 / 45.93</td></tr><tr><td>davinci-003</td><td>PG 69.77 / 64.73 / 61.50</td><td>69.75 / 58.76 / 57.05</td></tr><tr><td>gpt-3.5</td><td>PG 82.17 / 71.15 / 65.80</td><td>79.32 / 66.76 / 62.91</td></tr><tr><td>gpt-4</td><td>PG 82.56 / 79.16 / 75.59</td><td>78.40 / 74.11 / 70.56</td></tr></table>
+
+Table 4: Compare different instruction and API endpoint. Best performing system(s) are marked bold. PG, QG, RG denote permutation generation, query generation and relevance generation, respectively.
+
+# 6.4 Compare with Different Instructions
+
+We conduct a comparison with the proposed permutation generation (PG) with previous query generation (QG) (Sachan et al., 2022) and relevance generation (RG) (Liang et al., 2022) on TREC-DL19. An example of the three types of instructions is in Figure 2, and the detailed implementation is in Appendix B. We also compare four LLMs provided
+
+<table><tr><td>Method</td><td>nDCG@1</td><td>nDCG@5</td><td>nDCG@10</td></tr><tr><td>BM25</td><td>54.26</td><td>52.78</td><td>50.58</td></tr><tr><td>gpt-3.5-turbo</td><td>82.17</td><td>71.15</td><td>65.80</td></tr><tr><td colspan="4">Initial passage order</td></tr><tr><td>(1) Random order</td><td>26.36</td><td>25.32</td><td>25.17</td></tr><tr><td>(2) Reverse order</td><td>36.43</td><td>31.79</td><td>32.77</td></tr><tr><td colspan="4">Number of re-ranking</td></tr><tr><td>(3) Re-rank 2 times</td><td>78.29</td><td>69.37</td><td>66.62</td></tr><tr><td>(4) Re-rank 3 times</td><td>78.29</td><td>69.74</td><td>66.97</td></tr><tr><td>(5) gpt-4 Rerank</td><td>80.23</td><td>76.70</td><td>73.64</td></tr></table>
+
+Table 5: Ablation study on TREC-DL19. We use gpt-3.5-turbo with permutation generation with different configuration.
+
+in the OpenAI  $\mathsf{API}^3$ : curie-001 - GPT-3 model with about 6.7 billion parameters (Brown et al., 2020); davinci-003 - GPT-3.5 model trained with RLHF and about 175 billion parameters (Ouyang et al., 2022); gpt-3.5-turbo - The underlying model of ChatGPT (OpenAI, 2022); gpt-4 - GPT-4 model (OpenAI, 2023).
+
+The results are listed in Table 4. From the results, we can see that: (i) The proposed PG method outperforms both QG and RG methods in instructing LLMs to re-rank passages. We suggest two explanations: First, from the result that PG has significantly higher top-1 accuracy compared to other methods, we infer that LLMs can explicitly compare multiple passages with PG, allowing subtle differences between passages to be discerned. Second, LLMs gain a more comprehensive understanding of the query and passages by reading multiple passages with potentially complementary information, thus improving the model's ranking ability. (ii) With PG, ChatGPT performs comparably to GPT-4 on nDCG@1, but lags behind it on nDCG@10. The Davinci model (text-davinci-003) performs poorly compared to ChatGPT and GPT-4. This may be because of the generation stability of Davinci and ChatGPT trails that of GPT-4. We delve into the stability analysis of Davinci, ChatGPT, and GPT-4 in Appendix F.
+
+# 6.5 Ablation Study on TREC
+
+We conducted an ablation study on TREC to gain insights into the detailed configuration of permutation generation. Table 5 illustrates the results.
+
+Initial Passage Order While our standard implementation utilizes the ranking result of BM25 as the initial order, we examined two alternative variants: random order (1) and reversed BM25 order (2). The results reveal that the model's performance is highly sensitive to the initial passage order. This could be because BM25 provides a relatively good starting passage order, enabling satisfactory results with only a single sliding window re-ranking.
+
+Number of Re-Ranking Furthermore, we studied the influence of the number of sliding window passes. Models (3-4) in Table 5 show that re-ranking more times may improve nDCG@10, but it somehow hurts the ranking performance on top passages (e.g., nDCG@1 decreased by 3.88). Re-ranking the top 30 passages using GPT-4 showed notable accuracy improvements (see the model (5)). This provides an alternative method to combine ChatGPT and GPT-4 in passage re-ranking to reduce the high cost of using the GPT-4 model.
+
+# 6.6 Results of LLMs beyond ChatGPT
+
+We further test the capabilities of other LLMs beyond the OpenAI series on TREC DL-19. As shown in Table 6, we evaluate the top-20 BM25 passage re-ranking nDCG of proprietary LLMs from OpenAI, Cohere, Antropic, and Google, and three open-source LLMs. We see that: (i) Among the proprietary LLMs, GPT-4 exhibited the highest re-ranking performance. Cohere Re-rank also showed promising results; however, it should be noted that it is a supervised specialized model. In contrast, the proprietary models from Antropic and Google fell behind ChatGPT in terms of re-ranking effectiveness. (ii) As for the open-source LLMs, we observed a significant performance gap compared to ChatGPT. One possible reason for this discrepancy could be the complexity involved in generating permutations of 20 passages, which seems to pose a challenge for the existing open-source models.
+
+We analyze the model's unexpected behavior in Appendix F, and the cost of API in Appendix H.
+
+# 7 Experimental Results of Specialization
+
+As mentioned in Section 4, we randomly sample 10K queries from the MSMARCO training set and employ the proposed permutation distillation to distill ChatGPT's predicted permutation into specialized re-ranking models. The specialized re-ranking models could be DeBERTa-v3-Large with a cross-encoder architecture or LLaMA-7B with relevance
+
+![](images/934d71cd62edb665e348276abd1a5cdbcbb928af0010efe6a40b2dec90730738.jpg)
+
+![](images/925935ec0c2aa4ffde9f8c8a886f643231f33146a9c477bccf1886d78daa2368.jpg)  
+Model size: Log of number of parameters
+
+![](images/c5227e28859d0c8bf72786dd48abc877a2bee19eb515a711178c96ed1a4c2cc2.jpg)  
+Figure 4: Scaling experiment. The dashed line indicates the baseline methods: GPT-4, monoT5, monoBERT, and ChatGPT. The solid green line and solid gray line indicate the specialized Deberta models obtained by the proposed permutation distillation and by supervised learning on MS MARCO, respectively. This figure compares the models' performance on TREC and BEIR across varying model sizes (70M to 435M) and training data sizes (500 to 10K).
+
+![](images/bfb4b2904ab4ac22d3ea1b7017e04646a32b4d9c9cf1a3824404496b5d057313.jpg)  
+Data size: Number of training samples
+
+![](images/f70a8cfbf53e803ef84acb67ff4656615898ff2cf5423ccc2c632d78734c618f.jpg)
+
+of training samples
+
+<table><tr><td>Method</td><td>ND1</td><td>ND5</td><td>ND10</td></tr><tr><td>OpenAI text-davinci-003</td><td>70.54</td><td>61.90</td><td>57.24</td></tr><tr><td>OpenAI gpt-3.5-turbo</td><td>75.58</td><td>66.19</td><td>60.89</td></tr><tr><td>OpenAI gpt-4</td><td>79.46</td><td>71.65</td><td>65.68</td></tr><tr><td>Cohere rerank-english-v2.0</td><td>79.46</td><td>71.56</td><td>64.78</td></tr><tr><td>Antropic claude-2</td><td>66.66</td><td>59.33</td><td>55.91</td></tr><tr><td>Antropic claude-instant-1</td><td>81.01</td><td>66.71</td><td>62.23</td></tr><tr><td>Google text-bison-001</td><td>69.77</td><td>64.46</td><td>58.67</td></tr><tr><td>Google bard-2023.10.21</td><td>81.01</td><td>65.57</td><td>60.11</td></tr><tr><td>Google flan-t5-xxl</td><td>52.71</td><td>51.63</td><td>50.26</td></tr><tr><td>Tsinghua ChatGLM-6B</td><td>54.26</td><td>52.77</td><td>50.58</td></tr><tr><td>LMSYS Vicuna-13B</td><td>54.26</td><td>51.55</td><td>49.08</td></tr></table>
+
+Table 6: Results of different LLMs on re-ranking top-20 passages on DL-19. ND{1,5,10} denote nDCG@{1,5,10}, respectively.  
+
+<table><tr><td>Label</td><td>Method</td><td>DL19</td><td>DL20</td><td>BEIR (Avg)</td></tr><tr><td>∅</td><td>BM25</td><td>50.58</td><td>47.96</td><td>43.42</td></tr><tr><td>∅</td><td>ChatGPT</td><td>65.80</td><td>62.91</td><td>49.37</td></tr><tr><td>MARCO</td><td>monoT5 (3B)</td><td>71.83</td><td>68.89</td><td>51.36</td></tr><tr><td>MARCO</td><td>DeBERTa-Large</td><td>68.89</td><td>61.38</td><td>42.64</td></tr><tr><td>MARCO</td><td>LLaMA-7B</td><td>69.24</td><td>58.97</td><td>47.71</td></tr><tr><td>ChatGPT</td><td>DeBERTa-Large</td><td>70.66</td><td>67.15</td><td>53.03</td></tr><tr><td>ChatGPT</td><td>LLaMA-7B</td><td>71.78</td><td>66.89</td><td>51.68</td></tr></table>
+
+Table 7: Results (nDCG@10) of specialized models. Best performing specialized model(s) are marked bold. The label column denotes the relevance judgements used in model training, where MARCO denotes use MS MARCO annotation, ChatGPT denotes use the outputs of permutation generation instructed ChatGPT as labels. BEIR (Avg) denotes average nDCG on eight BEIR datasets, and the detailed results are at Table 13.
+
+generation instructions. We also implemented the specialized model trained using the original MS MARCO labels (aka supervised learning) for com
+
+parison4.
+
+# 7.1 Results on Benchmarks
+
+Table 7 lists the results of specialized models, and Table 13 includes the detailed results. Our findings can be summarized as follows: (i) Permutation distillation outperforms the supervised counterpart on both TREC and BEIR datasets, potentially because ChatGPT's relevance judgments are more comprehensive than MS MARCO labels (Arabzadeh et al., 2021). (ii) The specialized DeBERTa model outperforms previous state-of-the-art (SOTA) baselines, monoT5 (3B), on BEIR with an average nDCG of 53.03. This result highlights the potential of distilling LLMs for IR since it is significantly more cost-efficient. (iii) The distilled specialized model also surpasses ChatGPT, its teacher model, on both datasets. This is probably because the re-ranking stability of specialized models is better than ChatGPT. As shown in the stability analysis in Appendix F, ChatGPT is very unstable in generating permutations.
+
+# 7.2 Analysis on Model Size and Data Size
+
+In Figure 4, we present the re-ranking performance of specialized DeBERTa models obtained through permutation distillation and supervised learning of different model sizes (ranging from 70M to 435M) and training data sizes (ranging from 500 to 10K). Our findings indicate that the permutation-distilled models consistently outperform their supervised counterparts across all settings, particularly on the BEIR datasets. Notably, even with only 1K training queries, the permutation-distilled DeBERTa model
+
+achieves superior performance compared to the previous state-of-the-art monoT5 (3B) model on BEIR. We also observe that increasing the number of model parameters yields a greater improvement in the ranking results than increasing the training data. Finally, we find that the performance of supervised models is unstable for different model sizes and data sizes. This may be due to the presence of noise in the MS MARCO labels, which leads to overfitting problems (Arabzadeh et al., 2021).
+
+# 8 Conclusion
+
+In this paper, we conduct a comprehensive study on passage re-ranking with LLMs. We introduce a novel permutation generation approach to fully explore the power of LLMs. Our experiments on three benchmarks have demonstrated the capability of ChatGPT and GPT-4 in passage re-ranking. To further validate LLMs on unfamiliar knowledge, we introduce a new test set called NovelEval. Additionally, we propose a permutation distillation method, which demonstrates superior effectiveness and efficiency compared to existing supervised approaches.
+
+# Limitations
+
+The limitations of this work include the main analysis for OpenAI ChatGPT and GPT-4, which are proprietary models that are not open-source. Although we also tested on open-source models such as FLAN-T5, ChatGLM-6B, and Vicuna-13B, the results still differ significantly from ChatGPT. How to further exploit the open-source models is a question worth exploring. Additionally, this study solely focuses on examining LLMs in the re-ranking task. Consequently, the upper bound of the ranking effect is contingent upon the recall of the initial passage retrieval. Our findings also indicate that the re-ranking effect of LLMs is highly sensitive to the initial order of passages, which is usually determined by the first-stage retrieval, such as BM25. Therefore, there is a need for further exploration into effectively utilizing LLMs to enhance the first-stage retrieval and improve the robustness of LLMs in relation to the initial passage retrieval.
+
+# Ethics Statement
+
+We acknowledge the importance of the ACM Code of Ethics and totally agree with it. We ensure that this work is compatible with the provided code,
+
+in terms of publicly accessed datasets and models. Risks and harms of large language models include the generation of harmful, offensive, or biased content. These models are often prone to generating incorrect information, sometimes referred to as hallucinations. We do not expect the studied model to be an exception in this regard. The LLMs used in this paper were shown to suffer from bias, hallucination, and other problems. Therefore, we are not recommending the use of LLMs for ranking tasks with social implications, such as ranking job candidates or ranking products, because LLMs may exhibit racial bias, geographical bias, gender bias, etc., in the ranking results. In addition, the use of LLMs in critical decision-making sessions may pose unspecified risks. Finally, the distilled models are licensed under the terms of OpenAI because they use ChatGPT. The distilled LLaMA models are further licensed under the non-commercial license of LLaMA.
+
+# Acknowledgements
+
+This work was supported by the Natural Science Foundation of China (62272274, 61972234, 62072279, 62102234, 62202271), the Natural Science Foundation of Shandong Province (ZR2021QF129, ZR2022QF004), the Key Scientific and Technological Innovation Program of Shandong Province (2019JZZZY010129), the Fundamental Research Funds of Shandong University, the China Scholarship Council under grant nr. 202206220085.
+
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+Weijia Shi, Sewon Min, Michihiro Yasunaga, Minjoon Seo, Rich James, Mike Lewis, Luke Zettlemoyer, and Wen tau Yih. 2023. Replug: Retrieval-augmented black-box language models. ArXiv, abs/2301.12652.  
+Weiwei Sun, Lingyong Yan, Zheng Chen, Shuaiqiang Wang, Haichao Zhu, Pengjie Ren, Zhumin Chen, Dawei Yin, M. de Rijke, and Zhaochun Ren. 2023. Learning to tokenize for generative retrieval. In NeruIPS 2023.  
+Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B. Hashimoto. 2023. Stanford alpaca: An instruction-following llama model. https://github.com/tatsu-lab/stanford_alpaca.  
+Yi Tay, Vinh Q. Tran, Mostafa Dehghani, Jianmo Ni, Dara Bahri, Harsh Mehta, Zhen Qin, Kai Hui, Zhe Zhao, Jai Gupta, Tal Schuster, William W. Cohen, and Donald Metzler. 2022. Transformer memory as a differentiable search index. In NeurIPS 2022.  
+Nandan Thakur, Nils Reimers, Andreas Ruckl'e, Abhishek Srivastava, and Iryna Gurevych. 2021. Beir: A heterogenous benchmark for zero-shot evaluation of information retrieval models. In NeurIPS 2021.
+
+Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothee Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, Aur'elien Rodriguez, Armand Joulin, Edouard Grave, and Guillaume Lample. 2023. Llama: Open and efficient foundation language models. *ArXiv*, abs/2302.13971.  
+Liang Wang, Nan Yang, and Furu Wei. 2023a. Query2doc: Query expansion with large language models. ArXiv, abs/2303.07678.  
+Xuanhui Wang, Cheng Li, Nadav Golbandi, Michael Bendersky, and Marc Najork. 2018. The lambdaloss framework for ranking metric optimization. In CIKM 2018.  
+Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A. Smith, Daniel Khashabi, and Hannaneh Hajishirzi. 2023b. Self-instruct: Aligning language model with self generated instructions. In ACL 2023.  
+Wenhao Yu, Dan Iter, Shuohang Wang, Yichong Xu, Mingxuan Ju, Soumya Sanyal, Chenguang Zhu, Michael Zeng, and Meng Jiang. 2023. Generate rather than retrieve: Large language models are strong context generators. In ICLR 2023.  
+Xinyu Zhang, Xueguang Ma, Peng Shi, and Jimmy J. Lin. 2021. Mr. tydi: A multi-lingual benchmark for dense retrieval. In MRL.  
+Yutao Zhu, Huaying Yuan, Shuting Wang, Jiongnan Liu, Wenhan Liu, Chenlong Deng, Zhicheng Dou, and Ji rong Wen. 2023. Large language models for information retrieval: A survey. ArXiv, abs/2308.07107.  
+Lixin Zou, Shengqiang Zhang, Hengyi Cai, Dehong Ma, Suqi Cheng, Daiting Shi, Shuaiqiang Wang, Zhicong Cheng, and Dawei Yin. 2021. Pre-trained language model based ranking in baidu search. In KDD 2021.
+
+# A Instructions
+
+# A.1 Query Generation Instruction
+
+The query generation instruction (Sachan et al., 2022) uses the log-probability of the query.
+
+Please write a question based on this passage.
+
+Passage:{{passage}}
+
+Question: {{query}}
+
+# A.2 Relevance Generation Instruction (few-shot)
+
+Following HELM (Liang et al., 2022), the relevance generation instruction use 4 in-context examples.
+
+Given a passage and a query, predict whether the passage includes an answer to the query by producing either 'Yes' or 'No'.
+
+Passage: Its 25 drops per ml, you guys are all wrong. If it is water, the standard was changed 15 - 20 years ago to make 20 drops  $= 1\mathrm{mL}$ . The viscosity of most things is temperature dependent, so this would be at room temperature. Hope this helps.
+
+Query: how many eye drops per ml
+
+Does the passage answer the query?
+
+Answer: Yes
+
+Passage: RE: How many eyedrops are there in a  $10\mathrm{ml}$  bottle of Cosopt? My Kaiser pharmacy insists that 2 bottles should last me 100 days but I run out way before that time when I am using 4 drops per day. In the past other pharmacies have given me 3 10-ml bottles for 100 days.E: How many eyedrops are there in a  $10\mathrm{ml}$  bottle of Cosopt? My Kaiser pharmacy insists that 2 bottles should last me 100 days but I run out way before that time when I am using 4 drops per day.
+
+Query: how many eye drops per ml
+
+Does the passage answer the query?
+
+Answer: No
+
+Passage: : You can transfer money to your checking account from other Wells Fargo. accounts through Wells Fargo Mobile Banking with the mobile app, online, at any. Wells Fargo ATM, or at a Wells Fargo branch. 1 Money in — deposits.
+
+Query: can you open a wells fargo account online
+
+Does the passage answer the query?
+
+Answer: No
+
+Passage: You can open a Wells Fargo banking account from your home or even online. It is really easy to do, provided you have all of the appropriate documentation. Wells Fargo has so many bank account options that you will be sure to find one that works for you. They offer free checking accounts with free online banking.
+
+Query: can you open a wells fargo account online
+
+Does the passage answer the query?
+
+Answer: Yes
+
+Passage:{{passage}}
+
+Query:{{query}}
+
+Does the passage answer the query?
+
+Answer:
+
+# A.3 Relevance Generation Instruction (zero-shot)
+
+This instruction is used to train LLaMA-7B specialized models.
+
+Given a passage and a query, predict whether the passage includes an answer to the query by producing either 'Yes' or 'No'.
+
+Passage:{{passage}}
+
+Query: {{query}}
+
+Does the passage answer the query?
+
+Answer:
+
+# A.4 Permutation Generation Instruction (Text)
+
+Permutation generation (text) is used for text-davinci-003.
+
+This is RankGPT, an intelligent assistant that can rank passages based on their relevancy to the query.
+
+The following are  $\{\{\mathsf{num}\}\}$  passages, each indicated by number identifier []. I can rank them based on their relevance to query: {{query}}
+
+[1] {{passage_1}}  
+[2] {{passage_2}}
+
+(more passages) ...
+
+The search query is: {{query}}
+
+I will rank the  $\{\{\mathsf{num}\}\}$  passages above based on their relevance to the search query. The passages will be listed in descending order using identifiers, and the most relevant passages should be listed first, and the output format should be  $[ ] > [ ] > \text{etc}$ , e.g.,  $[1] > [2] > \text{etc}$ .
+
+The ranking results of the  $\{\{\mathsf{num}\}\}$  passages (only identifiers) is:
+
+# A.5 Permutation Generation Instruction (Chat)
+
+Permutation generation instruction (chat) is used for gpt-3.5-turbo and gpt-4.
+
+# system:
+
+You are RankGPT, an intelligent assistant that can rank passages based on their relevancy to the query.
+
+# user:
+
+I will provide you with {{num}} passages, each indicated by number identifier []. Rank them based on their relevance to query: {{query}}.
+
+# assistant:
+
+Okay, please provide the passages.
+
+# user:
+
+[1] {{passage_1}}
+
+# assistant:
+
+Received passage [1]
+
+# user:
+
+[2] {{passage_2}}
+
+# assistant:
+
+Received passage [2]
+
+(more passages) ...
+
+# user
+
+Search Query: {{query}}.
+
+Rank the  $\{\{\mathsf{num}\}\}$  passages above based on their relevance to the search query. The passages should be listed in descending order using identifiers, and the most relevant passages should be listed first, and the output format should be  $[ ] > [ ]$ , e.g.,  $[1] > [2]$ . Only response the ranking results, do not say any word or explain.
+
+# B Instructional Methods on LLMs as Rernaker
+
+This paper focuses on re-ranking task, given  $M$  passages for a query  $q$ , the re-ranking aims to use an agent  $f(\cdot)$  to output their ranking results  $\mathbf{R} = (r_1,\dots,r_M)$ , where  $r_i\in [1,2,\dots,M]$  denotes the rank of  $p_i$ . This paper studies using the LLMs as  $f(\cdot)$ .
+
+# B.1 Instructional Query Generation
+
+Query generation has been studied in Sachan et al. (2022); Muennighoff (2022), in which the relevance between a query and a passage is measured by the log-probability of the model to generate the query based on the passage. Figure 2 (a) shows an example of instructional query generation.
+
+Formally, given query  $q$  and a passage  $p_i$ , their relevance score  $s_i$  is calculated as:
+
+$$
+s _ {i} = \frac {1}{| q |} \sum_ {t} \log p \left(q _ {t} \mid q _ {<   t}, p _ {i}, \mathcal {I} _ {\text {q u e r y}}\right) \tag {1}
+$$
+
+where  $|q|$  denotes the number of tokens in  $q$ ,  $q_{t}$  denotes the  $t$ -th token of  $q$ , and  $\mathcal{I}_{\mathrm{query}}$  denotes the instructions, referring to Figure 2 (a). The passages are then ranked based on relevance score  $s_{i}$ .
+
+# B.2 Instructional Relevance Generation
+
+Relevance generation is employed in HELM (Liang et al., 2022). Figure 2 (b) shows an example of instructional relevance generation, in which LLMs are instructed to output "Yes" if the query and passage
+
+are relevant or "No" if they are irrelevant. The relevance score  $s_i$  is measured by the probability of LLMs generating the word 'Yes' or 'No':
+
+$$
+s _ {i} = \left\{ \begin{array}{l l} 1 + p (\text {Y e s}), & \text {i f o u t p u t i s Y e s} \\ 1 - p (\text {N o}), & \text {i f o u t p u t i s N o} \end{array} \right. \tag {2}
+$$
+
+where  $p(\mathrm{Yes} / \mathrm{No})$  denotes the probability of LLMs generating Yes or No, and the relevance score is normalized into the range [0, 2].
+
+The above two methods rely on the log probability of LLM, which is often unavailable for LLM API. For example, at the time of writing, OpenAI's ChatCompletion API does not provide the log-probability of generation<sup>5</sup>.
+
+# B.3 Instructional Permutation Generation
+
+The proposed instructional permutation generation is a listwise approach, which directly assigns each passage  $p_i$  a unique ranking identifier  $a_i$  (e.g., [1], [2]) and places it at the beginning of  $p_i$ :  $p_i' = \operatorname{Concat}(a_i, p_i)$ . Subsequently, a generative LLM is instructed to generate a permutation of these identifiers:  $\mathbf{Perm} = f(q, p_1', \dots, p_M')$ , where the permutation  $\mathbf{Perm}$  indicates the rank of the identifiers  $a_i$  (e.g., [1], [2]). We then simply map the identifiers  $a_i$  to the passages  $p_i$  to obtain the ranking of the passages.
+
+<table><tr><td>Domain</td><td>Question</td><td>Reference Answer</td></tr><tr><td>Sport</td><td>What is Messi&#x27;s annual income after transferring to Miami?</td><td>$50M-$60M</td></tr><tr><td>Sport</td><td>How many goals did Haaland scored in the 2023 Champions League Final?</td><td>0</td></tr><tr><td>Sport</td><td>Where did Benzema go after leaving Real Madrid?</td><td>Saudi Arabia</td></tr><tr><td>Sport</td><td>Where was the 2023 Premier League FA Cup Final held?</td><td>Wembley Stadium</td></tr><tr><td>Sport</td><td>Who won 2023 Laureus World Sportsman Of The Year Award?</td><td>Lionel Messi</td></tr><tr><td>Sport</td><td>Who wins NBA Finals 2023?</td><td>Denver Nuggets</td></tr><tr><td>Tech</td><td>What is the screen resolution of vision pro?</td><td>4K with one eye</td></tr><tr><td>Tech</td><td>What is the name of the combined Deepmind and Google Brain?</td><td>Google DeepMind</td></tr><tr><td>Tech</td><td>How much video memory does the DGX GH200 have?</td><td>144TB</td></tr><tr><td>Tech</td><td>What are the new features of PyTorch 2?</td><td>faster, low memory, dynamic shapes</td></tr><tr><td>Tech</td><td>Who will be the CEO of Twitter after Elon Musk is no longer the CEO?</td><td>Linda Yaccarino</td></tr><tr><td>Tech</td><td>What are the best papers of CVPR 2023?</td><td>Visual Programming: Compositional [...]</td></tr><tr><td>Movie</td><td>Who sang the theme song of Transformers Rise of the Beasts?</td><td>Notorious B.I.G</td></tr><tr><td>Movie</td><td>Who is the villain in The Flash?</td><td>Eobard Thawne/Professor Zoom</td></tr><tr><td>Movie</td><td>How many different Spider-Men are there in Across the Spider-Verse?</td><td>280 variations</td></tr><tr><td>Movie</td><td>Who does Momoa play in Fast X?</td><td>Dante</td></tr><tr><td>Movie</td><td>The Little Mermaid first week box office?</td><td>$163.8 million worldwide</td></tr><tr><td>Movie</td><td>Which film was the 2023 Palme d&#x27;Or winner?</td><td>Anatomy of a Fall</td></tr><tr><td>Other</td><td>Where will Blackpink&#x27;s 2023 world tour concert in France be held?</td><td>the Stade de France</td></tr><tr><td>Other</td><td>What is the release date of song Middle Ground?</td><td>May 19, 2023</td></tr><tr><td>Other</td><td>Where did the G7 Summit 2023 take place?</td><td>Hiroshima</td></tr></table>
+
+Table 8: Questions and reference answers on NovelEval-2306.
+
+# C NovelEval-2306
+
+Table 8 lists the collected 21 questions. These questions come from four domains and include hot topics from the past few months. For each question, we used Google search to obtain 20 passages. When using Google search, in order to avoid all pages containing the answer, we used not only the question itself as a search query, but also the entities that appear in the question as an alternative search query to obtain some pages that are relevant but do not contain the answer. For example, for the first question "What is Messi's annual income after transferring to Miami?", we used "Messi" and "Messi transferring" as search queries to get some pages that do not contain the answer. When searching, we collected the highest-ranking web pages, news, and used a paragraph or paragraphs from the web pages related to the search term as candidate passages. Table 9 shows the statistical information of the data. All of the LLMs (including
+
+gpt-4-0314 and gpt-4-0613) we tested achieved  $0\%$  question-answering accuracy on the obtained test set.
+
+We searched for 20 candidate passages for each question using Google search. These passages were manually labeled for relevance by a group of annotators, including the authors and their highly educated colleagues. To ensure consistency, the annotation process was repeated twice. Each passage was assigned a relevance score: 0 for not relevant, 1 for partially relevant, and 2 for relevant. When evaluating the latest LLMs, we found that all non-retrieval-augmented models tested achieved  $0\%$  accuracy in answering the questions on the test set. This test set provides a reasonable evaluation of the latest LLMs at the moment. Since LLMs may be continuously trained on new data, the proposed test set should be continuously updated to counteract the contamination of the test set by LLMs.
+
+<table><tr><td>Number of questions</td><td>21</td></tr><tr><td>Number of passages</td><td>420</td></tr><tr><td>Number of relevance annotation</td><td>420</td></tr><tr><td>Average number words of passage</td><td>149</td></tr><tr><td>Number of score 0</td><td>290</td></tr><tr><td>Number of score 1</td><td>40</td></tr><tr><td>Number of score 2</td><td>90</td></tr></table>
+
+Table 9: Data Statistics of NovelEval.
+
+# D Implementation Details
+
+# D.1 Training Configuration
+
+We use DeBERTa-V3-base, which concatenates the query and passage with a [SEP] token and utilizes the representation of the [CLS] token. To generate candidate passages, we randomly sample 10k queries and use BM25 to retrieve 20 passages for each query. We then re-rank the candidate passages using the gpt-3.5-turbo API with permutation generation instructions, at a cost of approximately $40. During training, we employ a batch size of 32 and utilize the AdamW optimizer with a constant learning rate of  $5 \times 10^{-5}$ . The model is trained for two epochs. Additionally, we implement models using the original MS MARCO labels for comparison.
+
+The LLaMA-7B model is optimized with the AdamW optimizer, a constant learning rate of  $5 \times 10^{-5}$ , and with mixed precision of bf16 and Deepspeed Zero3 strategy. All the experiments are conducted on 8 A100-40G GPUs.
+
+Figure 5 illustrates the detailed model architecture of BERT-like and GPT-like specialized models.
+
+![](images/d628c131a966a73d7c11425fac106b1bdaf55b31caf048a52438d6773bbdc856.jpg)  
+(a) BERT-like Specialized Model
+
+![](images/b6f9d427d4bbde26b7e86c1080c814beaabd26363d772188f8e08fe3229403cc.jpg)  
+(b) GPT-like Specialized Model  
+Figure 5: Model architecture of BERT-like and GPT-like specialized models.
+
+# D.2 Training Objective
+
+Using the permutation generated by ChatGPT, we consider the following losses to optimize the student model:
+
+Listwise Cross-Entropy (CE) (Bruch et al., 2019). Listwise CE is the wide-use loss for passage ranking, which considers only one positive passage and defines the list-wise softmax cross-entropy on all candidate's passages:
+
+$$
+\mathcal {L} _ {\mathrm {L i s t w i s e \_ C E}} = - \sum_ {i = 1} ^ {M} \mathbb {1} _ {r _ {i} = 1} \log (\frac {\exp (s _ {i})}{\sum_ {j} \exp (s _ {j})})
+$$
+
+where  $\mathbb{1}$  is the indicator function.
+
+RankNet (Burges et al., 2005). RankNet is a pairwise loss that measures the correctness of relative passage orders:
+
+$$
+\mathcal {L} _ {\text {R a n k N e t}} = \sum_ {i = 1} ^ {M} \sum_ {j = 1} ^ {M} \mathbb {1} _ {r _ {i} <   r _ {j}} \log \left(1 + \exp \left(s _ {i} - s _ {j}\right)\right)
+$$
+
+when using permutation generated by ChatGPT, we can construct  $M(M - 1) / 2$  pairs.
+
+LambdaLoss (Wang et al., 2018). The LambdaLoss further accounts for the nDCG gains of the model ranks. LambdaLoss uses the student model's rank, denoted as  $\pi = (\pi_1, \dots, \pi_M)$ , where  $\pi_i$  is the model predicted rank of  $p_i$  with a similar definition with ChatGPT rank  $R$ . The loss function is defined as:
+
+$$
+\mathcal {L} _ {\mathrm {L a m b d a}} = \sum_ {r _ {i} <   r _ {j}} \Delta \mathrm {N D C G} \log_ {2} (1 + \exp (s _ {i} - s _ {j}))
+$$
+
+in which  $\Delta$  NDCG is the delta of NDCG which could be computed as  $\Delta$  NDCG =  $|G_i - G_j||\frac{1}{D(\pi_i)} -\frac{1}{D(\pi_j)}|$ , where  $D(\pi_i)$  and  $D(\pi_j)$  are the position discount functions and  $G_{i}$  and  $G_{j}$  are the gain functions used in NDCG (Wang et al., 2018).
+
+Pointwise Binary Cross-Entropy (BCE). We also include the Pointwise BCE as the baseline loss for supervised methods, which is calculated based on each query-document pair independently:
+
+$$
+\mathcal {L} _ {\mathrm {B C E}} = - \sum_ {i = 1} ^ {M} \mathbb {1} _ {r _ {i} = 1} \log \sigma (s _ {i}) + \mathbb {1} _ {r _ {i} \neq 1} \log \sigma (1 - s _ {i})
+$$
+
+where  $\sigma (x) = \frac{1}{1 + \exp(-x)}$  is the logistic function.
+
+# E Baselines Details
+
+We include state-of-the-art supervised and unsupervised passage re-ranking methods for comparison. The supervised baselines are:
+
+- monoBERT (Nogueira and Cho, 2019): A cross-encoder re-ranker based on BERT-large, trained on MS MARCO.  
+- monoT5 (Nogueira et al., 2020): A sequence-to-sequence re-ranker that uses T5 to calculate the relevance score $^6$ .  
+- Cohere Rerank: A passage reranking API rerank-english-v2.0 developed by Cohere<sup>7</sup>. Cohere does not provide details on the structure and training method of the model.  
+- mmarcoCE (Bonifacio et al., 2021): A 12-layer mMiniLM-v2 cross-encoder model trained on mmarco, a translated version of MS MARCO. mmarcoCE serves as a baseline for Mr.TyDi.
+
+# The unsupervised baselines are:
+
+- UPR (Sachan et al., 2022): Unsupervised passage ranking with instructional query generation. Due to its superior performance, we use the FLAN-T5-XL (Chung et al., 2022) as the LLM of UPR.  
+- InPars (Bonifacio et al., 2022): monoT5-3B trained on pseudo data generated by GPT-3.  
+- Promptagator++ (Dai et al., 2023): A 110M cross-encoder re-ranker trained on pseudo queries generated by FALN 137B.
+
+<table><tr><td>Method</td><td>Repetition↓</td><td>Missing↓</td><td>Rejection</td><td>RBO↑</td></tr><tr><td>text-davinci-003</td><td>0</td><td>280</td><td>0</td><td>72.30</td></tr><tr><td>gpt-3.5-turbo</td><td>14</td><td>153</td><td>7</td><td>81.49</td></tr><tr><td>gpt-4</td><td>0</td><td>1</td><td>11</td><td>82.08</td></tr></table>
+
+Table 10: Analysis of model stability on TREC. Repetition refers to the number of times the model generates duplicate passage identifiers. Missing refers to the number of missing passage identifiers in model output. Rejection refers to the number of times the model rejects to perform the ranking. RBO, i.e., rank biased overlap, refers to the consistency of the model in ranking the same group of passages twice.
+
+# F Model Behavior Analysis
+
+In the permutation generation method, the ranking of passages is determined by the list of model-output passage identifiers. However, we have observed that the models do not always produce the desired output, as evidenced by occasional duplicates or missing identifiers in the generated text. In Table 10, we present quantitative results of unexpected model behavior observed during experiments with the GPT models.
+
+Repetition. The repetition metric measures the occurrence of duplicate passage identifiers generated by the model. The results indicate that ChatGPT produced 14 duplicate passage identifiers during re-ranking 97 queries on two TREC datasets, whereas text-davinci-003 and GPT-4 did not exhibit any duplicates.
+
+Missing. We conducted a count of the number of times the model failed to include all passages in the re-ranked permutation output<sup>9</sup>. Our findings revealed that text-davinci-003 has the highest number of missing passages, totaling 280 instances. ChatGPT also misses a considerable number of passages, occurring 153 times. On the other hand, GPT-4 demonstrates greater stability, with only one missing passage in total. These results suggest that GPT-4 has higher reliability in generating permutations, which is critical for effective ranking.
+
+Rejection. We have observed instances where the model refuses to re-rank passages, as evidenced by responses such as "None of the provided passages is directly relevant to the query ..." To quantify this behavior, we count the number of times this occurred and find that GPT-4 rejects ranking the most frequently, followed by ChatGPT, while the Davinci model never refused to rank. This finding suggests that chat LLMs tend to be more adaptable compared to completion LLMs, and may exhibit more subjective responses. Note that we do not explicitly prohibit the models from rejecting ranking in the instructions, as we find that it does not significantly impact the overall ranking performance.
+
+RBO. The sliding windows strategy involves re-ranking the top-ranked passages from the previous window in the next window. The models are expected to produce consistent rankings in two windows for the same group of passages. To measure the consistency of the model's rankings, we use RBO (rank biased overlap $^{10}$ ), which calculates the similarity between the two ranking results. The findings turn out that ChatGPT and GPT-4 are more consistent in ranking passages compared to the Davinci model. GPT-4 also slightly outperforms ChatGPT in terms of the RBO metric.
+
+# G Analysis on Hyperparameters of Sliding Window
+
+To analyze the influence of parameters of the sliding window strategy, we adjust the window size and set the step size to half of the window size. The main motivation for this setup is to keep the expected
+
+<table><tr><td>API</td><td>Instruction</td><td>Tokens</td><td>Requests</td><td>USD</td></tr><tr><td>text-curie-001</td><td>Relevance generation</td><td>52,970</td><td>100</td><td>0.106</td></tr><tr><td>text-curie-001</td><td>Query generation</td><td>10,954</td><td>100</td><td>0.022</td></tr><tr><td>text-davinci-003</td><td>Query generation</td><td>11,269</td><td>100</td><td>0.225</td></tr><tr><td>text-davinci-003</td><td>Permutation generation</td><td>17,370</td><td>10</td><td>0.347</td></tr><tr><td>gpt-3.5-turbo</td><td>Permutation generation</td><td>19,960</td><td>10</td><td>0.040</td></tr><tr><td>gpt-4</td><td>Permutation generation</td><td>19,890</td><td>10</td><td>0.596</td></tr><tr><td>-rerank top-30</td><td>Permutation generation</td><td>3,271</td><td>1</td><td>0.098</td></tr></table>
+
+Table 11: Average token cost, number API request, and $USD per query on TREC.  
+
+<table><tr><td>Window size</td><td>Step size</td><td>nDCG@1</td><td>nDCG@5</td><td>nDCG@10</td></tr><tr><td>20</td><td>10</td><td>75.58</td><td>70.50</td><td>67.05</td></tr><tr><td>40</td><td>20</td><td>78.30</td><td>71.32</td><td>65.51</td></tr><tr><td>60</td><td>30</td><td>75.97</td><td>69.23</td><td>65.03</td></tr><tr><td>80</td><td>40</td><td>72.09</td><td>70.59</td><td>65.57</td></tr></table>
+
+Table 12: Analysis on Hyperparameters of Sliding Window on TREC-DL19.
+
+overhead of the method (number of tokens required for computation) low; i.e., most tokens in this setup are used for PG only twice. The experimental results are shown in Table  $12^{11}$ . The results show that the effect varies over a certain range of arrivals for different values of window size: window size=20 performs best in terms of nDCG@10, while window size=40 performs best in terms of nDCG@5 and nDCG@1. We speculate that a larger window size will increase the model's ranking horizon but will also present challenges in processing long contexts and large numbers of items.
+
+# H API Cost
+
+In Table 11, we provide details on the average token cost, API request times, and USD cost per query. In terms of average token cost, the relevance generation method is the most expensive, as it requires 4 in-context demonstrations. On the other hand, the permutation generation method incurs higher token costs compared to the query generation method, as it involves the repeated processing of passages in sliding windows. Regarding the number of requests, the permutation generation method requires 10 requests for sliding windows, while other methods require 100 requests for re-ranking 100 passages. In terms of average USD cost, GPT-4 is the most expensive, with a cost of  $0.596 per query. However, using GPT-4 for re-ranking the top-30 passages can result in significant cost savings, with a cost of$ 0.098 per query for GPT-4 usage, while still achieving good results. As a result, we only utilize GPT-4 for re-ranking the top 30 passages of ChatGPT on BEIR and Mr.TyDi. The total cost of our experiments with GPT-4 amounts to $556.
+
+Since the experiments with ChatGPT and GPT-4 are conducted using the OpenAI API, the running time is contingent on the OpenAI service, e.g., API latency. Besides, the running time can also vary across different API versions and network environments. In our testing conditions, the average latency for API calls for gpt-3.5-turbo and gpt-4 was around 1.1 seconds and 3.2 seconds, respectively. Our proposed sliding window-based permutation generation approach requires 10 API calls per query to re-rank 100 passages. Consequently, the average running time per query is 11 seconds for gpt-3.5-turbo and 32 seconds for gpt-4.
+
+# I Results of Specialized Models
+
+Table 13 lists the detailed results of specialized models on TREC and BEIR.
+
+<table><tr><td>Method</td><td>DL19</td><td>DL20</td><td>Covid</td><td>NFCorpus</td><td>Touche</td><td>DBPedia</td><td>SciFact</td><td>Signal</td><td>News</td><td>Robust04</td><td>BEIR (Avg)</td></tr><tr><td>BM25</td><td>50.58</td><td>47.96</td><td>59.47</td><td>30.75</td><td>44.22</td><td>31.80</td><td>67.89</td><td>33.05</td><td>39.52</td><td>40.70</td><td>43.42</td></tr><tr><td colspan="12">Supervised train on MS MRACO</td></tr><tr><td>monoBERT (340M)</td><td>70.50</td><td>67.28</td><td>70.01</td><td>36.88</td><td>31.75</td><td>41.87</td><td>71.36</td><td>31.44</td><td>44.62</td><td>49.35</td><td>47.16</td></tr><tr><td>monoT5 (220M)</td><td>71.48</td><td>66.99</td><td>78.34</td><td>37.38</td><td>30.82</td><td>42.42</td><td>73.40</td><td>31.67</td><td>46.83</td><td>51.72</td><td>49.07</td></tr><tr><td>monoT5 (3B)</td><td>71.83</td><td>68.89</td><td>80.71</td><td>38.97</td><td>32.41</td><td>44.45</td><td>76.57</td><td>32.55</td><td>48.49</td><td>56.71</td><td>51.36</td></tr><tr><td>Cohere Rerank-v2</td><td>73.22</td><td>67.08</td><td>81.81</td><td>36.36</td><td>32.51</td><td>42.51</td><td>74.44</td><td>29.60</td><td>47.59</td><td>50.78</td><td>49.45</td></tr><tr><td colspan="12">Unsupervised instructional permutation generation</td></tr><tr><td>ChatGPT</td><td>65.80</td><td>62.91</td><td>76.67</td><td>35.62</td><td>36.18</td><td>44.47</td><td>70.43</td><td>32.12</td><td>48.85</td><td>50.62</td><td>49.37</td></tr><tr><td>GPT-4</td><td>75.59</td><td>70.56</td><td>85.51</td><td>38.47</td><td>38.57</td><td>47.12</td><td>74.95</td><td>34.40</td><td>52.89</td><td>57.55</td><td>53.68</td></tr><tr><td>Specialized Models</td><td colspan="11">train on MARCO labels or ChatGPT predicted permutations</td></tr><tr><td>MARCO Pointwise BCE</td><td>65.57</td><td>56.72</td><td>70.82</td><td>33.10</td><td>17.08</td><td>32.28</td><td>55.37</td><td>19.30</td><td>41.52</td><td>46.00</td><td>39.43</td></tr><tr><td>MARCO Listwise CE</td><td>65.99</td><td>57.97</td><td>66.31</td><td>32.61</td><td>20.15</td><td>30.79</td><td>37.57</td><td>18.09</td><td>38.11</td><td>39.93</td><td>35.45</td></tr><tr><td>MARCO RankNet</td><td>66.34</td><td>58.51</td><td>70.29</td><td>34.23</td><td>20.27</td><td>29.62</td><td>49.01</td><td>23.22</td><td>39.82</td><td>43.87</td><td>38.79</td></tr><tr><td>MARCO LambdaLoss</td><td>64.82</td><td>56.16</td><td>72.86</td><td>34.20</td><td>19.51</td><td>32.55</td><td>51.88</td><td>26.22</td><td>42.47</td><td>45.28</td><td>40.62</td></tr><tr><td>ChatGPT Listwise CE</td><td>65.39</td><td>58.80</td><td>76.29</td><td>35.73</td><td>38.19</td><td>40.24</td><td>64.49</td><td>31.37</td><td>47.61</td><td>48.00</td><td>47.74</td></tr><tr><td>ChatGPT RankNet</td><td>65.75</td><td>59.34</td><td>81.26</td><td>36.57</td><td>39.03</td><td>42.10</td><td>68.77</td><td>31.55</td><td>52.54</td><td>52.44</td><td>50.53</td></tr><tr><td>ChatGPT LambdaLoss</td><td>67.17</td><td>60.56</td><td>80.63</td><td>36.74</td><td>36.73</td><td>43.75</td><td>68.21</td><td>32.58</td><td>49.00</td><td>50.51</td><td>49.77</td></tr><tr><td>deberta-v3-xsmall (70M)</td><td>64.75</td><td>55.07</td><td>78.21</td><td>35.95</td><td>35.42</td><td>41.37</td><td>67.86</td><td>30.04</td><td>47.68</td><td>49.91</td><td>48.31</td></tr><tr><td>deberta-v3-small (142M)</td><td>67.85</td><td>58.84</td><td>78.88</td><td>36.55</td><td>36.16</td><td>40.99</td><td>66.66</td><td>30.29</td><td>49.17</td><td>49.73</td><td>48.55</td></tr><tr><td>deberta-v3-base (184M)</td><td>70.28</td><td>62.52</td><td>80.81</td><td>36.15</td><td>37.25</td><td>44.06</td><td>71.70</td><td>32.45</td><td>50.84</td><td>51.33</td><td>50.57</td></tr><tr><td>deberta-v3-large (435M)</td><td>70.66</td><td>67.15</td><td>84.64</td><td>38.48</td><td>39.27</td><td>47.36</td><td>74.18</td><td>32.53</td><td>51.19</td><td>56.55</td><td>53.03</td></tr><tr><td>deberta-v3-large 5K</td><td>70.93</td><td>64.32</td><td>84.43</td><td>38.66</td><td>40.72</td><td>46.28</td><td>73.88</td><td>31.93</td><td>52.24</td><td>55.89</td><td>53.00</td></tr><tr><td>deberta-v3-large 3K</td><td>70.79</td><td>63.91</td><td>84.21</td><td>38.73</td><td>39.83</td><td>45.74</td><td>74.41</td><td>31.92</td><td>52.29</td><td>57.42</td><td>53.07</td></tr><tr><td>deberta-v3-large 1K</td><td>69.90</td><td>64.81</td><td>83.38</td><td>38.94</td><td>36.65</td><td>44.46</td><td>71.96</td><td>30.19</td><td>50.73</td><td>53.74</td><td>51.26</td></tr><tr><td>deberta-v3-large 500</td><td>69.71</td><td>62.00</td><td>83.54</td><td>37.23</td><td>33.68</td><td>44.56</td><td>70.48</td><td>28.70</td><td>45.64</td><td>42.67</td><td>48.31</td></tr><tr><td>deberta-v3-large label 10K</td><td>66.61</td><td>57.26</td><td>74.36</td><td>33.94</td><td>18.09</td><td>34.95</td><td>35.35</td><td>21.38</td><td>39.00</td><td>44.94</td><td>37.75</td></tr><tr><td>deberta-v3-large label 5K</td><td>68.98</td><td>61.38</td><td>80.73</td><td>35.68</td><td>20.48</td><td>37.34</td><td>54.63</td><td>24.25</td><td>36.94</td><td>51.13</td><td>42.64</td></tr><tr><td>deberta-v3-large label 3K</td><td>67.41</td><td>60.42</td><td>79.82</td><td>35.49</td><td>24.54</td><td>37.39</td><td>47.31</td><td>23.29</td><td>39.87</td><td>50.65</td><td>42.29</td></tr><tr><td>deberta-v3-large label 1K</td><td>65.55</td><td>60.93</td><td>77.70</td><td>33.29</td><td>23.36</td><td>36.38</td><td>31.10</td><td>21.71</td><td>34.28</td><td>38.31</td><td>37.01</td></tr><tr><td>deberta-v3-large label 500</td><td>60.59</td><td>54.45</td><td>76.20</td><td>32.93</td><td>19.66</td><td>31.54</td><td>45.66</td><td>13.99</td><td>33.48</td><td>44.49</td><td>37.24</td></tr><tr><td>deberta-v3-large monoT5-3B</td><td>73.05</td><td>68.82</td><td>84.78</td><td>38.55</td><td>34.43</td><td>43.61</td><td>75.45</td><td>30.75</td><td>49.85</td><td>56.80</td><td>51.78</td></tr><tr><td>deberta-v3-large chatgpt+label</td><td>72.42</td><td>67.30</td><td>85.96</td><td>38.75</td><td>35.06</td><td>45.43</td><td>71.81</td><td>28.52</td><td>45.91</td><td>55.57</td><td>50.88</td></tr><tr><td>deberta-v3-base label 10k</td><td>65.66</td><td>59.84</td><td>71.63</td><td>34.65</td><td>16.53</td><td>32.59</td><td>34.65</td><td>22.64</td><td>37.60</td><td>44.02</td><td>36.79</td></tr><tr><td>deberta-v3-small label 10k</td><td>63.63</td><td>52.83</td><td>68.17</td><td>30.48</td><td>18.12</td><td>31.72</td><td>33.62</td><td>18.02</td><td>34.57</td><td>36.09</td><td>33.85</td></tr><tr><td>deberta-v3-xsmall label 10k</td><td>60.89</td><td>51.15</td><td>63.58</td><td>28.67</td><td>14.87</td><td>27.12</td><td>20.60</td><td>18.97</td><td>32.61</td><td>32.67</td><td>29.89</td></tr><tr><td>llama-7b</td><td>71.33</td><td>66.06</td><td>78.23</td><td>37.60</td><td>34.87</td><td>45.46</td><td>76.13</td><td>34.17</td><td>51.79</td><td>55.22</td><td>51.68</td></tr><tr><td>vicuna-7b</td><td>71.80</td><td>66.89</td><td>78.32</td><td>36.87</td><td>31.81</td><td>45.40</td><td>74.23</td><td>34.28</td><td>51.13</td><td>52.91</td><td>50.62</td></tr><tr><td>llama-7b 10k label</td><td>65.22</td><td>56.85</td><td>75.36</td><td>36.24</td><td>20.88</td><td>37.34</td><td>69.04</td><td>25.22</td><td>41.21</td><td>49.21</td><td>44.31</td></tr><tr><td>llama-7b 5k label</td><td>69.24</td><td>58.97</td><td>80.49</td><td>37.55</td><td>28.23</td><td>39.66</td><td>71.79</td><td>26.04</td><td>44.09</td><td>53.83</td><td>47.71</td></tr></table>
+
+Table 13: Results (nDCG@10) on TREC and BEIR. Best performing specialized and overall system(s) are marked bold. The specialized models are fine-tined on sampled queries using relevance judgements from MARCO or ChatGPT.

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+# It Ain't Over: A Multi-aspect Diverse Math Word Problem Dataset
+
+Jiwoo Kim Youngbin Kim Ilwoong Baek JinYeong Bak Jongwuk Lee\*
+
+Sungkyunkwan University, Republic of Korea
+
+{jindog1210, andyk3603, alltun100, jy.bak,jongwuklee}@skku.edu
+
+# Abstract
+
+The math word problem (MWP) is a complex task that requires natural language understanding and logical reasoning to extract key knowledge from natural language narratives. Previous studies have provided various MWP datasets but lack diversity in problem types, lexical usage patterns, languages, and annotations for intermediate solutions. To address these limitations, we introduce a new MWP dataset, named DMath (Diverse Math Word Problems), offering a wide range of diversity in problem types, lexical usage patterns, languages, and intermediate solutions. The problems are available in English and Korean and include an expression tree and Python code as intermediate solutions. Through extensive experiments, we demonstrate that the DMath dataset provides a new opportunity to evaluate the capability of large language models, i.e., GPT-4 only achieves about  $75\%$  accuracy on the DMath<sup>1</sup> dataset.
+
+# 1 Introduction
+
+The math word problem (MWP) is a challenging and intriguing task that requires a deep understanding of natural language narratives and logical reasoning (Bobrow, 1964; Kushman et al., 2014). The narratives typically involve several numbers and unknown variables. Also, some problems demand commonsense reasoning. Solving these problems requires a comprehensive understanding of world knowledge and the reasoning between mathematical representations within a given context.
+
+As the first step to developing MWP models, it is vital to collect a representative subset of MWP to construct MWP benchmark datasets. Although many existing studies (Koncel-Kedziorski et al., 2016; Roy and Roth, 2017; Miao et al., 2020) have published various MWP corpora, they mostly lack
+
+![](images/9036ef81e76af6a8206ecd7415a56d92d060447fcefbb8c3d06ee762a5f46c19.jpg)  
+Figure 1: The accuracy of two LLMs on MWP datasets. The result of ChatGPT (gpt-3.5-turbo; OpenAI) and GPT-4 (OpenAI, 2023), using a few-shot CoT (Wei et al., 2022) prompting method, indicate that DMath is the most challenging benchmark. GPT-4 shows about  $90\%$  accuracy on three existing datasets and approximately  $75\%$  on DMath.
+
+multi-aspect diversity regarding problem types, lexical usage patterns, languages, and intermediate solution forms, as reported in Table 1. The low-diversity dataset leads to over-optimistic results for MWP models by memorizing frequent patterns.
+
+With the advent of large language models (LLMs), they have shown remarkable performances in various reasoning tasks. Notably, the adoption of GPT-4 (OpenAI, 2023) has yielded an impressive  $92\%$  accuracy on the GSM8K dataset (Cobbe et al., 2021), which is widely used as a representative MWP benchmark. This result has led to the belief that LLMs demonstrate exceptional proficiency in mathematical reasoning. However, our empirical findings show that the true capability of LLMs has not been revealed because of the limited MWP benchmarks. As illustrated in Figure 1, GPT-4 achieves more than  $90\%$  accuracy on the existing three MWP datasets, but its accuracy drops to approximately  $75\%$  on our dataset with multi-aspect diversity. This significant gap motivates us to develop more diverse datasets with greater complexity and challenges in real-world problems than existing ones.
+
+<table><tr><td>Dataset</td><td>Language</td><td>Annotation</td><td>Data size</td><td>CLD</td><td># Eq. templates</td><td># Total ops</td></tr><tr><td>MAWPS (Koncel-Kedziorski et al., 2016)</td><td>EN</td><td>Expression tree</td><td>1,921</td><td>0.26</td><td>39</td><td>4</td></tr><tr><td>MathQA (Amini et al., 2019)</td><td>EN</td><td>Expression tree</td><td>37,259</td><td>0.05</td><td>6,599</td><td>58</td></tr><tr><td>ASDiv-A (Miao et al., 2020)</td><td>EN</td><td>Expression tree</td><td>1,218</td><td>0.50</td><td>19</td><td>4</td></tr><tr><td>SVAMP (Patel et al., 2021)</td><td>EN</td><td>Expression tree</td><td>1,000</td><td>0.22</td><td>26</td><td>4</td></tr><tr><td>GSM8K (Cobbe et al., 2021)</td><td>EN</td><td>Natural language</td><td>8,792</td><td>0.81</td><td>-</td><td>4</td></tr><tr><td>Math23K (Wang et al., 2017)</td><td>ZH</td><td>Expression tree</td><td>23,160</td><td>-</td><td>2,187</td><td>4</td></tr><tr><td>Ape210K (Zhao et al., 2020)</td><td>ZH</td><td>Expression tree</td><td>210,488</td><td>-</td><td>56,532</td><td>4</td></tr><tr><td>DMath (Ours)</td><td>EN, KO</td><td>Expression tree, Python code</td><td>10,022</td><td>0.49</td><td>2,855</td><td>50</td></tr></table>
+
+Table 1: Statistics of DMath and other MWP datasets. We used corpus lexicon diversity (CLD) proposed in Miao et al. (2020) to quantify the diversity of lexical usage patterns. The higher, the more diverse. The underlined numbers represent the top-3 values in each column. Let EN, KO, and ZH denote English, Korean, and Chinese, respectively, and 'ops' denotes operators.
+
+In this study, we introduce a multi-aspect diverse MWP dataset, called DMath, which has the following key features: (1) DMath fully covers problem types across five categories outlined in the math education guideline of grade schools in the USA (CDE, 2006) and Korea (MOE, 2022). These categories include arithmetic (ARI), comparison (COM), correspondence (COR), geometry (GEO), and possibility (POS). Thus, various mathematical reasoning skills can be evaluated on DMath. (2) DMath consists of about 10,000 problems manually created by 43 human workers covering various lexical usage patterns. This diversity in lexical usage patterns helps evaluate the general performance of MWP models. (3) DMath supports bilingual input languages, i.e., English and Korean, to evaluate the effect of input languages for MWP models. (4) We offer the annotation of expression trees and Python code as intermediate solutions to evaluate the effect of expression forms in training MWP models. To annotate the expression trees, we adopt 50 operators, some newly designed to handle the operators for list structures. (Details are given in Appendix B.)
+
+To analyze the performance of various MWP models on our dataset, we employ fine-tuning and prompting approaches. For the fine-tuning method, we employ three representative MWP models with pre-trained language models, i.e., RoBERTa (Liu et al., 2019), GPT-2 (Radford et al., 2019), and CodeGPT (Lu et al., 2021). For the prompting method, we adopt representative LLMs, i.e., GPT-3 (Brown et al., 2020), ChatGPT (gpt-3.5-turbo; OpenAI), and GPT-4 (OpenAI, 2023), with various reasoning prompting methods, i.e., zero-shot (Brown et al., 2020), zero-shot CoT (Kojima et al., 2022), few-shot CoT (Wei et al., 2022), and PAL (Gao et al., 2022).
+
+Through our empirical studies on DMath, we
+
+![](images/ff10d3ec85855a7f7904091fbbe7dd6981d509f5ec7995e0d0f8a6155ab2554d.jpg)  
+Figure 2: Accuracy comparison over various reasoning categories on DMath for ChatGPT (gpt-3.5-turbo; OpenAI) and GPT-4 (OpenAI, 2023) are presented, respectively. The few-shot CoT (Wei et al., 2022) prompting is used for inference in these models.
+
+found several interesting observations. (1) Due to the multi-aspect diversity, all the MWP models on DMath yield lower performance than other datasets, with ChatGPT and GPT-4 achieving about  $60\%$  and  $75\%$  accuracy, respectively. (2) The problem types heavily affect the accuracy. As shown in Figure 2, correspondence (COR) and possibility (POS) show a relatively low accuracy, i.e.,  $44 - 49\%$  and  $62 - 65\%$  for ChatGPT and GPT-4, respectively. We conjecture that math examples are biased for training LLMs. (3) For different languages, English-based prompting methods perform better than Korean-based ones. As reported in OpenAI (2023), we also confirm that LLMs show more favorable performance on English corpora. (4) For different expression forms, Python code is more effective than other forms. As also observed in Gao et al. (2022), Python code is more robust for addressing logical expressions using external tools.
+
+# 2 Dataset Formulation
+
+The MWP sample comprises a natural narrative (input) and an answer (output). The input includes natural sentences, symbols, and math equations. The output represents a unique numeric or string value. Besides, each sample is associated with its
+
+<table><tr><td>Question(English)</td><td>You want to pick 2 fruits out of an apple, a peach,a pear and place them in different fruit baskets.What is the number of cases?</td></tr><tr><td>Question(Korean)</td><td>사과,복수어, 때 2개를 빼아 썸이다운과일 substant구nio에 갔로려고 기다于此.가通過한 겨울의수는 Many 퍻 가지일수噬?</td></tr><tr><td>Humansolution</td><td>len([apple, peach, pear]) permutation 2</td></tr><tr><td>Equation</td><td>[LIST_SOL] apple peach pear [LIST_EOL][LIST_LEN] 2 [PERM]</td></tr><tr><td>Code</td><td>a = &#x27;apple&#x27; b = &#x27;peach&#x27; c = &#x27;pear&#x27; d = 2li= [] li.append(a) li.append(b) li.append(c)e = len(li) f = 1for i, elem in enumerate(range(d)): f = f * (e - i)print(int(f))</td></tr><tr><td>Answer</td><td>6</td></tr></table>
+
+intermediate solution, e.g., a natural language, an expression tree, or Python code, to derive the answer. Because it is difficult to infer the answer from the narrative directly, the intermediate solution is used as a hint to perform math reasoning and to infer world knowledge from the narrative.
+
+To construct the MWP dataset, we annotate the sample as a triplet of  $\langle$  natural language narrative, intermediate solution, answer  $\rangle$ . In this process, we focus on extending the diversity of problem types, lexical usage patterns, languages, and intermediate solutions. Table 2 shows a sample with two input languages, i.e., English and Korean, intermediate expression forms for the expression tree and Python code, and the final answer.
+
+Diversity in problem types. To cover diverse math concepts, we refer to the math education guidelines of grade schools in the USA (CDE, 2006) and Korea (MOE, 2022). We identify four important reasoning skills in mathematics: arithmetic, relationship, geometric, and possibility. Arithmetic reasoning encompasses four fundamental math operations. Relationship reasoning requires the ability to discern relationships between objects in various phenomena. Geometric reasoning entails understanding the nature and relationship of geometric shapes. Possibility reasoning requires the ability to represent uncertainty numerically.
+
+Based on these reasoning tasks, we categorize five problem types, i.e., arithmetic (ARI) for arith-
+
+Table 2: Example of a math word problem with two languages (English and Korean), two expression forms (an equation and its corresponding Python code), a human solution, and the answer. More examples of DMath for each category can be found in Appendix A.  
+
+<table><tr><td></td><td>ARI</td><td>COM</td><td>COR</td><td>GEO</td><td>POS</td><td>Total</td></tr><tr><td>Train</td><td>2,476</td><td>1,338</td><td>1,656</td><td>1,417</td><td>1,056</td><td>7,943</td></tr><tr><td>Test</td><td>669</td><td>334</td><td>402</td><td>383</td><td>291</td><td>2,079</td></tr><tr><td>Total</td><td>3,145</td><td>1,672</td><td>2,058</td><td>1,800</td><td>1,347</td><td>10,022</td></tr></table>
+
+Table 3: The number of samples per category on DMath.
+
+metic reasoning, comparison (COM) and correspondence (COR) for relationship reasoning, geometry (GEO) for geometric reasoning, and possibility (POS) for possibility reasoning. We split the relationship reasoning into two groups due to their distinct characteristics. Please refer to Appendix A for examples of both categories. Table 3 reports the number of samples for each category.
+
+Diversity in lexical patterns. We use corpus lexicon diversity (CLD) introduced by Miao et al. (2020) to quantify lexical usage patterns. Compared to existing MWP datasets, the CLD of our dataset is 0.49. Although it is similar to ASDiv, the number of equation templates in our dataset is 2,855, much greater than ASDiv. It indicates that our problems cover various problem types with high diversity. For detail, a template represents the process of performing an operation. If the order or the type of operators is different, we regard that they are different templates.
+
+Diversity in language narratives. Existing datasets (Amini et al., 2019; Wang et al., 2017; Cobbe et al., 2021) are primarily based on monolingual language, i.e., English or Chinese. Our dataset provides bilingual languages, i.e., English and Korean. It is beneficial for validating the effect of languages on LLMs.
+
+Diversity in solution forms. To extend the usage, we annotate two expression formats, an expression tree and Python code, as illustrated in Table 2. The math equation has been widely used as an expression tree (Koncel-Kedziorski et al., 2016; Xie and Sun, 2019). Some categories require us to enumerate and select a specific number/string from a list/sequence of numbers/strings. GEO also demands extensive knowledge of geometric shapes like triangles, rectangles, and circles.
+
+To annotate our collected problems, we introduce 50 operators. (See Appendix B.) Following are some rules for defining these operators. First, we create operator names to match actual math symbols as closely as possible. (e.g., [ADD], [FLOOR], [GCD], [LIST_MAX]) Second, when some operators perform the same action, we use similar names. (e.g., (a) [LIST_GET_PERM], (b)
+
+[LIST_GET_PRODUCT], (c) [LIST_GET_DIVISOR]. (a), (b), and (c) all take a LIST as the input and return a LIST as the output through some operation (PERM, PRODUCT, DIVISOR), so "LIST_GET_" overlaps.) Third, we employ concise names, (e.g., [COMB], [LCM], [LIST_LEN], [LIST2NUM].) Lastly, if a single operator performs multiple operations, we represent the goal for operations. (e.g., [DIGIT_UNKSolver]. This operator takes an expression, and the string corresponding to the digits in the expression and finds the unknown numeric value (UNK) of the string.) Given a postfix expression tree, we also convert it into Python code automatically using our Python code generator. As the byproduct of our code generator, we can thus utilize Python code as another solution form.
+
+# 3 Dataset Construction
+
+While other MWP datasets are typically collected from the web and annotated with relevant equations, the DMath dataset exclusively comprises human-generated problems. The linguistic diversity is higher than others regarding natural languages and expression trees. Specifically, we provide a comprehensive overview of collecting, augmenting, annotating, validating, and translating the DMath dataset.
+
+Collection. Instead of curating existing math problems, we ask human workers to create new problems. We recruit 43 undergraduate and graduate students and let them develop new and diverse grade school-level math problems. Each worker contributes to creating about 100-200 samples, resulting in a total collection of 4,184 seed samples. These samples were distributed across five math categories, with 960 for arithmetic, 1,092 for comparison, 943 for correspondence, 401 for geometry, and 788 for possibility.
+
+Augmentation. Human workers manually augment seed samples using three policies: paraphrasing, domain word changes, and expanding equation trees (using a few more equations from the original sentence problem or adding other equations). We carefully augment seed samples to minimize linguistic similarities and superficial differences. Human workers manually boost 1-3 samples from each seed sample using different expressions. We also verify the similarity between seed and augmented samples using BLEU (Papineni et al., 2002) scores and remove some samples with high similarities. The statistics for BLEU score between seeds and
+
+augmented problems are 0.0 for min, 0.24 for mean, 0.23 for median, and 0.92 for max. Refer to the detailed histogram in Appendix C.
+
+Annotation. We request the worker to annotate its answer and the intermediate solution as an expression tree using pre-defined operators. This expression tree follows the postfix notation and consists of numbers, strings, and operators, as exemplified in Table 2. (See Appendix A for more examples.) While existing studies (Koncel-Kedziorski et al., 2015; Wang et al., 2017; Cobbe et al., 2021) solely focus on variables for single numbers, we introduce new variables and operators for list structure, which can be used to solve complex and various math problems. We implement an automatic code generator to convert the expression tree into Python code. We also use the Python code to validate whether the human-annotated answer is correct.
+
+Validation. We recruit 13 graduate students majoring in computer science who participate in the previous process (collection, augmentation and annotation). They are familiar with the annotation format of the MWP dataset and can solve elementary-level mathematical problems well. We perform the following process sequentially: (1) Question-answer validation, (2) Question-expression tree validation, (3) Expression tree validation, and (4) Conciseness validation of expression tree for multi-expression tree matching problems. If any error was detected during steps (1) to (3), we return to step (1) for re-validation. After that, we perform step (4).
+
+We go through these procedures to reduce potential risks to the correctness of the annotated data. For step (1) and step (2), we ensure that the questions assigned to human workers do not overlap so that they do not receive the same questions in each step, which can act as a cross-check. We employ code to check step (3). For step (4), 2-3 human workers are assigned per question. More detailed procedures are as follows.
+
+Step (1): Question-answer validation. After the annotation process, we assign natural language questions to human workers and ask them to solve the provided questions. There are two cases where their answers differ from the annotated answers. The first is when the natural language problem is unsolvable, and the second is when the annotated answer is incorrect. When a worker encounters these errors while solving a problem, the worker corrects the error manually. In the first case, the
+
+worker should correct the natural language question. In the second case, the worker should correct the annotated answer. Besides, two or more workers cross-check the corrected questions to ensure no errors.
+
+Step (2): Question-expression tree validation. Natural language questions that are solvable and correctly annotated with correct answers are given to human workers along with expression trees. The human workers check whether the given natural language question and the expression tree are correctly paired. If not, they modify the expression tree to match the natural language problem.
+
+Step (3): Expression tree validation. After the natural language question and the expression tree have been properly matched in the previous step, we verify that the expression tree produces the correct answer. The operators used in expression trees can be converted to Python code. After converting each expression tree to code, we verify if the outcome produced upon execution corresponds to the correct answer. Otherwise, return to step (1).
+
+Step (4): Conciseness validation of expression tree for multi-expression tree matching problems. There can be various potential solutions to a mathematical problem, and we maintain that selecting an expression tree is crucial to the model training. For example, the following problem has multiple expression trees. "There are six people. Everyone shook hands with each other once. Find the total number of handshakes." We can make the expression tree as one of  $6 \times (6 - 1) / 2$  or 6C2. Here, both equations lead to a reasonable correct answer. We choose the expression tree with as short an equation length as possible. (For this example, we choose 6C2.) We considered this direction of reducing the equation length because the most concise solution process captures the essence of the problem. However, even if a formula is not the shortest, we choose it if most workers agree.
+
+Translation. Once we build the Korean MWP dataset, we translate it into English. First, we use machine translation to translate Korean into English to improve the quality and quantity of translations in a limited time using Google Translator. Then, we ask nine English-majored students to revise any incorrect translations. This revision ensures that the English and Korean problems share the same meaning. It can also improve the linguistic diversity of the English language. For the whole data (# = 10,022), translators change  $71\%$  of prob
+
+lems (# = 7,121) from machine-translated ones. We further inspect  $29\%$  problems (# = 2,901) to ensure no semantic/grammatical errors. Afterward, all questions (# = 10,022) are checked for those errors. This is done by three graduate students who are not involved in the translation and are proficient in English and Korean. The results show that  $5.24\%$  (# = 525) of the questions had semantic/grammatical errors.
+
+# 4 Experimental Setup
+
+Datasets. We use three datasets to compare with DMath, which are GSM8K (Cobbe et al., 2021), SVAMP (Patel et al., 2021), and ASDiv (Miao et al., 2020). GSM8K is a commonly used dataset for evaluating math reasoning and has high quality. SVAMP is a variation of the previous dataset (MAWPS) (Koncel-Kedziorski et al., 2016), and it allows us to evaluate the robustness of the methods. ASDiv is a highly diverse dataset, showing the importance of increasing the lexical diversity of the problem. We did not run experiments on the MathQA (Amini et al., 2019) dataset because we found that it has incorrect answers, as also discussed in existing studies (Austin et al., 2021; Jie et al., 2022; Miao et al., 2020). Also, we did not compare DMath with MATH (Hendrycks et al., 2021) since there is a discrepancy in domain knowledge levels. We aimed to tackle math problems at the elementary school level (grades 1-6), while MATH is designed for the high school level (grades 8-12). See more details in Appendix D.
+
+Baselines. We evaluate the MWP solvers with the fine-tuning method and the prompting method. For the fine-tuning method, we use pre-trained language models. We use two representative models, RoBERTa (Liu et al., 2019) and GPT-2 (Radford et al., 2019) for the expression tree output and use CodeGPT (Lu et al., 2021) for the Python code output. They are fine-tuned with DMath train data. For more information on how the framework works, refer to Appendix E.
+
+For the prompting method, we use GPT-based models. We use babbage, curie, davinci (Brown et al., 2020), gpt-3.5-turbo (OpenAI), and gpt-4 (OpenAI, 2023) model using API provided by OpenAI. We denote babbage as GPT-3 [1B], curie as GPT-3 [6.7B], davinci as GPT-3 [175B], gpt-3.5-turbo as ChatGPT [175B], and gpt-4 as GPT-4 [Unknown]. Besides, we use four prompting methods: zero-shot (Brown et al., 2020), zero-shot
+
+<table><tr><td>Framework</td><td># Params.</td><td>Model</td><td>Prompt method</td><td>ARI</td><td>COM</td><td>COR</td><td>GEO</td><td>POS</td><td>Total</td></tr><tr><td rowspan="4">Fine-tuning</td><td>124M</td><td>GPT-2BASE</td><td>-</td><td>39.46</td><td>44.31</td><td>41.46</td><td>20.45</td><td>38.03</td><td>36.92</td></tr><tr><td>125M</td><td>RoBERTaBASE</td><td>-</td><td>41.60</td><td>36.92</td><td>42.37</td><td>26.28</td><td>29.90</td><td>36.54</td></tr><tr><td>355M</td><td>RoBERTaLARGE</td><td>-</td><td>45.99</td><td>42.12</td><td>49.01</td><td>32.03</td><td>35.05</td><td>41.85</td></tr><tr><td>774M</td><td>GPT-2LARGE</td><td>-</td><td>50.67</td><td>51.10</td><td>57.30</td><td>31.15</td><td>44.44</td><td>47.56</td></tr><tr><td rowspan="9">Prompting</td><td>1B</td><td rowspan="3">GPT-3</td><td rowspan="3">Few-shot CoT</td><td>4.63</td><td>25.75</td><td>4.98</td><td>6.53</td><td>8.25</td><td>8.95</td></tr><tr><td>6.7B</td><td>6.58</td><td>20.66</td><td>3.48</td><td>4.44</td><td>8.93</td><td>8.18</td></tr><tr><td>175B</td><td>18.68</td><td>37.13</td><td>9.20</td><td>10.44</td><td>10.31</td><td>17.12</td></tr><tr><td rowspan="3">175B</td><td rowspan="3">ChatGPT</td><td>Zero-shot</td><td>47.68</td><td>38.32</td><td>23.13</td><td>37.08</td><td>29.90</td><td>36.99</td></tr><tr><td>Zero-shot CoT</td><td>64.87</td><td>69.76</td><td>45.77</td><td>64.23</td><td>36.77</td><td>57.91</td></tr><tr><td>Few-shot CoT</td><td>67.26</td><td>68.26</td><td>49.00</td><td>68.67</td><td>44.67</td><td>60.99</td></tr><tr><td rowspan="3">Unknown</td><td rowspan="3">GPT-4</td><td>Zero-shot</td><td>49.93</td><td>50.00</td><td>28.11</td><td>46.21</td><td>35.74</td><td>43.05</td></tr><tr><td>Zero-shot CoT</td><td>85.65</td><td>87.43</td><td>65.92</td><td>81.72</td><td>62.54</td><td>78.16</td></tr><tr><td>Few-shot CoT</td><td>84.45</td><td>76.35</td><td>65.17</td><td>78.07</td><td>62.54</td><td>75.18</td></tr></table>
+
+Table 4: Accuracy comparison results of MWP models using expression tree solution form, GPT-2 (Radford et al., 2019), RoBERTa (Liu et al., 2019), GPT-3 (Brown et al., 2020), ChatGPT (OpenAI), and GPT-4 (OpenAI, 2023), on the English-based DMath dataset. Due to space limitation, we omit zero-shot (Brown et al., 2020) and zero-shot CoT (Kojima et al., 2022) results for GPT-3, which follow a similar trend to that of few-shot CoT.
+
+CoT (Kojima et al., 2022), few-shot CoT (Wei et al., 2022), and PAL (Gao et al., 2022) to compare the effect of different prompting methods.
+
+Evaluation metrics. To evaluate MWP solvers, we use accuracy (Acc.), commonly used in existing studies. The accuracy checks whether the final answer is correct without considering intermediate solution forms. To extract the answers from the MWP model, we use the following methods. For the fine-tuning method, we convert the expression tree solution form generated by models to Python code and take the result of the code as the answer. A model that generates Python code as the intermediate output also takes the result of the code as the answer. For the prompting method, we adopt the majority voting method. It selects the most frequent answer among the possible answers as the final answer. We treat any answer after "answer is" as a possible answer.
+
+Implementation details. For the fine-tuning models, we use pre-trained models from the huggingface hub. We set the batch size to 32 and the maximum token length to 50. We fine-tune models for three learning rates  $\{1\mathrm{e} - 5,3\mathrm{e} - 5,5\mathrm{e} - 5\}$  to find the best performance. We also run experiments with three different seed values for each learning rate, then select the best-performing learning rate and report the average value over the three seeds. We run our experiments using an NVIDIA Titan-RTX GPU with 24GB memory.
+
+For prompting-based methods, we set the temperature as 1.0 and top_p as 1.0. We also set the number of few-shot examples as 8 for
+
+GPT-3 (babbage, curie, davinci) and ChatGPT (gpt-3.5-turbo-0301), and set 5 for GPT-4 (gpt-4-0314) following the conventions (Wei et al., 2022; OpenAI, 2023). For GPT-3, we set the maximum token length to 128. Also, we set few-shot examples of GSM8K, SVAMP, and ASDiv as Wei et al. (2022) and of DMath as Appendix F. We take them differently for a fair comparison.
+
+# 5 Empirical Results
+
+Overall performance results. Table 4 presents the overall accuracies of fine-tuning and prompting MwP models. First, owing to the impressive capabilities of LLMs, GPT-4 with few-shot CoT shows the highest accuracy, achieving  $75.18\%$ . For GPT-3 [175B] and ChatGPT with the same number of parameters, there exists a notable performance gap. We conjecture that ChatGPT has undergone more optimization for mathematical reasoning compared to GPT-3. It is also worth noting that all fine-tuning models surpass GPT-3, and even the fine-tuned GPT-2  $_{LARGE}$  [774M] exhibits comparable accuracy to GPT-4 with zero-shot. This suggests that the fine-tuning approach proves effective in optimizing the MwP task.
+
+Second, the worst problem categories differ across MWP models. Both GEO and POS rely on world knowledge, impacting the performance of fine-tuning models, i.e., RoBERTa  $LARGE$  and GPT-2  $LARGE$ , differently. Fine-tuned models excel at POS due to condensed operations but struggle with expression tree-based problems in GEO. Conversely, prompting models, i.e., ChatGPT and GPT
+
+<table><tr><td>Expression form</td><td>Model</td><td># Params.</td><td>Prompt method</td><td>ARI</td><td>COM</td><td>COR</td><td>GEO</td><td>POS</td><td>Total</td></tr><tr><td>Expression tree</td><td>RoBERTaBASE</td><td>125M</td><td>-</td><td>41.60</td><td>36.92</td><td>42.37</td><td>26.28</td><td>29.90</td><td>36.54</td></tr><tr><td>Python code</td><td>CodeGPTSMALL</td><td>124M</td><td>-</td><td>42.25</td><td>35.83</td><td>32.75</td><td>23.24</td><td>33.34</td><td>34.63</td></tr><tr><td>NL prompt</td><td rowspan="2">ChatGPT</td><td rowspan="2">175B</td><td>Few-shot CoT</td><td>67.26</td><td>68.26</td><td>49.00</td><td>68.67</td><td>44.67</td><td>60.99</td></tr><tr><td>Python code prompt</td><td>PAL</td><td>74.74</td><td>52.99</td><td>52.49</td><td>61.62</td><td>46.39</td><td>60.56</td></tr><tr><td>NL prompt</td><td rowspan="2">GPT-4</td><td rowspan="2">Unknown</td><td>Few-shot CoT</td><td>84.45</td><td>76.35</td><td>65.17</td><td>78.07</td><td>62.54</td><td>75.18</td></tr><tr><td>Python code prompt</td><td>PAL</td><td>88.94</td><td>83.83</td><td>69.40</td><td>81.72</td><td>67.35</td><td>79.99</td></tr></table>
+
+Table 5: Accuracy comparison results of MWP models on the DMath dataset per expression forms in English. NL prompts used by ChatGPT (OpenAI) and GPT-4 (OpenAI, 2023) mean natural language prompts. We set few-shot CoT (Wei et al., 2022) as NL prompts method and PAL (Gao et al., 2022) as Python code prompt. We choose RoBERTa<sub>BASE</sub> (Liu et al., 2019) as the comparison model for CodeGPT<sub>SMALL</sub> (Lu et al., 2021) because it has the most similar parameter sizes.
+
+4 with few-shot CoT, trained on extensive world knowledge, perform better in GEO but falter with the Number of Cases problems in POS. In COR, the models' difficulty understanding specific problem formats contributes to performance degradation.
+
+Third, the prompting methods in LLMs also incur distinct results. ChatGPT and GPT-4 show the lowest performance for the zero-shot prompting. They can be significantly improved by using CoT prompting. However, when model sizes are too small, the impact of few-shot CoT prompting is insignificant, implying that model capacity is an important factor in prompting-based models.
+
+Lastly, we summarize our observations on five problem types. ARI and COM can be regarded as common math types frequently encountered in natural language corpora. These properties explain the relatively higher accuracies of ARI and COM than other types in both fine-tuning and prompting methods. Meanwhile, COR is a less frequent problem type in ordinary language corpora, but an appropriate substitution can solve it. This unique characteristic of COR lends itself to the clear advantage of fine-tuning approach and CoT. GEO often requires world knowledge, thus, the prompting method with LLMs is more advantageous than the fine-tuning methods. Finally, POS is represented by relatively longer equation trees, indicating a challenging problem type in general. The operations and mathematical expressions for POS are also domain-specific, limiting the generalization power of LLMs and hindering their performance in this problem type.
+
+Expression form results. Table 5 presents the result of different expression formats. Firstly, ChatGPT achieves  $60.99\%$  with natural language prompts and  $60.56\%$  with Python code prompts. While the performance of the models using natural language prompts and those using Python code
+
+prompts appear similar, a closer look reveals that a specific prompt type is preferred depending on the problem. Among the 2,079 questions in the full test set,  $15.39\%$  (# = 320) of the questions are correctly solved only on the natural language prompt,  $45.60\%$  (# = 948) are correctly solved on both the natural language prompt and the Python code prompt,  $14.96\%$  (# = 311) are correctly solved on only the Python code prompt, and  $24.05\%$  (# = 500) were incorrect.
+
+We further analyze these results by problem type. For ARI types,  $8.97\%$  of problems are correct using only natural language prompts and  $16.44\%$  are correct using only Python code prompts. For COM, the corresponding percentages are  $29.34\%$  and  $14.07\%$ , respectively. ARI and COM show the largest performance differences among the five categories between natural language prompt and Python code prompt. Python code prompts perform better on ARI types because LLM often needs correction in its calculations. The higher accuracy of natural language prompts in COM types can be attributed to the concise language expression of large and small relationships between two objects, compared to Python code.
+
+Lastly, the fine-tuning and prompting methods show similar tendencies in model performance. This tendency indicates that various forms of expression have their preferred categories. To elaborate, when we state that form of expression A outperforms form B, it does not imply that every type within A uniformly surpasses every type within B. Rather, it suggests that certain types within A outperform B, while some types in B excel over A. Within the fine-tuning framework, we compare the RoBERTa<sub>BASE</sub> with the CodeGPT<sub>SMALL</sub>. The RoBERTa<sub>BASE</sub> model uses an expression tree as the solution form, whereas the CodeGPT<sub>SMALL</sub> model uses Python code. Here,
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Model</td><td colspan="2">Prompt method</td></tr><tr><td>Zero-shot CoT</td><td>Few-shot CoT</td></tr><tr><td rowspan="2">GSM8K</td><td>ChatGPT</td><td>78.85</td><td>80.82</td></tr><tr><td>GPT-4</td><td>93.25</td><td>91.81</td></tr><tr><td rowspan="2">SVAMP</td><td>ChatGPT</td><td>77.70</td><td>82.50</td></tr><tr><td>GPT-4</td><td>88.10</td><td>91.60</td></tr><tr><td rowspan="2">ASDiv</td><td>ChatGPT</td><td>79.71</td><td>83.80</td></tr><tr><td>GPT-4</td><td>88.55</td><td>90.03</td></tr><tr><td rowspan="2">DMath</td><td>ChatGPT</td><td>57.91</td><td>60.99</td></tr><tr><td>GPT-4</td><td>78.16</td><td>75.18</td></tr></table>
+
+the length of the output sequence emerges as the most significant impact. In detail, for ARI and POS types, CodeGPTSMALL using Python code performs better, and for COM, COR, and GEO types, RoBERTaBASE model using expression tree performs better. The average token length and std. for COR types with expression tree are (6.61, 4.13), which is lower than the POS type of (10.81, 4.51). That of POS type with Python code is (129.54, 57.55), which is lower than COR type of (147.61, 205.04). In common, GEO types seem to have lower token lengths but lower performance due to the lack of domain knowledge of pre-trained models.
+
+Comparison on different datasets. Table 6 shows the results of two different prompting methods on four datasets, including DMath. Except for DMath, the GSM8K, SVAMP, and ASDiv datasets, all achieve the accuracy higher than  $90\%$  on GPT-4 and surpass  $80\%$  on ChatGPT in few-shot prompts. (Figure 1 showcases the few-shot prompt results per dataset.) The zero-shot CoT results show a similar trend. This trend can be attributed to the fact that these datasets primarily handle arithmetic reasoning problems.
+
+Instead of intentionally inflating the difficulty to undermine model performance, we have noted significant performance differences between models on our dataset. Specifically, DMath exhibits average deviations of  $13.07\%$  and  $15.35\%$  in zero-shot CoT and few-shot CoT prompting methods, respectively, on the GPT-4 model. This suggests that our dataset contains problems that can be incrementally solved as model capacity improves. The problems are challenging yet reasonable and tailored to grade school levels. In brief, our dataset pinpoints areas
+
+Table 6: Accuracy comparison between DMath and GSM8K (Cobbe et al., 2021), SVAMP (Patel et al., 2021), ASDiv (Miao et al., 2020) for different prompt methods in English.  
+
+<table><tr><td>Few-shot CoT Prompt</td><td>Acc. (%)</td></tr><tr><td>Few-shot examples of (Wei et al., 2022)</td><td>57.96</td></tr><tr><td>Uniform category random</td><td>58.97</td></tr><tr><td>Reverse uniform category random</td><td>58.68</td></tr><tr><td>Random</td><td>59.31</td></tr><tr><td>One category random</td><td>60.99</td></tr></table>
+
+Table 7: Accuracy for several few-shot CoT (Wei et al., 2022) prompting methods on the English-based DMath dataset.
+
+where large language models falter, setting a pathway for future enhancements.
+
+Few-shot selection. The few-shot prompt is given DMath and other datasets (GSM8K, SVAMP, and ASDiv) differently. Other datasets used the example of Wei et al. (2022) as in previous studies. Unlike them, DMath is a mix of different mathematical categories. We consider evaluating DMath with the same prompt as other arithmetic mathematical reasoning datasets to be unfair because there are several problem types in DMath. If we give few-shot examples of only arithmetic type, then the model will not do well except arithmetic. Therefore, various prompt selection methods were taken, and the highest-performance prompt method, one category random method was used as the final few-shot prompt examples in this paper. (See more details in Appendix F.)
+
+We validate the best-performing prompt method by comparing five few-shot CoT prompts. Table 7 shows the performance for each prompt method. First, we use the few-shot example of Wei et al. (2022) as a baseline. The other few-shot CoT prompt selects examples from DMath train data. The uniform category random selects examples according to the proportion of problems in each category; it selects 2 examples from ARI, COR, and GEO and 1 example from COM and POS each. The reverse uniform category random selects 1 problem from ARI, COR, GEO and 2 problems from COM, POS each. The Random selects examples randomly from the whole dataset. Finally, the one category random selects few-shot examples based on the type of question, i.e., if the model gets an ARI type question, it randomly selects few-shot examples of ARI type, and if it gets a POS type question, it selects few-shot examples of POS type.
+
+Language-specific performance of LLMs. Table 8 provides the results of different input languages, English and Korean. By using ChatGPT and GPT-4, we observe that the English-based prompt method performs better than its Korean
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Prompt method</td><td colspan="2">Language</td></tr><tr><td>EN</td><td>KO</td></tr><tr><td>ChatGPT</td><td rowspan="2">Few-shot CoT</td><td>60.99</td><td>46.03</td></tr><tr><td>GPT-4</td><td>75.18</td><td>65.37</td></tr></table>
+
+Table 8: Accuracy comparison results of MWP models, ChatGPT (OpenAI) and GPT-4 (OpenAI, 2023), on DMath. Few-shot CoT (Wei et al., 2022) is used as the prompting method.
+
+based counterparts despite both English and Korean problems being identical in content but expressed in different languages. Ideally, if the language understanding is independent of the mathematical reasoning, it should have produced the same accuracy. However, accuracy has shown more than a  $13\%$  and  $24\%$  difference between the two on GPT-4 model and ChatGPT, respectively. We conjecture that the data imbalance issue of LLMs leads to performance bias, as pointed out in several papers (Blodgett et al., 2020; Lai et al., 2023).
+
+Qualitative analysis of GPT-4 failure cases. We conduct a qualitative analysis on failure cases of GPT-4 with few-shot CoT. (See several examples in Appendix G.) For ARI, COM, and GEO examples, as the length of the reasoning path increases, GPT-4 generates incorrect answers more frequently. For COR, the problems about the number of digits in a number mostly incur incorrect answers. For GEO, GPT-4 failed to elicit certain domain knowledge, e.g., the rectangle that can be made to have the largest area given a perimeter is a square. For POS, we observe GPT-4 found difficulties in solving problems related to the Number of Cases.
+
+# 6 Related Work
+
+Math word problem solving datasets. Automatic MWP-solving has been explored since the 1960s (Bobrow, 1964), with work primarily focused on corpus collection and model development. Initially, small datasets were used (Kushman et al., 2014; Upadhyay and Chang, 2015; Koncel-Kedziorski et al., 2015; Hosseini et al., 2014; Roy et al., 2015; Roy and Roth, 2017; Seo et al., 2014; Shi et al., 2015). The MAWPS dataset (Koncel-Kedziorski et al., 2016) unified these small-scale datasets and incorporated various problem types. Following studies like (Huang et al., 2016; Ling et al., 2017; Amini et al., 2019; Zhao et al., 2020) enriched this further, but they were limited by their reliance on multiple choice and a lack of diverse lexical usage patterns. Recent works (Cobbe et al.,
+
+2021; Hendrycks et al., 2021) targeted a broader diversity, but more enhancement is needed. Our dataset addresses this by providing diversity in problem types, lexical usage patterns, languages, and expression forms.
+
+Math word problem solving models. Early MWP models used symbolic approaches (Kintsch and Greeno, 1985; Fletcher, 1985), but their domain specificity limited their use. Later, template-based and statistical methods (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Koncel-Kedziorski et al., 2015) improved performance but faced challenges with diverse datasets (Huang et al., 2016). Deep neural networks became popular, with RNN-based models (Wang et al., 2017, 2019), tree generation models (Xie and Sun, 2019; Zhang et al., 2020; Wu et al., 2021), and relation extraction models (Jie et al., 2022). Recent models leverage pre-trained language models like BERT (Devlin et al., 2019) to enhance performance (Tan et al., 2021; Li et al., 2021; Kim et al., 2020). Large language models have also shown significant performance improvements with techniques like step-by-step reasoning (Wei et al., 2022; Nye et al., 2021), calculation verifiers (Cobbe et al., 2021), and various prompting methods (Kojima et al., 2022; Wei et al., 2022; Gao et al., 2022). Recent studies (Huang et al., 2022; Wang et al., 2022; Madaan et al., 2023) indicate that large language models can improve reasoning capabilities autonomously without supervised data, surpassing current techniques in accuracy.
+
+# 7 Conclusion
+
+This paper proposed DMath, a collection of 10K high-quality grade school-level math word problems. It mainly pursued multi-aspect diversity for problem types, lexical usage patterns, languages, and expression forms. We evaluated various MWP models on DMath and other datasets. We observed that the logical reasoning capability of the MWP model was mainly focused on arithmetic reasoning. Because of various features, our dataset is more beneficial for inspecting the diverse reasoning abilities of models. Our dataset can also help evaluate MWP models for diverse aspects.
+
+# Limitations
+
+There are several limitations to this work. (1) Translating and annotating math problems require high human costs. Although we carefully and manually
+
+check all the samples and their annotations, our dataset might include a few samples with incorrect answers. (2) Although it is interesting to observe various model scales, evaluating pre-trained language models with different model sizes requires GPU resources and training time. Therefore, we employ three well-known pre-trained models for evaluation.
+
+# Ethics Statement
+
+Following the ACL Code of Ethics, we emphasize the ethical facets of data collection, use, and the potential ramifications of our research within artificial intelligence. This study presents a new mathematical reasoning dataset, and we have carefully examined and addressed all ethical considerations tied to its creation and usage.
+
+The construction of this mathematical reasoning dataset involved authors and human workers in the data collection, creation, and augmentation phases. All contributors have strictly followed ethical guidelines, ensuring a respectful and fair environment. We have prioritized maintaining the privacy and anonymity of all parties involved.
+
+We have gone to great lengths to confirm that the data gathered does not pose any risk of harm to grade school students, the primary demographic of our study. The content has been conscientiously curated to exclude harmful or inappropriate material, fostering a safe learning environment.
+
+The dataset's accuracy is of utmost importance, and every attempt has been made to ensure the validity of the labels. Human reviewers have manually checked all answer labels in the dataset. However, despite our rigorous efforts, we acknowledge that some errors may still exist due to the inherent limitations of manual review and the complexity of the task. We encourage users of the dataset to remain mindful of this limitation and to report any errors they encounter for continuous improvement of the dataset.
+
+We also recognize the potential misuse of the dataset, and we ardently advocate for its ethical and responsible usage within the AI community. This dataset aims to advance the understanding of mathematical reasoning among grade school students, and any use that could compromise fairness or propagate biases in AI systems is strongly discouraged.
+
+In conclusion, we strive to ensure our dataset contributes to the field of AI and mathematical rea
+
+soning in a manner that aligns with the ACL's Code of Ethics. We encourage ongoing scrutiny and discussion around the dataset's ethical implications within the research community. We are committed to balancing research innovation with ethical considerations and stand ready to address any concerns raised by the ethics committee or users of the dataset.
+
+# Acknowledgments
+
+This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2019-0-00421, No.2022-0-00006, No.2022-0-00680, and RS-2023-00219919).
+
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+
+# Table of Contents
+
+A. More examples of DMath  
+B. Operators used in expression tree solutions  
+C. Statistics for BLEU score  
+D. Characteristics of other benchmark datasets  
+E. MWP solving framework for fine-tuning methods  
+F. Prompt examples  
+G. Failed examples in GPT-4
+
+# CATEGORY: ARITHMETIC CALCULATION
+
+# Question in English
+
+There are three numbers 10, 11 and 12. What is the remainder when the smallest number is divided by the second smallest number?
+
+# Question in Korean
+
+3개의수 10, 11, 12가 옷存在一定.그증에서 가상acht는수와 2면재로acht은수로 나머지는일마일
+
+
+.
+
+# Equation
+
+[LIST_SOL] 10 11 12 [LIST_EOL] 1 [LIST_MIN] 2 [LIST_MIN] [MOD]
+
+# Code
+
+```bazel
+var_a = 10\n var_b = 11\n var_c = 12\n list_a = []\n  
+if "/" in str(var_c):n var_c = eval(str(var_c))\n list_a.append(var_c)\n  
+if "/" in str(var_b):n var_b = eval(str(var_b))\n list_a.append(var_b)\n  
+if "/" in str(var_a):n var_a = eval(str(var_a))\n list_a.append(var_a)\n  
+list_a.reverse()\n var_d = 1\n list_b = list_a.copy()\n list_b.sort()\n  
+var_e = list_b[var_d-1]\n var_f = 2\n list_c = list_a.copy()\n list_c.sort()\n  
+var_g = list_c[var_f-1]\n var_h = var_e % var_g\n  
+print(int(var_h))
+```
+
+# Answer
+
+10
+
+# CATEGORY: COMPARISON
+
+# Question in English
+
+A is 49 plus 33, B is 9 multiplied by 9. Which of the two numbers A and B is greater?
+
+# Question in Korean
+
+A是49从33到10的数，B是9从9到10的数。
+
+# Equation
+
+[LIST_SOL] A B [LIST_EOL] [LIST_SOL] 4933 [ADD] 99 [MUL] [LIST_EOL] 1 [LIST_MAX] [LIST_INDEX] [LIST_POP] [LIST_GET]
+
+# Code
+
+var_a = 'A'\n var_b = 'B'\n list_a = []\n
+
+if "/"/ in str(var_b): \n var_b = eval(str(var_b))\n list_a.append(var_b)\n
+
+if "\/" in str(var_a):\n var_a = eval(str(var_a))\n list_a.append(var_a)\n
+
+list_a.reverse()\n var_c = 49\n var_d = 33\n var_e = var_c + var_d\n
+
+var_f = 9\n var_g = 9\n var_h = var_f * var_g\n list_b = []\n
+
+if "/"/ in str(var_h):n var_h = eval(str(var_h))\n list_b.append(var_h)\n
+
+if "\/'' in str(var_e):n var_e = eval(str(var_e))\n list_b.append(var_e)\n
+
+list_b.reverse()\n var_i = 1\n list_c=list_b.copy()\n list_c.sort()\n
+
+var_j = list_c[-var_i] \n var_k = list_b.index(var_j) + 1 \n var_l = list_a[var_k-1]
+
+print(var_l)
+
+# Answer
+
+A
+
+# CATEGORY: CORRESPONDENCE
+
+# Question in English
+
+If the six-digit number 341ABC is divisible by 7, 9, and 13, how much is the three-digit number ABC?
+
+# Question in Korean
+
+341ABC7,9,13oRnupnreepelpe,Se ruiu ABCn enanin johra.
+
+# Equation
+
+341ABC [GEN_POSSIBLE_LIST] 7 [LIST_DIVISIBLE] 9 [LIST_DIVISIBLE] 13 [LIST_DIVISIBLE]  
+341ABC A [LIST_FIND_UNK] 100 [MUL] 341ABC B [LIST_FIND_UNK] 10 [MUL] 341ABC C [LIST_FIND_UNK] [ADD] [ADD]
+
+# Code
+
+var_a = '341ABC'\n ans_dict = dict()\n var_a = str(var_a)\n list_a = []\n
+
+variable_candi = set(['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'])\n
+
+for v in set(var_a):n if v in variable_candi:\n ans_dict[v] = 0\n
+
+candi = list(itertools.product('0123456789', repeat=len(ANS_dict))\n
+
+for c in candi:\n temp = var_a\n for i, (k, __) in enumerate(ans_dict.items():\n temp = temp.replace(k, str(c[i]))\n
+
+if len(var_a) == len(str(int(temp))):n new_element = int(temp)\n list_a.append(new_element)\n
+
+var_b = 7\n list_b = []; \n var_b = int(var_b)\n for i in list_a:\n i = int(i)\n if i % var_b == 0:\n list_b.append(i)\n var_c = 9\n list_c = [];
+
+var_c = int(var_c) \n for i in list_b: \n i = int(i) \n if i % var_c == 0: \n list_c.append(i) \n
+
+var_d = 13\n list_d = []\n var_d = int(var_d)\n for i in list_c:\n i = int(i)\n
+
+if i % var_d == 0:\n list_d.append(i)\n var_e = '341ABC'\n var_f = 'A'\n var_e = str(var_e)\n
+
+var_f = str(var_f)\n unk_idx = var_e.index(var_f)\n var_g = 0\n for elem in list_d:\n
+
+$\mathrm{elem} = \mathrm{str(elem)}\backslash \mathrm{n}\quad \mathrm{var\_g} = \mathrm{int(elem[unk\_idx])\backslash n}\quad \mathrm{var\_h} = 100\backslash \mathrm{n}\quad \mathrm{var\_i} = \mathrm{var\_g}^{*}\mathrm{var\_h}\backslash \mathrm{n}$
+
+var_j = '341ABC'\n var_k = 'B'\n var_j = str(var_j)\n var_k = str(var_k)\n
+
+unk_idx = var_j.index(var_k)\n var_l = 0\n for elem in list_d:\n elem = str(elem)\n
+
+var_l = int(elem[unk_idx])\n var_m = 10\n var_n = var_l * var_m\n var_o = '341ABC'\n
+
+var_p = 'C'\n var_o = str(var_o)\n var_p = str(var_p)\n unk_idx = var_o.index(var_p)\n
+
+var_q = 0\n for elem in list_d:\n elem = str(elem)\n var_q = int(elem[unk_idx])\n
+
+var_r = var_n + var_q\n var_s = var_i + var_r\n
+
+print(int(var_s))
+
+# Answer
+
+523
+
+# CATEGORY: GEOMETRY
+
+# Question in English
+
+We are trying to stick a tape in a straight line. The three tapes cut are 36 centimeters (cm), 42 centimeters (cm), and 48 centimeters (cm), respectively, and if the same part is overlapped and attached, the total length is 97 centimeters (cm). Find the length of the overlapping part.
+
+# Question in Korean
+
+TeiFlT 3-36-90 (cm), 42-90 (cm), 48-90 (cm) 90.
+
+# Equation
+
+36 42 [ADD] 48 [ADD] 97 [SUB] 31 [SUB] [DIV]
+
+# Code
+
+$$
+\operatorname {v a r} _ {-} \mathrm {a} = 3 6 \backslash \mathrm {n} \quad \operatorname {v a r} _ {-} \mathrm {b} = 4 2 \backslash \mathrm {n} \quad \operatorname {v a r} _ {-} \mathrm {c} = \operatorname {v a r} _ {-} \mathrm {a} + \operatorname {v a r} _ {-} \mathrm {b} \backslash \mathrm {n} \quad \operatorname {v a r} _ {-} \mathrm {d} = 4 8 \backslash \mathrm {n}
+$$
+
+$$
+\operatorname {v a r} _ {-} e = \operatorname {v a r} _ {-} c + \operatorname {v a r} _ {-} d \backslash n \quad \operatorname {v a r} _ {-} f = 9 7 \backslash n \quad \operatorname {v a r} _ {-} g = \operatorname {v a r} _ {-} e - \operatorname {v a r} _ {-} f \backslash n
+$$
+
+$$
+\operatorname {v a r} _ {\mathrm {h}} = 3 \backslash \mathrm {n} \quad \operatorname {v a r} _ {\mathrm {i}} = 1 \backslash \mathrm {n} \quad \operatorname {v a r} _ {\mathrm {j}} = \operatorname {v a r} _ {\mathrm {h}} - \operatorname {v a r} _ {\mathrm {i}} \backslash \mathrm {n} \quad \operatorname {v a r} _ {\mathrm {k}} = \operatorname {v a r} _ {\mathrm {g}} / \operatorname {v a r} _ {\mathrm {j}} \backslash \mathrm {n}
+$$
+
+$$
+\operatorname {p r i n t} \left(^ {\prime}:: 2 f ^ {\prime}. \text {f o r m a t} (\text {r o u n d} (\text {v a r} _ {-} k + 1 e - 1 0, 2))\right)
+$$
+
+# Answer
+
+14.50
+
+# CATEGORY: POSSIBILITY
+
+# Question in English
+
+You want to form a four-digit number using the four numbers 7, 2, 5, and 9 only once. How many four-digit numbers can you make? Question in Korean
+
+4개의 sounds 7,2,5,9을 기재 썸이어 사용해내 Auto 次를 힘들려고 픜다.만들수在哪里 Auto Auto 
+
+모두 如果
+
+# Equation
+
+[LIST_SOL] 7 2 5 9 [LIST_EOL] 4 [LIST_GET_PERM] [LIST_LEN]
+
+# Code
+
+```txt
+print(int(var_AF))  
+var_a = 7\n var_b = 2\n var_c = 5\n var_d = 9\n list_a = []\n  
+if "/" in str(var_d):n var_d = eval(str(var_d))\n list_a.append(var_d)\n  
+if "/" in str(var_c):n var_c = eval(str(var_c))\n list_a.append(var_c)\n  
+if "/" in str(var_b):n var_b = eval(str(var_b))\n list_a.append(var_b)\n  
+if "/" in str(var_a):n var_a = eval(str(var_a))\n list_a.append(var_a)\n  
+list_a.reverse()\n var_e = 4\n list_b = [str(i) for i in list_a]\n  
+list_b = list(itertools.permutations(list_b, var_e))\n list_b = ["".join(num_list) for num_list in list_b]\n  
+list_b = [str_num for str_num in list_b if str_num[0] != '0']\n list_b = [float(i) for i in list_b]\n  
+var_f = len(list_b)\n  
+print(int(var_f))
+```
+
+# Answer
+
+24
+
+# B Operators used in expression tree solutions
+
+$\mathcal{R}$  : real number,  $\mathcal{N}$  : Natural number,  $\mathcal{L}$  : List,  $\mathcal{S}$  : String,  $\mathcal{V}$  : Variable,  $\mathcal{E}$  : Equation
+
+<table><tr><td>Operation</td><td>Explanation</td><td>Examples</td></tr><tr><td>[ADD]</td><td>Get R1, R2 ⇒ Return R1 + R2</td><td>1 2 [ADD] → 3</td></tr><tr><td>[SUB]</td><td>Get R1, R2 ⇒ Return R1 - R2</td><td>2 1 [SUB] → 1</td></tr><tr><td>[DIV]</td><td>Get R1, R2 ⇒ Return R1 / R2</td><td>6 2 [DIV] → 3</td></tr><tr><td>[MUL]</td><td>Get R1, R2 ⇒ Return R1 * R2</td><td>7 5 [MUL] → 35</td></tr><tr><td>[FDIV]</td><td>Get R1, R2 ⇒ Return R1 // R2</td><td>5 3 [FDIV] → 1</td></tr><tr><td>[MOD]</td><td>Get R1, R2 ⇒ Return R1 % R2</td><td>5 3 [MOD] → 2</td></tr><tr><td>[POW]</td><td>Get R1, R2 ⇒ Return R1 ^ R2</td><td>5 2 [POW] → 25</td></tr><tr><td>[CEIL]</td><td>Get R, N ⇒ Return the value that round up R from the Nth decimal place</td><td>1.13 2 [CEIL] → 1.2</td></tr><tr><td>[FLOOR]</td><td>Get R, N ⇒ Return the value that round down R to the Nth decimal place</td><td>34.72 1 [FLOOR] → 34.7</td></tr><tr><td>[ROUND]</td><td>Get R, N ⇒ Return the value that round R to the Nth decimal place</td><td>22.679 2 [ROUND] → 22.68</td></tr><tr><td>[ABS]</td><td>Get R ⇒ Return Absolute of R</td><td>-13 [ABS] → 13</td></tr><tr><td>[COMB]</td><td>Get N1, N2 ⇒ Return N1 combination N2</td><td>3 2 [COMB] → 3</td></tr><tr><td>[PERM]</td><td>Get N1, N2 ⇒ Return N1 permutation N2</td><td>3 2 [PERM] → 6</td></tr><tr><td>[GCD]</td><td>Get N1, N2 ⇒ Return Greatest Common Divisor of N1, N2</td><td>6 3 [GCD] → 3</td></tr><tr><td>[LCM]</td><td>Get N1, N2 ⇒ Return Least Common Multiple of N1, N2</td><td>2 3 [LCM] → 6</td></tr><tr><td>[LIST SOL]</td><td>Declare start and end of LIST, Used in pairs</td><td>[LIST SOL] 1 2 [LIST_EOL] → [1 2]</td></tr><tr><td>[LIST EOL]</td><td></td><td></td></tr><tr><td>[LIST ARANGE]</td><td>Get N1, N2 and Step N3 ⇒ Return arithmetic progression LIST</td><td>0 4 1 [LIST_ARANGE] → [0 1 2 3 4]</td></tr><tr><td>[LIST Odd]</td><td>Get N1, N2 ⇒ Return odd number list between LIST N1 and N2</td><td>0 4 [LIST_ODD] → [1 3]</td></tr><tr><td>[LIST EVEN]</td><td>Get N1, N2 numbers ⇒ Return even number list between N1 and N2</td><td>0 4 [LIST EVEN] → [0 2 4]</td></tr><tr><td>[LIST POP]</td><td>Pops the topmost LIST from the stack</td><td></td></tr><tr><td>[LIST_GET_PERM]</td><td>Get L with Ns, N1 ⇒ Return all possible N1 digit natural numbers by using Ns once</td><td>[LIST SOL] 2 3 [LIST_EOL] 2
+[LIST_GET_PERM] → [23 32]</td></tr><tr><td>[LIST_GET_PRODUCT]</td><td>Get L with Ns, N1 ⇒ Return all possible N1 digit natural numbers allowing duplicate Ns</td><td>[LIST SOL] 2 3 [LIST_EOL] 2
+[LIST_GET_PRODUCT] → [22 23 32 33]</td></tr><tr><td>[GEN_POSSIBLE_LIST]</td><td>Get S with V1, V1 ⇒ Return all possible numbers by substituting 1-9 to V1</td><td>3A [GEN_POSSIBLE_LIST] → [30, ..., 39]</td></tr><tr><td>[LIST_MAX]</td><td>Get L, N ⇒ Sort L in descending order ⇒ Return Nth value in sorted L</td><td>[LIST SOL] 11 10 12 [LIST_EOL] 2
+[LIST_MAX] → 11</td></tr><tr><td>[LIST_MIN]</td><td>Get L, N ⇒ Sort L in ascending order ⇒ Return Nth value in sorted L</td><td>[LIST SOL] 11 10 12 [LIST_EOL] 1
+[LIST_MIN] → 10</td></tr><tr><td>[LIST_SUM]</td><td>Get L ⇒ Return sum of the L</td><td>[LIST SOL] 11 10 12 [LIST_EOL]
+[LIST_SUM] → 33</td></tr><tr><td>[LIST_LEN]</td><td>Get L ⇒ Return length of the L</td><td>[LIST SOL] 11 10 12 [LIST_EOL]
+[LIST_LEN] → 3</td></tr><tr><td>[LIST_GET]</td><td>Get L, N1 ⇒ Return N1th value of L (N1 starts from 1)</td><td>[LIST SOL] 11 10 12 [LIST_EOL] 3
+[LIST_GET] → 12</td></tr><tr><td>[LIST_INDEX]</td><td>Get L, N1 ⇒ Find N1 in L1 and Return index of N1 from L (index starts from 1)</td><td>[LIST SOL] 11 10 12 [LIST_EOL] 11
+[LIST_INDEX] → 1</td></tr><tr><td>[LIST_find_NUM]</td><td>Get L, N1 ⇒ Return total number of N1 in L</td><td>[LIST SOL] 1 2 3 2 1 [LIST_EOL] 1
+[LIST_find_NUM] → 2</td></tr><tr><td>[LISTMORE]</td><td>Get L, N1 ⇒ Return LIST with L's elements bigger than N1</td><td>[LIST_SOL] 11 10 12 [LIST_EOL] 11 [LIST_MORE] → 12</td></tr><tr><td>[LIST LESS]</td><td>Get L, N1 ⇒ Return LIST with L's elements smaller than N1</td><td>[LIST_SOL] 11 10 12 [LIST_EOL] 11 [LIST LESS] → 10</td></tr><tr><td>[LIST MORE EQUAL]</td><td>Get L, N1 ⇒ Return LIST with L's elements same or bigger than N1</td><td>[LIST_SOL] 11 10 12 [LIST_EOL] 11 [LIST_MORE_EQUAL] → [11 12]</td></tr><tr><td>[LIST LESS EQUAL]</td><td>Get L, N1 ⇒ Return LIST with L's elements same or smaller than N1</td><td>[LIST_SOL] 11 10 12 [LIST_EOL] 11 [LIST LESS_EQUAL] → [11 10]</td></tr><tr><td>[SET UNION]</td><td>Get L1, L2 ⇒ Return LIST which is union of L1, L2</td><td>[LIST_SOL] 1 2 3 [LIST_EOL] [LIST_SOL] 2 3 4 [LIST_EOL] [SET UNION] → [1 2 3 4]</td></tr><tr><td>[SET DIFFERENCE]</td><td>Get L1, L2 ⇒ Return L1 differnt from L2</td><td>[LIST_SOL] 1 2 3 [LIST_EOL] [LIST_SOL] 2 3 4 [LIST_EOL] [SET_DIFFERENCE] → 1</td></tr><tr><td>[SET INTERSECT]</td><td>Get L1, L2 ⇒ Return LIST which is intersect of L1, L2</td><td>[LIST_SOL] 1 2 3 [LIST_EOL] [LIST_SOL] 2 3 4 [LIST_EOL] [SET_INTERSECT] → [2 3]</td></tr><tr><td>[LIST_DIVISIBLE]</td><td>Get L, N1 ⇒ Return L's element which is divisible by N1 in LIST</td><td>[LIST_SOL] 4 10 12 [LIST_EOL] 4 [LIST_DIVISIBLE] → [4 12]</td></tr><tr><td>[LIST_DIVIDE_AND_REMAIN]</td><td>Get L, N1, N2 ⇒ Return LIST of L's element if the remainder of dividing L's element by N1 is N2.</td><td>[LIST_SOL] 4 7 12 [LIST_EOL] 3 1 [LIST_DIVIDE_AND_REMAIN] → [4 7]</td></tr><tr><td>[LIST_GET_DIVISOR]</td><td>Get N ⇒ Return LIST of divisors of N</td><td>6 [LIST_GET_DIVISOR] → [1 2 3 6]</td></tr><tr><td>[LIST_COND_MAX_MIN]</td><td>Get L1, L2 ⇒ Return LIST in which L1 is sorted in descending order according to the condition of L2</td><td>[LIST_SOL] (A) (B) (C) (D) [LIST_EOL] [LIST_SOL] (B) (D) &gt; (B) (A) &gt; (C) (B) &gt; [LIST_EOL] [LIST_COND_MAX_MIN] → (C) (B) (D) (A)</td></tr><tr><td>[LIST2NUM]</td><td>Get L ⇒ Return N with each number of digits in order of L's element</td><td>[LIST_SOL] 1 2 3 [LIST_EOL] [LIST2NUM] → 123</td></tr><tr><td>[NUM2LIST]</td><td>Get N ⇒ Return LIST of the digits of each digit of N</td><td>123 [NUM2LIST] → [1 2 3]</td></tr><tr><td>[LIST_NUM2SUM]</td><td>Get L ⇒ Return LIST of each L's element's sum of the digits</td><td>[LIST_SOL] 10 23 77 [LIST_EOL] [LIST_NUM2SUM] → [1 5 14]</td></tr><tr><td>[LIST_SEARCH FIXED_DIGIT]</td><td>Get L, N1, N2 ⇒ Return LIST, which has only elements of L with Return N1th digit are Return N2.</td><td>[LIST_SOL] 112 14 32 [LIST_EOL] 2 1 [LIST_SEARCH FIXED_DIGIT] → [112 14]</td></tr><tr><td>[DIGIT_UNKSolver]</td><td>Get E, V ⇒ Return N, which is the value of V, satisfies E. If there are multiple values that can fit in V, return LIST. V is unit digit.</td><td>A2+4B=69 A [DIGIT_UNK Solver] → 2</td></tr><tr><td>[LIST_find_UNK]</td><td>Get L, S, V ⇒ Return N, which is the value of V. If there are multiple values that can fit in V, return LIST. It should be used as a pair with [GEN_POSSIBLE_LIST]</td><td>3A [GEN_POSSIBLE_LIST] 3A A [LIST_FIND_UNK] → [0, ..., 9]</td></tr><tr><td>[NUM_UNK Solver]</td><td>Get E, S ⇒ Return N, which is the value of S, satisfies E. If there are multiple values that can fit in S, return LIST. S is not a unit digit but a string.</td><td>3/7=6/A=B/21 A [NUM_UNK Solver] → 14</td></tr></table>
+
+![](images/78a85898898e02e72fba0d33b5518e569a997aee07baa9e191bb3de163e8dde1.jpg)  
+Figure 3: The histogram of BLEU score between seed sentences and augmented sentences.
+
+# C Statistics for BLEU score
+
+The histogram for BLEU score between seed sentences and augmented sentences is in Figure 3. The statistics for BLEU score between seeds and augmented problems are here: 0.0 for min, 0.24 for mean, 0.23 for median, and 0.92 for max.
+
+# D Characteristics of other benchmarkkark datasets
+
+A model can only be considered capable of reasoning if it is capable of elementary school-level logical reasoning. The mathematical reasoning abilities are diverse, as shown Section 2; however, the current MWP task is focused on arithmetical reasoning using four fundamental arithmetic operations (Koncel-Kedziorski et al., 2015; Roy and Roth, 2017; Miao et al., 2020; Cobbe et al., 2021).
+
+Data such as MATH (Hendrycks et al., 2021) or MathQA (Amini et al., 2019) have other reasoning problems. But MATH is too domain-specific. As mentioned in Liang et al. (2016), we think the MWP task is a good problem in evaluating the ability to understand and reason because natural language narratives of grade school-level math problems have less combined syntax and contain a small amount of domain knowledge. Our objective was to develop an elementary school-level (grades 1-6) math dataset, whereas MATH caters to high-school-level (grades 8-12) mathematics. It encompasses intricate mathematical problems from AMC10, AMC12, and AIME that necessitate comprehension of advanced mathematical concepts such as trigonometric functions or imaginary numbers. To ensure a fair comparison, we compared it with grade school-level datasets such as GSM8K, SVAMP, and ASDiv.
+
+Also, MathQA has too low a lexical diversity (Miao et al., 2020). It has been modified several times by Austin et al. (2021) and Jie et al. (2022) but still not enough. We inspect 20 problems that GPT-4 fails on in modified MathQA dataset (Austin et al., 2021) and find out that  $30\%$  of problems have incorrect annotation,  $10\%$  of problems have vague problems, and  $5\%$  of problems are unsolvable. Miao et al. (2020) got similar results, saying that  $67\%$  of problems have incorrect formulas,  $23\%$  of problems have problematic descriptions, and  $10\%$  of problems have valueless answers, randomly inspecting 30 inconsistent samples. So, we choose only GSM8K (Cobbe et al., 2021), SVAMP (Patel et al., 2021), and ASDiv (Miao et al., 2020) only.
+
+# E MWP solving framework for fine-tuning methods
+
+We adopt a general framework to evaluate MWP models. It consists of three modules: template-based conversion, MWP model, and equation-to-code conversion.
+
+First, we convert some tokens in the narrative to pre-defined symbol tokens. Using a rule-based template method, we only transform pre-defined token values into specific symbols. For instance, the numerical tokens in the narrative are converted to  $[N_1], [N_2], \ldots, [N_x]$ . Besides, some pre-defined tokens are converted to the elements in the list.
+
+Second, the MWP models are trained to translate a narrative with abstract symbols into a postfix equation. Although many existing studies have been proposed, (Xie and Sun, 2019; Zhang et al., 2020; Jie et al., 2022) some models are limited to handling various operators. In other words, these models are designed to solve the binary operator data like  $+, -, \times, \div$ . DMath has many operators that are not binary. So, in this paper, we employ MWP models using pre-trained language models, i.e., RoBERTa (Liu et al., 2019) and GPT-2 (Radford et al., 2019).
+
+Lastly, we convert the postfix expression to Python code. Because the operators are pre-defined, we can generate the executable Python code from the postfix expression. When the postfix expression is imprecise, it may fail to convert the postfix expression to the Python code. We simply return a NULL value as the answer for the exceptional case. When we execute the Python code, we utilize the values for the token mapping as the argument of the Python code.
+
+# F Prompt examples
+
+In this section, we describe prompting methods used in DMath. The zero-shot (Brown et al., 2020) prompting is written to give a question and generate an answer immediately, and the zero-shot CoT (Kojima et al., 2022) prompting is written to generate the answer after giving the question and 'Let's think step by step'. Prompt examples for zero-shot and zero-shot CoT per language can be found in Table 9.
+
+<table><tr><td rowspan="2">Zero-shot</td><td>EN</td><td>Q: {problem}A: The answer is</td></tr><tr><td>KO</td><td>典型案例: {problem}...\[\text{例如: 例如}\]</td></tr><tr><td rowspan="2">Zero-shot CoT</td><td>EN</td><td>[1 step]Q: {problem}A: Let&#x27;s think step by step.[2 step]Q: {problem}A: Let&#x27;s think step by step. {1 step output} The answer is</td></tr><tr><td>KO</td><td>[1 step]典型案例: {problem}...\[\text{例如: 例如}\]A: Let&#x27;s think step by step. {1 step output} The answer is</td></tr></table>
+
+Table 9: Prompt examples per language for zero-shot (Brown et al., 2020) and zero-shot CoT (Kojima et al., 2022).
+
+In section 5, we use one category random method as examples of few-shot CoT (Wei et al., 2022) in DMath. The following table shows the few-shot examples of one category random. When using the babbage, curie, and davinci models, the prompting before the target question was truncated if few-shot CoT prompting exceeds 2049 tokens.
+
+# ARI PROMPT
+
+Q: You sold 40 toys on Day 1. On Day 2, you sold 4 times the number of toys sold on Day 1. Find out the number of toys you sold more on Day 2 compared to Day 1.
+
+A: On the Day 1, you sold 40 toys. On the Day 2, you sold 4 times more toys than on the Day 1, so you sold  $4 * 40 = 160$  toys. Therefore, the Day 2 sold  $160 - 40 = 120$  more toys than the Day 1. Therefore the answer is 120.
+
+Q: There is a banner 20 meters (m) long. I'm thinking of fixating this banner with nails. Nails were driven 1 meter (m) apart from both ends of the banner, and the remaining nails were nailed in at regular intervals. A total of 7 nails were used. Find the distance between one nail and another.
+
+A: The interval between the first and last nails is  $20 - 1 * 2 = 18$ . Since there are a total of seven nails, there are  $7 - 1 = 6$  gaps between the nails. Therefore, the interval between nails is  $18 / 6 = 3$ . Therefore the answer is 3.
+
+Q: Yeongchan's group consists of 7 people. One person can fold two paper cranes in one minute. How many minutes will it take Yeongchan's group to fold 182 paper cranes?
+
+A: In Yeongchan's group, one person can fold two paper cranes per minute, and in Yeongchan's group, there are seven people, so Yeongchan's group can fold  $2 * 7 = 14$  paper cranes per minute. If Youngchan's group folds 182 paper cranes, it takes  $182 / 14 = 13$  minutes. Therefore the answer is 13.
+
+Q: Namjoon rode his bike and traveled 96.967 kilometers (km) in 1.3 hours. If Namjoon went at a steady speed, how many kilometers (km) did he travel in 1 hour?
+
+A: The distance Namjoon went for an hour is  $96.967 / 1.3 = 74.59$  kilometers (km). Therefore the answer is 74.59.
+
+Q: There are 24 female and male students in total. Among them, 50 sheets of colored paper were equally distributed to female students only, and 2 sheets were left. How many pieces of colored paper will the girls have if there are twice as many boys as girls?
+
+A: Female students have  $50 - 2 = 48$  colored papers. When the number of girls is x, the number of boys is 2x. Since there are 24 female and male students, it is  $x + 2x = 3x = 24$ . Therefore, the number of female students is 8. One female student has  $48 / 8 = 6$ . Therefore the answer is 6.
+
+Q: There is a train that runs at 95 kilometers (km) per hour and a car that runs at 65 kilometers (km) per hour. If the train and the car travel for 8 hours at a constant speed, by how many kilometers (km) does the train travel more than the car?
+
+A: The train traveled  $95 * 8 = 760$  kilometers (km) in 8 hours, and the car traveled  $65 * 8 = 520$  kilometers (km) in 8 hours. Therefore, the train went  $760 - 520 = 240$  kilometers (km) longer than the car. Therefore the answer is 240.
+
+Q: There are a total 12 of 10-won, 50-won, and 100-won coins. I checked the total amount and it was 500 won. If the number of 10-won and 50-won coins is the same, how many 100-won coins are there?
+
+A: Let's say the number of 10-won coins and 50-won coins is x and the number of 100-won coins is y. If so, there are 12 coins worth 10, 50, and 100-won, so  $x + x + y = 12$ . Since the total amount is 500-won, it is  $10 * x + 50 * x + 100 * y = 500$ . Solving this equation, x is 5 and y is 2. Therefore the answer is 2.
+
+Q: There is a scale that can weigh more than 2 kilograms (kg). If you have lifted 3 weights of 200 grams (g) so far, find how many more weights you need to lift to measure the weight.
+
+A: I've put up three 200 grams (g) weights, so there's an  $200 * 3 = 600$  grams (g) on the scale now. 2 *  $1000 - 600 = 1400$  grams (g) is needed to weigh 2 kilograms (kg) more. Therefore,  $1400 / 200 = 7$  additional 200 grams (g) scales are needed. Therefore the answer is 7.
+
+Q: {problem}
+
+A:
+
+# COMPROMPT
+
+Q: There are 24 balloons. Of these, there are 6 more blue balloons than red balloons, red balloons are  $1/4$  of the total, and the rest are all yellow balloons. What color balloons will be the most?
+
+A: Since the red balloons are  $1/4$  of the total,  $24 * (1 / 4) = 6$  balloons. Blue balloons are  $6 + 6 = 12$  because there are 6 more blue balloons than red ones. The rest are yellow balloons, so  $24 - 6 - 12 = 6$ . Therefore, blue balloons are the most common. Therefore the answer is blue.
+
+Q: How many of 0.8, 1/2, and 0.9 are greater than 0.4?
+
+A: Of 0.8, 1/2, and 0.9, three are greater than 0.4. Therefore the answer is 3.
+
+Q: Yoongi has 4 apples and Jungkook has 6 divided by 3 apples. Who has the greater number of apples?
+
+A: Jungkook has  $6 / 3 = 2$  apples because he has 6 divided by 3 apples. Yoongi has four apples, so he has more apples than Jungkook. Therefore the answer is Yoongi.
+
+Q: Choose the 2nd smallest number among 5, 8, 4, 3, and 2.
+
+A: The second smallest number of 5, 8, 4, 3, and 2 is 3. Therefore the answer is 3.
+
+Q: Eight students stand in a line to borrow books. How many students are standing between the student standing 1st from the front and the student standing 4th from the back?
+
+A: When a total of eight students are standing in a line, there are  $8 - 1 - 4 = 3$  students between the first student in the front and the fourth student in the back. Therefore the answer is 3.
+
+Q: Taehyung, Minju, Sangmin, Yoonjung, and Yoojeong took turns crossing the finish line. Who went in first?
+
+A: Taehyung is first place. Therefore the answer is Taehyung.
+
+Q: Find the number of numbers less than or equal to 0.4 among 0.8, 1/2, and 0.3.
+
+A: The number less than or equal to 0.4 of 0.8, 1/2, and 0.3 is 0.3. Therefore the answer is 1.
+
+Q: What is the smallest number among the numbers greater than 1.1 among the numbers 1.4, 9/10, 1.2, 0.5, and 13/10?
+
+A: Among 1.4, 9/10, 1.2, 0.5, and 13/10, the number greater than 1.1 is 1.4, 1.2, and 13/10. The smallest number of these is 1.2. Therefore the answer is 1.2.
+
+Q: {problem}
+
+A:
+
+# CORPROMPT
+
+Q: There are three natural numbers A, B, and C. When A is divided by 7, the quotient is B and the remainder is C. The quotient and remainder are equal in this equation. Find the largest number among A.
+
+A: When A is divided by 7, the remaining C can be 0, 1, 2, 3, 4, 5, and 6. In order to make A the largest, C must be 6 and B must be 6. Thus, the largest A is  $6 * 7 + 6 = 48$ . Therefore the answer is 48.
+
+Q: There is a single digit number A. When 7A7 is rounded up to the tens place is 730. What is the right value for A?
+
+A: The fact that 7A7 is raised from the decimal place to 730 means that A is 2. Therefore the answer is 2.
+
+Q: Jisoo had 6,000 won and she bought a ballpoint pen for 3,200 won, an eraser for 1,000 won, and candy for 500 won. Assuming that all remaining money is saved, find the amount saved.
+
+A: The amount of money Jisoo has left after buying the product is  $6000 - 3200 - 1000 - 500 = 1300$  won. Therefore the answer is 1300.
+
+Q: The length of Siwon's ribbon is 8.8 meters longer than Seojun's. If Seojun cuts his own ribbon 4.3 meters (m) and gives it to Siwon, find out what the difference between the lengths of the two people's ribbons.
+
+A: If Siwon's ribbon length is x, Seojun's ribbon length is x - 8.8. After Seojun gives the ribbon to Siwon, the length of Seojun's ribbon is x - 8.8 - 4.3, and the length of Siwon's ribbon is x + 4.3. The difference between the two is (x + 4.3) - (x - 8.8 - 4.3) = 17.40 Therefore the answer is 17.40.
+
+Q: 37 is 69 smaller than a number. What is the number that is 55 greater than the number?
+
+A: A number that is 69 smaller than the number is 37, so the number is  $69 + 37 = 106$ . Therefore, a number greater than the number by 55 is  $106 + 55 = 161$ . Therefore the answer is 161.
+
+Q: 24 is a result of subtracting 63 from a particular number by mistake when the original calculation was to subtract 36 from that particular number. Find the result of the original calculation.
+
+A: The number is  $24 + 63 = 87$ . Correctly calculated, the value obtained by subtracting 36 from the number is  $87 - 36 = 51$ . Therefore the answer is 51.
+
+Q: It was 40 that should be subtracted from, but mistakenly subtracting 21 from a number yields 52. How much do you get when you calculate it correctly?
+
+A: The number is  $52 + 21 = 73$ . Correctly calculated, subtracting 40 from the number is  $73 - 40 = 33$ . Therefore the answer is 33.
+
+Q: You need to subtract 46 from a certain number, but mistakenly subtracted 64, and got 122. Find the result of the correct calculation.
+
+A: The number is  $122 + 64 = 186$ . To calculate correctly, subtract 46 from the number is  $186 - 46 = 140$ . Therefore the answer is 140.
+
+Q: {problem}
+
+A:
+
+# GEO PROMPT
+
+Q: There is a parallelogram that has a base of 3.6 and a height of 2.5 times the base. Find the area of this parallelogram.
+
+A: The area of the parallelogram is the product of the base and the height. Since the base of this parallelogram is 3.6 and the height is  $3.6 * 2.5 = 9$ , the area is  $3.6 * 9 = 32.4$ . Therefore the answer is 32.4.
+
+Q: 12 friends, including Yoonseok, are standing as a dodecagon. Every student shook hands once with every friend except for the friend on either side of them. How many handshakes did Yoonseok shake?
+
+A: Yoon Seok shook hands  $12 - 2 - 1 = 9$  times because he shook hands with friends except for two on both sides of him and one on his own. Therefore the answer is 9.
+
+Q: There are pretty blankets whose shape is the same as a regular tetradecagon. When the length of all corners is 154 centimeters (cm). Find the length of one edge of the blanket.
+
+A: Since there are a total of 14 edges of a square, the length of one edge is  $\frac{154}{14} = 11$ . Therefore the answer is 11.
+
+Q: How many square centimeters  $(\mathrm{cm}^2)$  is the sum of the widths of two squares, every 11 centimeters (cm) and 5 centimeters (cm) long?
+
+A: The area of a square with a side length of 11 centimeters (cm) is  $11 * 11 = 121$  square centimeters (cm²), and the area of a square with a side length of 5 centimeters (cm) is  $5 * 5 = 25$  square centimeters (cm²). The sum of the widths of the two squares is  $121 + 25 = 146$  square centimeters (cm²). Therefore the answer is 146.
+
+Q: The perimeter of the square is 17.8 centimeters (cm). Find the length of one side of this square.
+
+A: The circumference of a square is four times the length of a side. Therefore, the length of one side of a square with a circumference of 17.8 centimeters (cm) is  $\frac{17.8}{4} = 4.45$  centimeters (cm). Therefore the answer is 4.45.
+
+Q: What is the number of edges of a cube?
+
+A: The number of edges of a cube is  $6 * 2 = 12$ . Therefore the answer is 12.
+
+Q: After arranging several cans of soda in a square shape, there were 6 cans left. So, I tried to increase the width and length by one row, but 11 cans were inadequate. If you arrange these cans in 7 rows, how many cans are there in one row?
+
+A: Let's say that the number of cans of soda currently on one side of the square is  $x$ . If you want to increase the width and length by one row, you need  $2 * x + 1$  cans of soda. Currently, there are 6 cans left, and 11 cans are insufficient when trying to increase it, so it can be considered  $2 * x + 1 = 6 + 11$ . So  $x$  is 8. The number of beverage cans currently in possession is  $x * x + 6 = 8 * 8 + 6 = 70$ . If these 70 cans are set in seven rows, there are  $70 / 7 = 10$  cans in the first row. Therefore the answer is 10.
+
+Q: There is a rhombus with an area of 64/5 square centimeters  $(\mathrm{cm}^2)$ . If one diagonal is 64/9 centimeters (cm), how long is the other diagonal in centimeters (cm)?
+
+A: The area of the rhombus is equal to the product of the two diagonals in the rhombus multiplied by one-half. Thus, when one diagonal is 64/9 centimeters (cm), the length of the other diagonal is  $(64 / 5)^{*}2 / (64 / 9) = 3.6$  centimeters (cm). Therefore, the answer is 3.6.
+
+Q: {problem}
+
+A:
+
+# POS PROMPT
+
+Q: There are two types of Korean language workbooks and four types of math workbooks. When choosing one book among them, in how many cases can you choose Korean workbook or math workbook?
+
+A: When there are two types of Korean workbooks and four types of math workbooks, the number of cases in which one Korean workbooks or one math workbooks is selected is  $2 + 4 = 6$ . Therefore the answer is 6.
+
+Q: You want to create a three-digit number by drawing three different numbers from 0, 1, 3, and 5. Find the sum of the largest and smallest possible numbers.
+
+A: The largest number that can be made is 531, and the smallest number is 103. The sum of the two is 531 + 103 = 634. Therefore the answer is 634.
+
+Q: Nine digits from 1 to 9 are used once to form a nine-digit number. If this number is a multiple of 55, find the largest 9-digit number.
+
+A: The largest number of nine digits, a multiple of 55, is 987642315. Therefore the answer is 987642315.
+
+Q: How many two-digit numbers can be formed by selecting two different numbers from 1, 3, and 4?
+
+A: The number of two digits that can be made by drawing two different numbers from 1, 3, and 4 is  $3\mathrm{P}2 = 6$ . Therefore the answer is 6.
+
+Q: There are 5 marbles: red, blue, yellow, purple, and black. You want to choose two of these and give one to your younger brother and the other to your older brother as a gift. Find the number of cases in this situation.
+
+A: The number of cases in which two of the five different colored beads are selected is  $5\mathrm{P}2 = 20$ . Therefore the answer is 20.
+
+Q: You have 4 blue pencils and 1 red pencil. How many different ways can you place 5 pencils in a row?
+
+A: When there are four blue pencils and one red pencil, there are a total of five ways to put these five pencils in one line. Therefore the answer is 5.
+
+Q: How many multiples of 4 are there among the four-digit numbers made using the number cards 1, 3, 5, and 6 once?
+
+A: The four digits that can be made using the number cards 1, 3, 5, and 6 once are 1356, 1365, 1536, 1563, 3156, 3165, 3516, 3516, 3561, 3615, 3651, 5136, 5163, 5361, 5613, 6135, 6153, 6351, 6513, 6531, 6531. Among them, the multiples of 4 are 1356, 1536, 3156, 3516, 5136, and 5316. Therefore the answer is 6.
+
+Q: Find the smallest number that can be made by using all the number cards 0, 2, 4, 6, 8 and 9 only once.
+
+A: The smallest number that can be made using the number cards of 0, 2, 4, 6, 8, and 9 once is 204689. Therefore the answer is 204689.
+
+Q: {problem}
+
+A:
+
+# ARI
+
+Question: How many four-digit numbers are divisible by the two numbers 3 and 5?
+
+Reasoning: A number that is divisible by both 3 and 5 is divisible by their least common multiple (LCM). The LCM of 3 and 5 is 15. To find the number of four-digit numbers divisible by 15, we need to find the range of these numbers. The smallest four-digit number is 1000, and the largest is 9999. The smallest four-digit number divisible by 15 is 1005  $(1000 + 5)$ , and the largest is 9990 (9999 - 9). Now, we need to find how many numbers are in this range that are divisible by 15. To do this, we can divide the difference between the largest and smallest numbers by 15 and add 1.  $(9990 - 1005) / 15 + 1 = 5985 / 15 + 1 = 399 + 1 = 400$ . So, there are 400 four-digit numbers that are divisible by both 3 and 5.
+
+Correct Answer: 600
+
+# COM
+
+Question: Nine people stand in a line in order from shortest to tallest. Hoseok stands in the front. If they line up again in order from the tallest to the shortest, what number will Hoseok stand from the back?
+
+Reasoning: Since Hoseok is the shortest and stands in the front when they line up from shortest to tallest, he will be the last person when they line up from tallest to shortest. So, Hoseok will stand 9th from the back. Therefore the answer is 9.
+
+Correct Answer: 1
+
+# COR
+
+Question: When you round 34AC to the nearest hundred, you get 3400. Find the sum of the possible As.
+
+Question: When rounding 34AC to the nearest hundred, the possible values for A are 3, 4, 5, and 6. This is because if A is 3 or 4, the number will round down to 3400, and if A is 5 or 6, the number will round up to 3400. The sum of the possible As is  $3 + 4 + 5 + 6 = 18$ . Therefore, the answer is 18.
+
+Correct Answer: 10
+
+# GEO
+
+Question: How many sides are there in a polygon which 12 diagonals can be drawn from one vertex?
+
+Reasoning: If 12 diagonals can be drawn from one vertex, then there are 12 other vertices that are not adjacent to the given vertex. Since a polygon has as many sides as it has vertices, there must be  $12 + 1$  (the given vertex) = 13 sides in the polygon. Therefore, the polygon has 13 sides.
+
+Correct Answer: 15
+
+# POS
+
+Question: You want to create a three-digit number by drawing three cards out of number cards with 1, 7, 0, and 3 written on them and using them only once. Find the value of multiplying the second largest number and the second smallest number that can be made.
+
+Reasoning: The second largest number that can be made is 371, and the second smallest number is 130. The value of multiplying the two is  $371 \times 130 = 48,230$ . Therefore the answer is 48,230.
+
+Correct Answer: 78110

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2023/Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks/full.md

@@ -0,0 +1,574 @@
+# Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks
+
+Zhaohui Yan $^{1,2}$ , Songlin Yang $^{3*}$ , Wei Liu $^{1,2}$ , Kewei Tu $^{1,2\dagger}$
+
+<sup>1</sup>School of Information Science and Technology, ShanghaiTech University
+
+$^{2}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging
+
+3MIT CSAIL
+
+{yanzhh, liuwei4, tukw}@shanghaitech.edu.cn
+
+yangsl66@mit.edu
+
+# Abstract
+
+Entity and Relation Extraction (ERE) is an important task in information extraction. Recent marker-based pipeline models achieve state-of-the-art performance, but still suffer from the error propagation issue. Also, most of current ERE models do not take into account higher-order interactions between multiple entities and relations, while higher-order modeling could be beneficial. In this work, we propose HyperGraph neural network for ERE (HGERE), which is built upon the PL-marker (a state-of-the-art marker-based pipeline model). To alleviate error propagation, we use a high-recall pruner mechanism to transfer the burden of entity identification and labeling from the NER module to the joint module of our model. For higher-order modeling, we build a hypergraph, where nodes are entities (provided by the span pruner) and relations thereof, and hyperedges encode interactions between two different relations or between a relation and its associated subject and object entities. We then run a hypergraph neural network for higher-order inference by applying message passing over the built hypergraph. Experiments on three widely used benchmarks (ACE2004, ACE2005 and SciERC) for ERE task show significant improvements over the previous state-of-the-art PL-marker.
+
+# 1 Introduction
+
+Entity and Relation Extraction (ERE) is a fundamental task in information extraction (IE), compromising two sub-tasks: Named Entity Recognition (NER) and Relation Extraction (RE). There is a long debate on joint vs. pipeline methods for ERE. Pipeline decoding extracts entities first and predicts relations solely on pairs of extracted entities, while joint decoding predicts entities and relations simultaneously.
+
+Recently, the seminal work of (Zhong and Chen, 2021) shows that pipeline decoding with a frustratingly simple marker-based encoding strategy — i.e., inserting solid markers (Baldini Soares et al., 2019; Xiao et al., 2020) around predicted subject and object spans in the input text — achieves state-of-the-art RE performance. Modified sentences (with markers) are fed into powerful pretrained large language models (LLM) to obtain more subject- and object-aware representations for RE classification, which is the key to the performance improvement. However, current marker-based pipeline models (e.g., the recent state-of-the-art ERE model PL-marker (Ye et al., 2022)) only send predicted entities from the NER module to the RE module, therefore missing entities would never have the chance to be re-predicted, suffering from the error propagation issue. On the other hand, for joint decoding approaches (e.g. Table Filling methods (Miwa and Sasaki, 2014; Zhang et al., 2017; Wang and Lu, 2020))—though they do not suffer from the error propagation issue—it is hard to incorporate markers for leveraging LLMs, since entities are not predicted prior to relations. Our desire is to obtain the best of two worlds, being able to use marker-based encoding mechanism for enhancing RE performance and meanwhile alleviating the error propagation problem. We adopt PL-marker as the backbone of our proposed model and a span pruning strategy to mitigate error propagation. That is, instead of sending only predicted entity spans to the RE module, we over-predict candidate spans so that the recall of gold entity spans is nearly perfect (but there also could be many non-entity spans), transferring the burden of entity classification and labeling from the NER module to the RE module of PL-marker. The number of over-predicted spans is upper-bounded, balancing the computational complexity of marker-based encoding and the recall of gold entity span. Empirically, we find this simple strategy by itself clearly improves PL-marker.
+
+We further incorporate a higher-order interaction module into our model. Most previous ERE models either implicitly model the interactions between instances by shared parameters (Wang and Lu, 2020; Yan et al., 2021; Wang et al., 2021) or use a traditional graph neural network that models pairwise connections between a relation and an entity (Sun et al., 2019). It is difficult for these approaches to explicitly model higher-order relationships among multi-instances, e.g. the dependency among a relation and its corresponding subject and object entities. Many recent works in structured prediction tasks show that explicit higher-order modeling is still beneficial even with powerful large pretrained encoders (Zhang et al., 2020a; Li et al., 2020; Yang and Tu, 2022; Zhou et al., 2022, inter alia), motivating us to use an additional higher-order module to enhance performance.
+
+A common higher-order modeling approach is by means of probabilistic modeling (i.e., conditional random field (CRF)) with end-to-end MeanField Variational Inference (MFVI), which can be seamlessly integrated into neural networks as a recurrent neural network layer (Zheng et al., 2015a), and has been widely used in various structured prediction tasks, such as dependency parsing (Wang et al., 2019), semantic role labeling (Li et al., 2020; Zhou et al., 2022), and information extraction (Jia et al., 2022). However, the limitations of CRF modeling with MFVI are i): CRF's potential functions are parameterized in log-linear forms with strong independence assumptions, suffering from low model capacities (Qu et al., 2022), ii) MFVI uses fully-factorized Bernoulli distributions to approximate the otherwise multimodal true posterior distributions, oversimplifying the inference problem and thus is sub-optimal. Therefore we need more expressive tools to improve the quality of higher-order inference. Fortunately, there are many recent works in the machine learning community showing that graph neural networks (GNN) can be used as an inference tool and outperform approximate statistical inference algorithms (e.g., MFVI) (Yoon et al., 2018; Zhang et al., 2020b; Kuck et al., 2020; Satorras and Welling, 2021) (see (Hua, 2022) for a survey). Inspired by these works, we employ a hypergraph neural network (HyperGNN) instead of MFVI for high-order inference and propose our model HGERE (HyperGraph Neural Network for ERE). Concretely, we build a hypergraph where nodes are candidate subjects and objects (obtained
+
+from the span pruner) and relations thereof, and hyperedges encode the interactions between either two relations with shared entities or a relation and its associated subject and object entity spans. In contrast, existing GNN models for IE (Sun et al., 2019; Nguyen et al., 2021) only model the pairwise interactions between a relation and one of its corresponding entity. We empirically show the advantages of our higher-order interaction module (i.e., hypergraph neural network) over MFVI and transitional GNN models.
+
+Our contribution is three-fold: i) We adopt a simple and effective span pruning method to mitigate the error propagation issue, enforcing the power of marker-based encoding. ii) We propose a novel hypergraph neural network enhanced higher-order model, outperforming higher-order CRF-based models with MFVI. iii) We show great improvements over the prior state-of-the-art PL-marker on three commonly used benchmarks for ERE: ACE2004, ACE2005 and SciERC.
+
+# 2 Background
+
+# 2.1 Problem formulation
+
+Given a sentence  $X$  with  $n$  tokens:  $x_{1}, x_{2}, \ldots, x_{n}$ , an entity span is a sequence of tokens labeled with an entity type and a relation is an entity span pair labeled with a relation type. We denote the set of all entity spans of the sentence with a span length limit  $L$  by  $S(X) = \{s_{1}, s_{2}, \ldots, s_{m}\}$  and define  $\mathrm{ST}(i)$  and  $\mathrm{ED}(i)$  as the start and end token indices of the span  $s_{i}$ .
+
+The joint ERE task is to simultaneously solve the NER and RE tasks. Let  $\mathcal{C}_e$  be the set of entity types and  $\mathcal{C}_r$  be the set of relation types. For each span  $s_i \in S(X)$ , the NER task is to predict an entity type  $y_e(s_i) \in \mathcal{C}_e$  or  $y_e(s_i) = \mathrm{nul}1$  if the span  $s_i$  is not an entity. The RE task is to predict a relation type  $y_r(r_{ij}) \in \mathcal{C}_r$  or  $y_r(r_{ij}) = \mathrm{nul}1$  for each span  $r_{ij} = (s_i, s_j), s_i, s_j \in S(X)$ .
+
+# 2.2 Packed levitated marker (PL-marker)
+
+Zhong and Chen (2021) insert two pairs of solid markers (i.e.,  $[S]$  and  $[\backslash S])$  to highlight both the subject and object entity spans in a given sentence, and this simple approach achieves state-of-the-art RE performance. We posit that this is because LLM is more aware of the subject and object spans (with markers) and thus can produce better span representations to improve RE. But this strategy needs to iterate over all possible entity span pairs and is
+
+![](images/c6db627f024be12aeb944a2e3412dc699f4e57072c83302181456d20f86058a2.jpg)  
+Figure 1: Illustration of our framework
+
+thus slow. To tackle the efficiency problem, Zhong and Chen (2021) propose an approximated variant wherein each possible entity span is associated with a pair of levitated markers (i.e.,  $[O]$  and  $\lfloor \backslash O\rfloor$  whose representations are initialized with the positional embedding of the span's start and end tokens, and all such levitated markers are concatenated to the end of the sentence. As such, levitated-marker-based encoding needs only one pass, significantly improving efficiency at the cost of slight performance drop. Zhong and Chen (2021) also propose a masked attention mechanism such that the original input text tokens are not able to attend to markers, while markers can attend to paired markers (but not unpaired markers) and all input text tokens. As a consequence, the relative positions of levitated markers in the concatenated sentence do not matter at all, eliminating potential implausible inductive bias on the concatenation order.
+
+However, marker-base encoding is only used in RE, not in NER. To leverage marker-based encoding in the NER module for modeling span interrelations, PL-marker (Ye et al., 2022) associates each possible span with two levitated markers and concatenates all of them to the end of the input sentence. However, this strategy could make the input sentence extremely long since there are quadratic number of spans. To solve this issue, PL-marker clusters the markers based on the starting position of their corresponding spans, and divides them into  $N$  groups. Then the input sentence is duplicated  $N$  times and each group of levitated markers is concatenated to the end of one sentence copy. Ye et al. (2022) refers to this strategy as neighborhood-
+
+oriented packing scheme. Furthermore, to balance the efficiency and the model expressiveness, Ye et al. (2022) combine solid markers and levitated markers, proposing Subject-oriented Packing for Span Pair in the RE module. That is, if there are  $m$  entities, they copy the sentence for  $m$  times, and for each copy, they use solid markers to mark a different entity as the subject and concatenate the levitated markers of all other entities (as objects) at the end of the sentence.
+
+# 3 Method
+
+Overview. Our method is built upon the state-of-the-art PL-marker. We employ a high-recall span pruner to obtain candidate entity spans, similar to the NER module in PL-marker. However, instead of aiming to accurately predict all possible entity spans, our pruner focuses on removing unlikely candidates to achieve a much higher recall. Then we feed the candidate span set to the RE module to obtain entity and relation representations, which are used to initialize the node representations of our hypergraph neural network for higher-order inference with a message passing scheme. Finally, we perform NER and RE based on the refined entity and relation representations. Fig. 1 depicts the neural architecture of our model.
+
+# 3.1 Span Pruner
+
+We adopt the neighborhood-oriented packing scheme from PL-marker for span encoding, except that we simply predict entity existence (i.e., binary classification) instead of predicting entity labels during the training phrase. See Appendix A.4 for
+
+details.
+
+To produce a candidate span set, we rank all the spans by their scores and take top  $K$  as our prediction  $S_{p}(X)$ . We assume that the number of entity spans of a sentence is linear to its length  $n$ , so  $K$  is set to  $\lambda \cdot n$  where  $\lambda$  is a coefficient. For a very long sentence, the number of entity spans is often sublinear to  $n$ , while for a very short sentence, we wish to keep enough candidate spans, so we additionally set an upper and lower bound:  $K = \max(l_{\min}, \min(\lambda \cdot n, l_{\max}))$ .
+
+In practice, with our span pruner, more than  $99\%$  gold entity spans are included in the candidate set for all three datasets. If we predict entities as in PL-marker instead of pruning, only around  $95\%$  and  $80\%$  gold entities are kept in the predicted entities for ACE2005 and SciERC respectively, leading to severe error propagation (see §5.1 for an ablation study).
+
+The span pruner is trained independently from the joint ERE model introduced in the next section. This is because the joint ERE training loss will be defined based on candidate entity spans produced by the span pruner. When sharing parameters, the pruner would provide a different candidate span set during training, leading to moving targets and thereby destabilizing the whole training process.
+
+# 3.2 Joint ERE Model: First-order Backbone
+
+The backbone module is based on the RE module of PL-marker. Concretely, given an input sentence  $X = \{x_{1}, x_{2}, \dots, x_{n}\}$  and a subject span  $s_{i} = (x_{\mathrm{ST}(i)}, x_{\mathrm{ED}(i)}) \in S_{p}(X)$  provided by the span pruner, every entity span  $s_{j} \in S_{p}(X), 1 \leq j \leq K, j \neq i$  could be a candidate object span of  $s_{i}$ . The module inserts a pair of solid markers  $[S]$  and  $[\backslash S]$  before and after the subject span and assign every object span  $s_{j}$  a pair of levitated markers  $[O]_{j}$  and  $[\backslash O]_{j}$ . As shown below, the levitated markers are packed together and inserted at the end of the input sequence to a PLM:
+
+$$
+\begin{array}{l} x _ {1}, \ldots , [ S ], x _ {\mathrm {S T} (i)}, \ldots , x _ {\mathrm {E D} (i)}, [ \backslash S ], \ldots , x _ {n}, \\ [ O ] _ {1}, \dots , [ O ] _ {K}, [ \backslash O ] _ {1}, \dots , [ \backslash O ] _ {K} \\ \end{array}
+$$
+
+Then we obtain the contextualized hidden representation  $\mathbf{h}_x$  of the modified input sequence and the final subject representation is:
+
+$$
+\mathbf {h} _ {s} (s _ {i}) = \mathrm {F F N} _ {s} ([ \mathbf {h} _ {x} ([ S ]); \mathbf {h} _ {x} ([ \backslash S ]) ])
+$$
+
+FFN represents a single linear layer in this work. The object representation of  $s_j$  for the current subject  $s_i$  and the representation of relation  $r_{ij} =$
+
+$$
+(s _ {i}, s _ {j}) \text {a r e :}
+$$
+
+$$
+\mathbf {h} _ {o} ^ {i} (s _ {j}) = \mathrm {F F N} _ {o} ([ \mathbf {h} _ {x} ([ O ] _ {j}); \mathbf {h} _ {x} ([ \backslash O ] _ {j} ]) ])
+$$
+
+$$
+\mathbf {h} _ {r} (r _ {i j}) = \mathrm {F F N} _ {r} ([ \mathbf {h} _ {s} (s _ {i}); \mathbf {h} _ {o} ^ {i} (s _ {j}) ])
+$$
+
+Repeating  $K$  times, we get all  $K$  subject representations and  $K(K - 1)$  relation representations. As the object representation of  $s_j$  is not identical for different subject span  $s_i$ , there are  $K$  object representation sets  $\mathbf{h}_o^i, 1 \leq i \leq K$ . We apply a max-pooling layer to obtain a unique object representation for each object span  $s_j \in S_p(X)$ :
+
+$$
+\mathbf {h} _ {o} (s _ {j}) = \operatorname {M a x p o o l i n g} _ {1 \leq i \leq K, i \neq j} \left(\mathbf {h} _ {o} ^ {i} (s _ {j})\right)
+$$
+
+# 3.3 Joint ERE Model: Higher-order Inference with Hypergraph Neural Networks
+
+Hypergraph Building So far, the representations of the entities and relations from the backbone module do not explicitly consider beneficial interactions among related instances. To model higher-order interactions among a relation and its associated subject and object entities as well as between any two relations sharing an entity, we build a hypergraph  $\mathcal{G} = (\mathcal{V},\mathcal{E})$  to connect the related instances. The nodes set  $\mathcal{V}$  is composed of candidate subjects, objects (provided by the span pruner) and all possible pairwise relations thereof, and we denote them as  $\mathcal{V}_s = \{v_s^i |i\in [1,K]\}$ ,  $\mathcal{V}_o = \{v_s^j |j\in [1,K]\}$  and  $\mathcal{V}_r = \{v_r^{ij}|i,j\in [1,K],i\neq j\}$ .
+
+Hyperedges  $\mathcal{E}$  capture the interactions we are concerned with, and they can be divided into two categories: the subject-object-relation (sub-object-rel) hyperedges  $\mathcal{E}_{sor}$  and the relation-relation (rel-rel) hyperedges  $\mathcal{E}_{rr}$ . Each hyperedge  $e_{sor}^{ij} \in \mathcal{E}_{sor}$  connects a subject node  $v_s^i$ , an object node  $v_o^j$  and the corresponding relation node  $v_r^{ij}$ , and we refer to these hyperedges as ternary edges (ter for short). Each rel-rel edge  $e_{rr}^{ijk} \in \mathcal{E}_{rr}$  connects two relation nodes with a shared subject or object entity. We assume in a relation, the subject is the parent node and the object is the child node, and then we can refine rel-rel edges into three subtypes, sibling (sib, connecting  $v_r^{ij}$  and  $v_r^{ik}$ ), co-parent (cop, connecting  $v_r^{ij}$  and  $v_r^{kj}$ ) and grand-parent (gp, connecting  $v_r^{ij}$  and  $v_r^{jk}$ ), following the common definitions in the dependency parsing literature.
+
+If we incorporate all aforementioned hyperedges into the hypergraph, we obtain the tersibcopgp variant which is illustrated in Fig. 1. By removing some types of hyperedges we can get different variants, but without loss of generality we describe
+
+the message passing scheme in the following using tersibcopgp.
+
+As such, we can define a CRF on the hypergraph and leverage probabilistic inference algorithms such as MFVI for higher-order inference. However, as discussed in §1, we can use a more expressive method to improve inference quality and introduce a HyperGraph Neural Network (HGNN) as described next.
+
+Initial node representation For a relation node  $v_{r}^{ij}$  with its associated subject node  $v_{s}^{i}$  and object node  $v_{o}^{j}$ , we use  $\mathbf{g}^l(v_{r}^{ij}), \mathbf{g}^l(v_{s}^{i}), \mathbf{g}^l(v_{o}^{j})$  to denote their respective representation outputs from the  $l$ -th HGNN layer. Initial node representations (before being fed to a HGNN) are  $\mathbf{g}^0(v_{s}^{i}) = \mathbf{h}_{s}(s_{i})$ ,  $\mathbf{g}^0(v_{o}^{j}) = \mathbf{h}_{o}(s_{j})$  and  $\mathbf{g}^0(v_{r}^{ij}) = \mathbf{h}_{r}(r_{ij})$ , respectively (from the backbone module).
+
+Message representation A hyperedge connecting to nodes serve as the bridge for message passing between nodes connected by it. Let  $\mathcal{N}_e(v)$  be the set of hyperedges connecting to a node  $v$ .
+
+For a ter hyperedge  $e_{ter}^{ij} \in \mathcal{E}_{sor}$  connecting a subject node  $v_{s}^{i}$ , a object node  $v_{o}^{j}$  and a relation node  $v_{r}^{ij}$ , the message representation it carries is:
+
+$$
+\mathbf {h r} _ {i j} ^ {l} = \mathrm {F F N} _ {r} ^ {t e r} \big (\mathbf {g} ^ {l - 1} \big (v _ {r} ^ {i j} \big) \big)
+$$
+
+$$
+\mathbf {h s} _ {i} ^ {l} = \mathrm {F F N} _ {s} ^ {t e r} \left(\mathbf {g} ^ {l - 1} \left(v _ {s} ^ {i}\right)\right)
+$$
+
+$$
+\mathbf {h o} _ {j} ^ {l} = \mathrm {F F N} _ {o} ^ {t e r} \left(\mathbf {g} ^ {l - 1} \left(v _ {o} ^ {j}\right)\right)
+$$
+
+$$
+\mathbf {m} ^ {l} (e _ {t e r} ^ {i j}) = \mathrm {F F N} _ {e} ^ {t e r} (\mathbf {h r} _ {i j} ^ {l} \circ \mathbf {h s} _ {i} ^ {l} \circ \mathbf {h o} _ {j} ^ {l})
+$$
+
+where  $\circ$  is the Hadamard product.
+
+A rel-rel edge  $e_{z}^{ijk}\in \mathcal{E}_{rr},z\in \{sib,cop,gp\}$  connects two relations sharing an entity. For simplicity, we denote them relation  $a$  and  $b$  .If we fix  $a$  as  $a\triangleq v_r^{ij}$  , then as previously described, relation  $b$  is  $v_{r}^{ik}$  for sib edge,  $v_{r}^{kj}$  for cop edge, and  $v_{r}^{jk}$  for gp edge. The message  $e_z^{ijk}$  carries is given by,
+
+$$
+\mathbf {h} _ {\mathbf {z}} ^ {l} (a) = \mathrm {F F N} _ {a} ^ {\mathbf {z}} (\mathbf {g} ^ {l - 1} (a))
+$$
+
+$$
+\mathbf {h} _ {z} ^ {l} (b) = \operatorname {F F N} _ {b} ^ {z} (\mathbf {g} ^ {l - 1} (b))
+$$
+
+$$
+\mathbf {m} ^ {l} \left(e _ {\mathbf {z}} ^ {i j k}\right) = \mathrm {F F N} _ {e} ^ {\mathbf {z}} \left(\mathbf {h} _ {\mathbf {z}} ^ {l} (a) \circ \mathbf {h} _ {\mathbf {z}} ^ {l} (b)\right)
+$$
+
+Node representation update We aggregate messages for each node  $v\in \mathcal{V}$  from adjacent edges  $\mathcal{N}_e(v)$  with an attention mechanism by taking a learned weighted sum, and add the aggregated message to the prior node representation,
+
+$$
+\beta^ {l} (e, v) = \mathbf {w} ^ {\top} \sigma (\mathbf {W} [ \mathbf {g} ^ {l - 1} (v); \mathbf {m} ^ {l} (e) ]
+$$
+
+$$
+\alpha^ {l} (e, v) = \frac {\exp \beta^ {l} (e , v)}{\sum_ {e ^ {\prime} \in \mathcal {N} _ {e} (v)} \exp \beta^ {l} (e ^ {\prime} , v)}
+$$
+
+$$
+\mathbf {g} ^ {l} (v) = \mathbf {g} ^ {l - 1} (v) + \sum_ {e \in N _ {e} (v)} \alpha^ {l} (e, v) \mathbf {m} ^ {l} (e)
+$$
+
+where  $\sigma (\cdot)$  is a non-linear activator and  $\mathbf{W}$ ,  $\mathbf{W}$  are two trainable parameters. An entity node would receive messages only from ter edges while a relation node would receive messages from both ter edges and rel-rel edges.
+
+Training We obtain refined  $\mathbf{g}^l (v)$  from the final layer of HGNN. Give an entity span  $s_i\in S_p(X)$  we concatenate the corresponding subject representation  $\mathbf{g}^l (v_s^i)$  and object representation  $\mathbf{g}^l (v_o^i)$  to obtain the entity representation, and compute the probability distribution over the types  $\{\mathcal{C}_e\} \bigcup \{\mathrm{nu11}\}$ :
+
+$$
+P _ {e} (\hat {y} _ {e} | s _ {i}) = \operatorname {S o f t m a x} \left(\mathrm {F F N} _ {e} ^ {c l s} \left([ \mathbf {g} ^ {l} (v _ {s} ^ {i}); \mathbf {g} ^ {l} (v _ {o} ^ {i}) ]\right)\right)
+$$
+
+Given a relation  $r_{ij} = (s_i,s_j),s_i,s_j\in S_p(X)$  , we compute the probability distribution over the types  $\{\mathcal{C}_r\} \bigcup \{\mathsf{nul1}\}$  ..
+
+$$
+P _ {r} (\hat {y} _ {r} | r _ {i j}) = \operatorname {S o f t m a x} \left(\mathrm {F F N} _ {r} ^ {c l s} \left(\mathbf {g} ^ {l} \left(v _ {r} ^ {i j}\right)\right)\right)
+$$
+
+We use the cross-entropy loss for both entity and relation prediction:
+
+$$
+L _ {e} = - \sum_ {s _ {i} \in S _ {p} (X)} \log (P _ {e} (y _ {e} ^ {*} (s _ {i}) | s _ {i}))
+$$
+
+$$
+L _ {r} = - \sum_ {s _ {i}, s _ {j} \in S _ {p} (X)} \log \left(P _ {r} \left(\left(y _ {r} ^ {*} \left(r _ {i j}\right) \mid r _ {i j}\right)\right) \right.
+$$
+
+where  $y_{e}^{*}$  and  $y_{r}^{*}$  are gold entity and relation types respectively. The total loss is  $L = L_{e} + L_{r}$ .
+
+# 4 Experiment
+
+Datasets We experiment on SciERC (Luan et al., 2018), ACE2004 (Doddington et al., 2004) and ACE2005 (Walker et al., 2006). We follow Ye et al. (2022) to split ACE2004 into 5 folds and split ACE2005 and SciERC into train/dev/test sets. See Appendix A.1 for detailed dataset statistics.
+
+Evaluation metrics We report micro labeled F1 measures for NER and RE. For RE, the difference between Rel and  $\mathrm{Rel + }$  is that the former requires correct prediction of subject and object entity spans and the relation type between them, while the latter additionally requires correct prediction of subject and object entity types.
+
+<table><tr><td rowspan="2">Models</td><td rowspan="2">Encoder</td><td colspan="3">ACE2005</td><td colspan="3">ACE2004</td><td colspan="3">SciERC</td></tr><tr><td>Ent</td><td>Rel</td><td>Rel+</td><td>Ent</td><td>Rel</td><td>Rel+</td><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td>(Wadden et al., 2019)*</td><td></td><td>88.6</td><td>63.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.5</td><td>48.4</td><td>-</td></tr><tr><td>(Wang et al., 2021)*</td><td></td><td>88.8</td><td>-</td><td>64.3</td><td>87.7</td><td>-</td><td>60.0</td><td>68.4</td><td>-</td><td>36.9</td></tr><tr><td>(Zhong and Chen, 2021)*</td><td></td><td>90.1</td><td>67.7</td><td>64.8</td><td>89.2</td><td>63.9</td><td>60.1</td><td>68.9</td><td>50.1</td><td>36.8</td></tr><tr><td>(Yan et al., 2021)</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>66.8</td><td>-</td><td>38.4</td></tr><tr><td>(Shen et al., 2021)*</td><td></td><td>87.6</td><td>66.5</td><td>62.8</td><td>-</td><td>-</td><td>-</td><td>70.2</td><td>52.4</td><td>-</td></tr><tr><td>(Nguyen et al., 2021)</td><td>BERTB/SciBERT</td><td>88.9</td><td>68.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Ye et al., 2022)re</td><td></td><td>89.1</td><td>68.3</td><td>65.1</td><td>88.5</td><td>66.3</td><td>62.2</td><td>68.8</td><td>51.1</td><td>38.3</td></tr><tr><td>Backbone*</td><td></td><td>90.0</td><td>69.8</td><td>66.7</td><td>89.5</td><td>66.6</td><td>62.1</td><td>71.3</td><td>52.3</td><td>40.2</td></tr><tr><td>GCN*</td><td></td><td>90.2</td><td>69.6</td><td>66.5</td><td>90.0</td><td>67.6</td><td>63.5</td><td>74.1</td><td>54.8</td><td>42.9</td></tr><tr><td>MFVI*</td><td></td><td>90.2</td><td>69.7</td><td>67.1</td><td>89.7</td><td>67.4</td><td>63.4</td><td>73.3</td><td>54.7</td><td>42.5</td></tr><tr><td>HGERE* (our model)</td><td></td><td>90.2</td><td>70.7</td><td>67.5</td><td>89.9</td><td>68.2</td><td>64.2</td><td>74.9</td><td>55.7</td><td>43.6</td></tr><tr><td>(Liu et al., 2022)</td><td>T53B</td><td>91.3</td><td>72.7</td><td>70.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Wang and Lu, 2020)</td><td></td><td>89.5</td><td>67.6</td><td>64.3</td><td>88.6</td><td>63.3</td><td>59.6</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Wang et al., 2021)*</td><td></td><td>90.2</td><td>-</td><td>66.0</td><td>89.5</td><td>-</td><td>63.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Zhong and Chen, 2021)*</td><td></td><td>90.9</td><td>69.4</td><td>67.0</td><td>90.3</td><td>66.1</td><td>62.2</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Yan et al., 2021)</td><td></td><td>89.0</td><td>-</td><td>66.8</td><td>89.3</td><td>-</td><td>62.5</td><td>-</td><td>-</td><td>-</td></tr><tr><td>(Ye et al., 2022)re</td><td>ALBERT</td><td>91.3</td><td>72.5</td><td>70.5</td><td>90.5</td><td>69.3</td><td>66.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Backbone*</td><td></td><td>91.5</td><td>72.9</td><td>70.2</td><td>91.6</td><td>70.2</td><td>66.6</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GCN*</td><td></td><td>91.7</td><td>73.1</td><td>69.9</td><td>92.0</td><td>71.5</td><td>67.9</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MFVI*</td><td></td><td>91.6</td><td>72.7</td><td>70.1</td><td>89.9</td><td>68.5</td><td>65.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>HGERE* (our model)</td><td></td><td>91.9</td><td>73.5</td><td>70.8</td><td>91.9</td><td>71.9</td><td>68.3</td><td>-</td><td>-</td><td>-</td></tr></table>
+
+Table 1: F1 scores and standard deviations on ACE2004, ACE2005 and SciERC. The models marked with  $\star$  leverage cross-sentence information. A model with subscript  $re$  means we re-evaluate the model with the evaluation method commonly used in other work $^{2}$ . Backbone, MFVI and GCN are our baseline models.
+
+Baseline Our baseline models include: i) Backbone. It is described in Sect. 3.2 and does not contain the higher-order interaction module. ii) GCN. It has a similar architecture to Sun et al. (2019); Nguyen et al. (2021) and does not contain higher-order hyperedges. See Appendix A.6 for a detailed description. iii) MFVI. It defines a CRF on the same hypergraph as our model and uses MFVI instead of hypergraph neural networks for higher-order inference. See Appendix A.5 for a detailed description.
+
+Implementation details For a fair comparison with previous work, we use bert-base-uncased(Devlin et al., 2019) and albert-xxlargev1(Lan et al., 2020) as the base encoders for ACE2004 and ACE2005, scibert-scivocab-uncased (Beltagy et al., 2019) as the base encoder for SciERC. GCN and MFVI are also built upon Backbone. The implementation details of experiments are in Appendix A.3.
+
+Main results For HGERE, we report the best results among the following variants of hypergraphs with different types of hyperedges: ter, cop, sib, gp, tersib, tercp, tergp, tersibcp, tersibgp, tercopgp, and tersibcopgp. The best variants of HGERE are tersibcop on SciERC and ACE2005 (BERT $_B$ ); tersib on ACE2005 (ALBERT); tercop
+
+on ACE2004. For MFVI we use the same variants as used in HGERE.
+
+Table 1 shows the main results. Surprisingly, Backbone outperforms prior approaches in almost all metrics by a large margin (except on ACE2004 with  $\mathrm{BERT}_B$  and ACE2005 with ALBERT), which we attribute to the reduction of error propagation with a span pruning mechanism. Our proposed model HGERE outperforms almost all baselines in all metrics (except the entity metric on ACE2004), validating that using hyperedges to encode higher-order interactions is effective (compared with GCN) and that using hypergraph neural networks for higher-order modeling and inference is better than CRF-based probabilistic modeling with MFVI. Finally, we remark that HGERE obtains state-of-the-art performances on all the three datasets.
+
+# 5 Analysis
+
+# 5.1 Effectiveness of the span pruner
+
+To study the effectiveness of the span pruner, we replace it with an entity identifier which is the original NER module from PL-marker and is trained only on entity existence. The performance of the span pruner and the entity identifier (denoted by Eid) on entity existence is shown in Table 2. We can observe that if we replace the span pruner with the entity identifier, the recall of gold unlabeled
+
+<table><tr><td rowspan="2" colspan="2"></td><td colspan="3">SciERC</td><td colspan="3">ACE2005 (BERTB)</td></tr><tr><td>P</td><td>R</td><td>F1</td><td>P</td><td>R</td><td>F1</td></tr><tr><td rowspan="3">Eid</td><td>train</td><td>98.8</td><td>98.2</td><td>98.5</td><td>100.0</td><td>99.9</td><td>99.9</td></tr><tr><td>dev</td><td>81.0</td><td>81.6</td><td>81.3</td><td>94.7</td><td>94.6</td><td>94.7</td></tr><tr><td>test</td><td>80.4</td><td>78.7</td><td>79.5</td><td>95.6</td><td>95.8</td><td>95.7</td></tr><tr><td rowspan="3">Pruner</td><td>train</td><td>38.0</td><td>99.2</td><td>54.9</td><td>37.2</td><td>99.9</td><td>54.2</td></tr><tr><td>dev</td><td>38.1</td><td>99.1</td><td>55.0</td><td>36.4</td><td>99.7</td><td>53.3</td></tr><tr><td>test</td><td>38.7</td><td>99.2</td><td>55.7</td><td>37.0</td><td>99.8</td><td>54.0</td></tr></table>
+
+Table 2: Evaluation results on entity existence of the span pruner vs. an entity identifier.  
+
+<table><tr><td colspan="2">SciERC</td><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td rowspan="2">Eid</td><td>Backbone</td><td>69.4</td><td>50.3</td><td>39.0</td></tr><tr><td>HGERE</td><td>69.4</td><td>51.5</td><td>39.5</td></tr><tr><td rowspan="2">pruner</td><td>Backbone</td><td>71.3</td><td>52.3</td><td>40.2</td></tr><tr><td>HGERE</td><td>74.9</td><td>55.7</td><td>43.6</td></tr><tr><td colspan="2">ACE2005 (BERTB)</td><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td rowspan="2">Eid</td><td>Backbone</td><td>89.5</td><td>68.3</td><td>65.3</td></tr><tr><td>HGERE</td><td>89.5</td><td>68.5</td><td>66.0</td></tr><tr><td rowspan="2">pruner</td><td>Backbone</td><td>90.0</td><td>69.8</td><td>66.7</td></tr><tr><td>HGERE</td><td>90.2</td><td>70.7</td><td>67.5</td></tr></table>
+
+entity spans drops from 99.2 to 78.7 on the Sci-ERC test set, and drops from 99.8 to 95.8 on the ACE2005 test set. We further investigate how the choice of the span pruner vs. the entity identifier influences NER and RE performances. The results are shown in Table 3. We can see that without a span pruner, both NER and RE performances drop significantly, validating the usefulness of using a span pruner. Moreover, it has a consequent influence on the higher-order inference module (i.e., HGNN). Without a span pruner, the improvement from using a HGNN over Backbone is marginal compared to that with a span pruner. We posit that without a pruner many gold entity spans could not exist in the hypergraph of HGNNs, making true entities and relations less connected in the hypergraph and thus diminishing the usefulness of HGNNs.
+
+# 5.2 Effect of the choices of hyperedges
+
+We compare different variants of HGNN with different combinations of hyperedges. Note that if  $\text{ter}$  is not used, entity nodes do not have any hyperedges connecting to them, so their representations would not be refined. We can see that in the  $\text{sib}$
+
+Table 3: F1 scores of Backbone and HGERE with and without a pre-trained span pruner on the SciERC and ACE2005 (BERT $_B$ ) test set.  
+
+<table><tr><td rowspan="2">HGERE</td><td colspan="3">SciERC</td></tr><tr><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td>Backbone</td><td>71.3</td><td>52.3</td><td>40.2</td></tr><tr><td>ter</td><td>74.2</td><td>55.1</td><td>42.6</td></tr><tr><td>sib</td><td>71.7</td><td>54.3</td><td>41.7</td></tr><tr><td>cop</td><td>71.7</td><td>52.9</td><td>40.8</td></tr><tr><td>gp</td><td>71.3</td><td>51.9</td><td>40.1</td></tr><tr><td>tersib</td><td>74.7</td><td>55.9</td><td>43.3</td></tr><tr><td>tercop</td><td>74.7</td><td>55.7</td><td>43.6</td></tr><tr><td>tergp</td><td>74.5</td><td>54.9</td><td>42.4</td></tr><tr><td>tersibcop</td><td>74.9</td><td>55.7</td><td>43.6</td></tr><tr><td>tersibgp</td><td>74.2</td><td>54.1</td><td>41.8</td></tr><tr><td>tercopgp</td><td>74.7</td><td>54.0</td><td>42.3</td></tr><tr><td>tersibcopgp</td><td>74.3</td><td>54.6</td><td>41.7</td></tr></table>
+
+Table 4: F1 scores of HGERE with different graph topologies on the SciERC test set.
+
+and cop variants, the NER performance improves slightly, which we attribute to the shared encoder of NER and RE tasks  $^{3}$ . On the other hand, in the ter variant, entity node representations are iteratively refined, resulting in significantly better NER performance than Backbone (74.2 vs. 71.3). Combining ter edges with other rel-rel edges (e.g., sib) is generally better than using ter alone in terms of NER performance, suggesting that joint (and higher-order) modeling of NER and RE indeed has a positive influence on NER, while prior pipeline approaches (e.g., PL-marker) cannot enjoy the benefit of such joint modeling.
+
+For RE,  $sib$  and  $cop$  have positive effects on the performance (despite  $gp$  having a negative effect somehow), showing the advantage of modeling interactions between two different relations. Further combining them with  $ter$  improves RE performances in all cases, indicating that NER also has a positive effect on RE and confirming again the advantage of joint modeling of NER and RE.
+
+# 5.3 Inference speed of higher-order module
+
+To analyze the computing cost of our higher-order module, we present the inference speed of HGERE with three baseline models Backbone, GCN and MFVI on the test sets of SciERC and ACE2005. Inference speed is measured by the number of candidate entities processed per second. The results are shown in Table 5. We can observe that
+
+when utilizing a relatively smaller PLM, HGERE, GCN and MFVI were slightly slower than the first-order model Backbone. However, the difference in speed between HGERE and the other models was relatively small. When using ALBERT, which is much slower than  $\mathrm{BERT}_B$ , all four models demonstrated comparable inference speeds.
+
+<table><tr><td></td><td>SciERC</td><td colspan="2">ACE2005</td></tr><tr><td></td><td>SciBERT</td><td>BERTB</td><td>ALBERT</td></tr><tr><td>Backbone</td><td>19.4</td><td>38.0</td><td>6.1</td></tr><tr><td>GCN</td><td>15.7</td><td>33.8</td><td>6.3</td></tr><tr><td>MFVI</td><td>16.5</td><td>36.9</td><td>6.1</td></tr><tr><td>HGERE</td><td>15.7</td><td>30.7</td><td>6.0</td></tr></table>
+
+Table 5: Comparison of inference speed (#entities/sec) between HGERE and three baseline models on test sets of SciERC and ACE2005.
+
+# 5.4 Error correction analysis
+
+We provide quantitative error correction analysis between our higher-order approach HGERE and the first-order baseline Backbone on the SciERC dataset in Fig. 2. We can see that most error corrections of entities and relations made by HGERE come from two categories. The first category is where Backbone incorrectly predicts a true entity or relation as null, and the second category is where Backbone incorrectly assigns a label to a null sample.
+
+# 6 Related Work
+
+Entity and relation extraction The entity and relation extraction task has been studied for a long time. The mainstream methods could be divided into pipeline and joint approaches. Pipeline methods tackle the two subtasks, named entity recognition and relation extraction, consecutively (Zelenko et al., 2003; Chan and Roth, 2011; Zhong and Chen, 2021; Ye et al., 2022). By utilizing a new marker-based embedding method, Ye et al. (2022) becomes the new state-of-the-art ERE model. However, pipeline models have the inherent error propagation problem and they could not fully leverage interactions across the two subtasks. Joint approaches, on the other hand, can alleviate the problem by simultaneously tackling the two subtasks, as empirically revealed by Yan et al. (2022). Various joint approaches have been proposed to tackle ERE. Miwa and Bansal (2016); Katiyar and Cardie (2017) use a stacked model for joint learning through shared
+
+![](images/27be78fdc2a20ac45b60f0e3869d4465af270bb566b0f0865bc807a573d54632.jpg)  
+(a) Error correction matrix of HGERE vs. Backbone of entities
+
+Figure 2: Error correction of entity and relation types on the SciERC dataset. Red color indicates positive corrections and blue color indicates negative corrections. Specifically, positive numbers on the diagonal of the matrix (in red color) indicate that HGERE makes more correct predictions compare to Backbone; negative numbers on non-diagonal entries (in red color) indicate that HGERE makes fewer wrong predictions compare to Backbone. Numbers in blue indicate the opposite. We do not count the null-null case.  
+![](images/c8970ef9329de4811e84ab754378f7e56f8f092dac729dfe08e6927b06fd856c.jpg)  
+(b) Error correction matrix of HGERE vs. Backbone of relations
+
+parameters. Miwa and Sasaki (2014); Gupta et al. (2016); Wang and Lu (2020); Wang et al. (2021); Yan et al. (2021) tackle both the NER and RE tasks as tagging entries of a table. Fu et al. (2019); Sun et al. (2019) leverage a graph convolutional network (GCN) on an instance dependency graph to enhance instance representations. (Nguyen et al., 2021) propose a framework to tackle multiple Information Extraction tasks jointly including the ERE task where a GCN is used to capture the interactions between related instances.
+
+Another line of research is based on text-to-text models for structure prediction including ERE. Normally they are not task-specialized and could solve
+
+several structure prediction tasks in a unified way (Paolini et al., 2021; Lu et al., 2022; Liu et al., 2022).
+
+This work is similar to Sun et al. (2019); Nguyen et al. (2021) for we both use a graph neural network to enhance the instance representations. The main difference is that the GCN they use cannot adequately model higher-order relationship among multiple instances, while our hypergraph neural network is designed for higher-order modeling.
+
+CRF-based higher-order model A commonly used higher-order model utilizes approximate inference algorithms (mean-field variational inference or loopy belief propagation) on CRFs. Zheng et al. (2015b) formulate the mean-field variational inference algorithm on CRFs as a stack of recurrent neural network layers, leading to an end-to-end model for training and inference. Many higher-order models employ this technique for various NLP tasks, such as semantic parsing (Wang et al., 2019; Wang and Tu, 2020) and information extraction (Jia et al., 2022).
+
+Hypergraph neural network Hypergraph neural network (HyperGNN) is another way to construct an higher-order model. Traditional Graph Neural Networks employ pairwise connections among nodes, whereas HyperGNNs use a hypergraph structure for data modeling. Feng et al. (2019) and Bai et al. (2021) proposed spectral-based HyperGNNs utilizing the normalized hypergraph Laplacian. Arya et al. (2020) is a spatial-based HyperGNN which aggregates messages in a two-stage procedure. Huang and Yang (2021) proposed UniGNN, a unified framework for interpreting the message passing process in HyperGNN. Gao et al. (2023) introduced a general high-order multi-modal data correlation modeling framework to learn an optimal representation in a single hypergraph based framework.
+
+# 7 Conclusion
+
+In this paper, we present HGERE, a joint entity and relation extraction model equipped with a span pruning mechanism and a higher-order interaction module (i.e., HGNN). We found that simply using the span pruning mechanism by itself greatly improves the performance over prior state-of-the-art PL-marker, indicating the existence of the error propagation problem for pipeline methods. We compared our model with prior transitional GNN-
+
+based models which do not contain hyperedges connecting multiple instances and showed the improvement, suggesting that modeling higher-order interactions between multiple instances is beneficial. Finally, we compared our model with the most popular higher-order CRF models with MFVI and showed the advantages of HGNN in higher-order modeling.
+
+# Limitations
+
+Our model achieves a significant improvement in most cases (on ACE2004, SciERC datasets and on ACE2005 with Bert<sub>base</sub>). While on ACE2005 with stronger encoder (e.g., ALBERT) we observe less significant improvements. We posit that, with powerful encoders, the recall of gold entity spans would increase, thereby mitigating the error propagation issue and diminishing the benefit of using a span pruning mechanism.
+
+Another concern regarding our model is computational efficiency. The time complexity of the Subject-oriented Packing for Span Pair encoding scheme from PL-marker grows linearly with the size of candidate span size. Recall that we overpredict many spans using a span pruning mechanism, which slows down the running time. In practice, our model's running time is around as three times as that of PL-marker.
+
+# Acknowledgments
+
+This work was supported by the National Natural Science Foundation of China (61976139).
+
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+
+# A Appendix
+
+# A.1 Datasets
+
+We use ACE2004, ACE2005 and SciERC datasets in our experiments, the data statistics of each dataset is shown in Table 6.
+
+<table><tr><td></td><td>#sent</td><td>#entity</td><td>#relation</td></tr><tr><td>ACE2004</td><td>8683</td><td>22735</td><td>4087</td></tr><tr><td>ACE2005</td><td>14525</td><td>38287</td><td>7070</td></tr><tr><td>SciERC</td><td>2687</td><td>8094</td><td>4648</td></tr></table>
+
+Table 6: The statistic of datasets
+
+# A.2 Bidirectional prediction of RE
+
+Following previous work (Eberts and Ulges, 2020; Ye et al., 2022), we establish an inverse relation for each asymmetric relation for a bidirectional prediction. The model can learn the inverse relations of asymmetric relations and improve the performance in this way.
+
+# A.3 Implementation details
+
+We adopt the same cross-sentence information incorporating method used in (Zhong and Chen, 2021; Ye et al., 2022) which extend the original sentence to a fixed window size  $W$  with its left and right context. We set  $W = 512$  for SciERC,  $W = 384$  for ACE2004 and  $W = 256$  for ACE2005. For
+
+the pruner training and inference, we consider the span length limitation  $L$  of 12 for SciERC and 8 for ACE2004 and ACE2005. For pruners of any datasets and PLMs, the top-K ratio  $\lambda = 0.5$ , the boundaries of  $K$  are  $l_{\min} = 3, l_{\max} = 18$ . We use three hypergraph convolution layers for GCN, MFVI and HGERE. As the entity recall is high enough, pruners use on ACE2004 and ACE2005 are only trained with  $\mathrm{BERT}_B$ . For all experiments, we run each configuration with 5 different seeds and report the average micro-F1 scores and standard deviation.
+
+For the pruner, the output sizes of  $\mathrm{FFN_{ST}},\mathrm{FFN_{ED}}$  and  $\mathrm{FFN}_q$  are  $d_m = 768$  the bi-affine embedding size  $d_{\mathrm{biaf}} = 256$  ,the output size of  $\mathrm{FFN_{attn}}$  is 256.
+
+For the backbone module, the output sizes of  $\mathrm{FFN}_s,\mathrm{FFN}_o$  and  $\mathrm{FFN}_r$  are tuned on [400, 512, 768] for all datasets.
+
+For the hypergraph neural network, the output sizes of  $\mathrm{FFN}_r^{ter}$ ,  $\mathrm{FFN}_s^{ter}$ ,  $\mathrm{FFN}_o^{ter}$ ,  $\mathrm{FFN}_a^z$ ,  $\mathrm{FFN}_b^z$  are tuned among [256, 400, 512] and fixed on 400 for all experiments on SciERC. The output sizes of  $\mathrm{FFN}_e^{ter}$ ,  $\mathrm{FFN}_e^z$  are tune on [256, 400, 512, 768] for all experiments. For GCN, MFVI and HGERE, we all use three layers to refine the node representations. We train our models with Adam optimizer and a liner scheduler with warmup ratio of 0.1. We tune the eps of Adam optimizer on  $[1e - 8, 1e - 9]$  for ACE2005, and  $\mathrm{eps} = 1e - 8$  for other datasets. The batch size of all experiments are 18. The learning rate of PLM are  $2e - 5$ , for other modules the learning rate is tune on  $[5e - 5, 1e - 4]$ . The epochs on SciERC for Backbone are 20, and 30 for other models. The epochs on ACE2004 and ACE2005 (BERT $_B$ ) are 15, on ACE2004 and ACE2005 (ALBERT) are 10. We do all experiments on a A40 GPU with apex fp16 training option on.
+
+# A.4 Details of the span pruner
+
+We obtain contextualized representations of the tokens  $\mathbf{x}$  and levitated marker representations xs (for  $[O])$  and xe (for  $\lfloor \backslash O\rfloor$  ). Then we concatenate two kinds of span representations—bi-affine (Dozat and Manning, 2016) and attentive pooling—as the final one. For a span  $s_i$  consisting of tokens  $x_{\mathrm{ST}(i)},\dots,x_{\mathrm{ED}(i)}$ , its bi-affine span representation
+
+is a  $d_{\mathrm{biaf}}$  -dimension vector,
+
+$$
+\mathbf {h} _ {\mathrm {S T}} (s _ {i}) = \operatorname {F F N} _ {\mathrm {S T}} \left(\mathbf {x} _ {\mathrm {S T} (i)}; \mathbf {x s} (i)\right)
+$$
+
+$$
+\mathbf {h} _ {\mathrm {E D}} (s _ {i}) = \mathrm {F F N} _ {\mathrm {E D}} (\mathbf {x} _ {\mathrm {E D} (i)}; \mathbf {x e} (i))
+$$
+
+$$
+\mathbf {h} _ {\mathrm {b i a f}} (s _ {i}) = \left[ \mathbf {h} _ {\mathrm {S T}} (s _ {i}); 1 \right] ^ {\top} W _ {p} \left[ \mathbf {h} _ {\mathrm {E D}} (s _ {i}); 1 \right]
+$$
+
+the symbol ; is the concatenation operation,  $\mathrm{FFN_{ST}}$  and  $\mathrm{FFN_{ED}}$  are feed-forward layers with an output size  $d_m$  and  $W_{p}\in \mathbb{R}^{(d_{m} + 1)*d_{\mathrm{biaf}}*(d_{m} + 1)}$  is a learn-able weight. The attentive pooling layer is a weighted average over the contextualize token representations in the span,
+
+$$
+w _ {j} = \mathrm {F F N} _ {q} (\mathbf {x} _ {j}); w _ {j} = \frac {\exp w _ {j}}{\sum_ {\mathrm {S T} (i) \leq l \leq \mathrm {E D} (i)} \exp w _ {l}}
+$$
+
+$$
+\mathbf{h}_{\mathrm{attn}}(s_{i}) = \sum_{\substack{\mathrm{ST}(i)\leq j\leq \mathrm{ED}(i)}}w_{j}\mathbf{x}_{j}
+$$
+
+and the final span representation is,
+
+$$
+\mathbf {h} (s _ {i}) = \mathrm {F F N} _ {\mathrm {a t t n}} [ \mathbf {h} _ {\mathrm {b i a f}} (s _ {i}); \mathbf {h} _ {\mathrm {a t t n}} (s _ {i}) ]
+$$
+
+Training and Inference Given the gold binary tag  $y(s_{i}) \in \{0,1\}$  (indicating the existence of a candidate span in the gold span set), we train the span pruner with the binary cross-entropy (BCE) loss:
+
+$$
+\hat {y} (s _ {i}) = \operatorname {S i g m o i d} (\operatorname {F F N} (\mathbf {h} (s _ {i})))
+$$
+
+$$
+\begin{array}{l} L = - \sum_ {1 \leq i \leq m} \left[ y (s _ {i}) \log \hat {y} (s _ {i}) \right. \\ + (1 - y \left(s _ {i}\right)) \left(1 - \log \hat {y} \left(s _ {i}\right) \right] \\ \end{array}
+$$
+
+# A.5 Mean-field Variant Inference
+
+Here we introduce the method used in baseline MFVI. The hyperedges in our graph are replaced by factors in MFVI, so there are also four kinds of factors: ter, sib, cop, gp.
+
+first-order scores We use the node representations to score the entities and relations for each label (include the nu11).
+
+$$
+\mathbf {u} _ {i} ^ {s} = \operatorname {F F N} _ {s} ^ {u} \left(\mathbf {g} \left(v _ {s} ^ {i}\right)\right)
+$$
+
+$$
+\mathbf {u} _ {j} ^ {o} = \mathrm {F F N} _ {o} ^ {u} (\mathbf {g} (v _ {o} ^ {j}))
+$$
+
+$$
+\mathbf {u} _ {i j} ^ {r} = \operatorname {F F N} _ {r} ^ {u} (\mathbf {g} \left(v _ {r} ^ {i j}\right))
+$$
+
+$$
+\mathbf {u} ^ {s}, \mathbf {u} ^ {o} \in R ^ {| \mathcal {C} _ {e} | + 1}, \mathbf {u} ^ {r} \in R ^ {| \mathcal {C} _ {r} | + 1}.
+$$
+
+Higher-order scores Each factor scores the joint distribution of the node types connected to it. For a ter factor connects a subject  $v_{s}^{i}$ , an object  $v_{o}^{j}$  and a relation  $v_{r}^{ij}$ , the factor score  $\mathbf{f}_{ij}^{ter} \in R^{|\mathcal{C}_e + 1|^2 |\mathcal{C}_r + 1|}$  is:
+
+$$
+\begin{array}{l} \mathbf {h} _ {i} ^ {s} = \mathrm {F F N} _ {s} ^ {t e r} \left(\mathbf {g} \left(v _ {s} ^ {i}\right)\right) \\ \mathbf {h} _ {j} ^ {o} = \mathrm {F F N} _ {o} ^ {t e r} \left(\mathbf {g} \left(v _ {o} ^ {j}\right)\right) \\ \mathbf {h} _ {i j} ^ {r} = \mathrm {F F N} _ {r} ^ {t e r} (\mathbf {g} (v _ {r} ^ {i j})) \\ \mathbf {f} _ {i j} ^ {t e r} = \mathrm {F F N} _ {f} ^ {t e r} (\mathbf {h} _ {i} ^ {s} \circ \mathbf {h} _ {j} ^ {o} \circ \mathbf {h} _ {i j} ^ {r}) \\ \end{array}
+$$
+
+For a factor  $z, z \in \{sib, cop, gp\}$  which connects two relations, we name them relation  $a$  and  $b$  for simplicity. If relation  $a$  is  $v_r^{ij}$ , then relation  $b$  is  $v_r^{ik}, v_r^{kj}$  and  $v_r^{jk}$  for  $sib, cop$  and  $gp$  respectively. We use  $\mathbf{g}(a), \mathbf{g}(b)$  to refer to the relation representations of relations  $a$  and  $b$ . The factor score  $\mathbf{f}_{ijk}^z \in R^{|\mathcal{C}_r + 1|^2}$  is defined as:
+
+$$
+\mathbf {h} _ {a} = \mathrm {F F N} _ {s} ^ {\text {t e r}} (\mathbf {g} (a))
+$$
+
+$$
+\mathbf {h} _ {b} = \mathrm {F F N} _ {o} ^ {\text {t e r}} (\mathbf {g} (b))
+$$
+
+$$
+\mathbf {f} _ {i j k} ^ {\mathsf {z}} = \mathrm {F F N} _ {f} ^ {t e r} (\mathbf {h} _ {a} \circ \mathbf {h} _ {b})
+$$
+
+higher-order inference In the model, computing the node distribution can be seen as doing posterior inference on a Conditional Random Field (CRF). MFVI iteratively updates a factorized variational distribution  $\mathbf{Q}$  to approximate the posterior label distribution. We use  $Q_{si}(e_1), Q_{oj}(e_2)$  to refer to the probability of subject  $v_s^i$  and object  $v_o^j$  has entity type  $e_1$  and  $e_2$  respectively and  $Q_{rij}(r)$  represents the relation  $v_r^{ij}$  has the relation type  $r$ . For simplicity, we use  $u_i^s(e_1), u_j^o(e_2), u_{ij}^r(r_1), f_{ij}^{ter}(e_1, e_2, r_1), f_{ijk}^z(r_1, r_2)$  to represent the first-order and higher-order scores when the subject  $v_s^i$ , the object  $v_o^j$  have entity type  $e_1, e_2$ , the relation  $a(v_r^{ij})$ , the relation  $b$  have relation types  $r_1, r_2$  respectively. Following is the iterately updating of the distribution  $Q_s, Q_o, Q_r$ . For a subject  $v_s^i$ , The message only passed from  $ter$  factor in the  $l$ -th iteration is:
+
+$$
+\begin{array}{l} F _ {s _ {i}} ^ {l} (e _ {1}) = \\ \sum_ {j} \sum_ {e _ {2}} Q _ {o _ {j}} ^ {l - 1} (e _ {2}) (\sum_ {l _ {1}} Q _ {r _ {i j}} ^ {l - 1} (r _ {1}) f _ {i j} ^ {t e r} (e _ {1}, e _ {2}, r _ {1})) \\ \end{array}
+$$
+
+similarly, the message passed from ter factor to the object  $v_{o}^{j}$  is:
+
+$$
+\begin{array}{l} F _ {o _ {j}} ^ {l} (e _ {2}) = \\ \sum_ {i} \sum_ {e _ {1}} Q _ {s _ {i}} ^ {l - 1} (e _ {1}) (\sum_ {l _ {1}} Q _ {r _ {i j}} ^ {l - 1} (r _ {1}) f _ {i j} ^ {t e r} (e _ {1}, e _ {2}, r _ {1})) \\ \end{array}
+$$
+
+For a relation  $v_r^{ij}$ , the message could be passed from four factors, we list them by the source. From ter factor:
+
+$$
+\begin{array}{l} T _ {r _ {i j}} ^ {l} (r _ {1}) = \\ \sum_ {e _ {1}} \sum_ {e _ {2}} Q _ {s _ {i}} ^ {l - 1} (e _ {1}) Q _ {o _ {j}} ^ {l - 1} (e _ {2}) f _ {i j} ^ {t e r} (e _ {1}, e _ {2}, r _ {1}) \\ \end{array}
+$$
+
+From sib factor:
+
+$$
+\begin{array}{l} S _ {r _ {i j}} ^ {l} (r _ {1}) = \\ \sum_ {k} \sum_ {r _ {2}} Q _ {r _ {i k}} ^ {l - 1} (r _ {2}) (f _ {i j k} ^ {s i b} (r _ {1}, r _ {2}) + f _ {i k j} ^ {s i b} (r _ {2}, r _ {1})) \\ \end{array}
+$$
+
+From the cop factor:
+
+$$
+\begin{array}{l} C _ {r _ {i j}} ^ {l} (r _ {1}) = \\ \sum_ {k} \sum_ {r _ {2}} Q _ {r _ {k j}} ^ {l - 1} (r _ {2}) (f _ {i j k} ^ {c o p} (r _ {1}, r _ {2}) + f _ {k j i} ^ {c o p} (r _ {2}, r _ {1})) \\ \end{array}
+$$
+
+From the  $gp$  factor:
+
+$$
+\begin{array}{l} G _ {r _ {i j}} ^ {l} (r _ {1}) = \\ \sum_ {k} \sum_ {r _ {2}} (Q _ {r _ {j k}} ^ {l - 1} (r _ {2}) f _ {i j k} ^ {g p} (r _ {1}, r _ {2}) \\ + Q _ {r _ {k i}} ^ {l - 1} (r _ {2}) f _ {k i j} ^ {g p} (r _ {2}, r _ {1})) \\ \end{array}
+$$
+
+The posterior distribution of entity  $e_i$  with respect to the subject  $s_i$  and object  $o_i$ :
+
+$$
+Q _ {s _ {i}} ^ {l} (e) \propto \exp \left(u _ {i} ^ {s} (e) + F _ {s _ {i}} ^ {l} (e)\right)
+$$
+
+$$
+Q _ {o _ {j}} ^ {l} (e) \propto \exp \left(u _ {j} ^ {o} (e) + F _ {o _ {j}} ^ {l} (e)\right)
+$$
+
+Then the entity distribution is:  $Q_{s_i}^l + Q_{o_i}^l$
+
+We initial the Q of subject  $v_{i}^{s}$ , object  $v_{j}^{o}$ , the relation  $v_{ij}^{r}$  by normalizing the unary potential  $\exp(u_{i}^{s}), \exp(u_{j}^{o}), \exp(u_{ij}^{r})$  respectively. The posterior distribution of the relation  $r_{ij}$  is:
+
+$$
+\begin{array}{l} Q _ {r _ {i j}} ^ {l} (r) \propto \exp \left(u _ {i j} ^ {r} (r) + \mathbb {1} _ {t e r} T _ {r _ {i j}} ^ {l} (r) \right. \\ \mathbb {1} _ {s i b} S _ {r _ {i j}} ^ {l} (r) + \mathbb {1} _ {c o p} C _ {r _ {i j}} ^ {l} (r) + \mathbb {1} _ {g p} G _ {r _ {i j}} ^ {l} (r)) \\ \end{array}
+$$
+
+The symbol  $\mathbb{1}_{z}, z \in \{\text{ter}, \text{sib}, \text{cop}, \text{gp}\}$  indicates whether the factor  $z$  exists in the graph.
+
+# A.6 GCN
+
+Here is the introduction of the baseline GCN. As in HGERE, we also build the graph  $\mathcal{G} = (\mathcal{V},\mathcal{E})$  with subject, object and relation nodes,  $\mathcal{V} = \mathcal{V}_s\bigcup \mathcal{V}_o\bigcup \mathcal{V}_r$ . For each relation node  $v_{r}^{ij}\in \mathcal{V}_{r}$  we build two edges connecting its subject node  $v_{s}^{i}\in \mathcal{V}_{s}$  and object node  $v_{o}^{j}\in \mathcal{V}_{o}$  respectively. the
+
+![](images/f36dd5553f583597abe3e66c212c08b72d7c1e5cd013e9c6394e1847b57fab45.jpg)  
+Figure 3: Illustration of an example graph of GCN
+
+model use  $l$  convolution layers to update the node representations. We define the neighbor set  $\mathcal{N}(v)$  of a node  $v$  is the nodes connected to it. The node representation update of  $l$ -th layer is as follow:
+
+$$
+\begin{array}{l} \beta^ {l} (v _ {1}, v) = \mathbf {w} ^ {\top} \sigma (\mathbf {W} [ \mathbf {g} ^ {l - 1} (v _ {1}); \mathbf {m} ^ {l - 1} (v) ] \\ \alpha^ {l} (v _ {1}, v) = \frac {\exp \beta^ {l} (v _ {1} , v)}{\sum_ {v _ {1} \in \mathcal {N} (v)} \exp \beta^ {l} (v _ {1} , v)} \\ \mathbf {g} ^ {l} (v) = \mathbf {g} ^ {l - 1} (v) + \sum_ {v _ {1} \in \mathcal {N} (v)} \alpha (v _ {1}, v) \mathbf {g} ^ {l - 1} (v _ {1}) \\ \end{array}
+$$
+
+A.7 Performance with part of the training data  
+
+<table><tr><td rowspan="2">ratio</td><td rowspan="2">model</td><td colspan="3">ACE2005 (BERTB)</td></tr><tr><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td rowspan="2">5%</td><td>Backbone</td><td>80.4</td><td>39.7</td><td>36.0</td></tr><tr><td>HGERE</td><td>79.5</td><td>42.0</td><td>38.1</td></tr><tr><td rowspan="2">10%</td><td>Backbone</td><td>83.9</td><td>51.3</td><td>47.2</td></tr><tr><td>HGERE</td><td>84.2</td><td>53.3</td><td>49.4</td></tr><tr><td rowspan="2">100%</td><td>Backbone</td><td>90.0</td><td>69.8</td><td>66.7</td></tr><tr><td>HGERE</td><td>90.2</td><td>70.1</td><td>67.3</td></tr></table>
+
+Table 7: F1 score of HGERE on ACE2005 test set when only provide  $5\%$  and  $10\%$  training samples.
+
+From the main results, we can see that the HGERE shows a significantly greater improvement in performance compared to the Backbone model on the SciERC dataset than on the ACE2005 dataset. We guess one of the reason is the size of the training data. Because with more training data, models could learn enough knowledge from a large number of samples and reduce the demand of higher-order information. So we compare HGERE to Backbone with  $5\%$  and  $10\%$  of training data on the ACE2005  $(\mathrm{BERT}_B)$  to see if higher-order inference is more effectiveness with small training data. From the
+
+<table><tr><td></td><td colspan="3">SciERC</td></tr><tr><td></td><td>Ent</td><td>Rel</td><td>Rel+</td></tr><tr><td>max</td><td>74.0</td><td>54.7</td><td>41.4</td></tr><tr><td>sum</td><td>73.6</td><td>54.5</td><td>41.5</td></tr><tr><td>attn</td><td>74.9</td><td>55.7</td><td>43.6</td></tr></table>
+
+Table 8: F1 scores of HGERE (the tersibcop variant) with different aggregation functions on the SciERC test set.
+
+results shown in Table 7 we can see that the increments of absolute F1 score on  $\mathrm{Rel + }$  metric from Backbone to HGERE are  $2.1\%$ $2.2\%$  on  $5 \%$  and  $10 \%$  of training set respectively, which are much higher than  $0.6\%$  on full training set.
+
+![](images/b80f165bf84284b69b2ef0d02caef1a3979138e6f0787652a2c13e77e45d062b.jpg)  
+A.8 Effect of the number of HGNN layers  
+Figure 4: The change of F1 scores with respect to the number of HGNN layers.
+
+From Fig.4 we can see that using three HGNN layers performs the best while more layers lead to worse results. We posit that this is because using more HGNN layers would suffer from the well-known over-smoothing problem (Cai and Wang, 2020).
+
+# A.9 Effect of the aggregation function in message passing
+
+We study the influence of using different message aggregation functions. HGERE uses an attention mechanism (attn) to update node representations while it is also possible to use max-pooling (max) or sum-pooling (sum). Table 8 shows that attn performs the best.

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+        "type": "text",
+        "text": "Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Qianjin Du $^{1}$ , Shiji Zhou $^{2}$ , Xiaohui Kuang $^{3}$ , Gang Zhao $^{3*}$ , Jidong Zhai $^{1*}$",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$^{1}$ Department of Computer Science and Technology, Tsinghua University",
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+    },
+    {
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+        "text": "$^{2}$ Department of Automation, Tsinghua University",
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+        "text": "$^{3}$ National Key Laboratory of Science and Technology on Information System Security",
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+    {
+        "type": "text",
+        "text": "dqj20@mails.tsinghua.edu.cn;zhaijidong@tsinghua.edu.cn",
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+    {
+        "type": "text",
+        "text": "zhoushiji00@gmail.com",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "xhkuang@bupt.edu.cn; bisezhaog@163.com",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "In code vulnerability detection tasks, a detector trained on a label-rich source domain fails to provide accurate prediction on new or unseen target domains due to the lack of labeled training data on target domains. Previous studies mainly utilize domain adaptation to perform cross-domain vulnerability detection. But they ignore the negative effect of private semantic characteristics of the target domain for domain alignment, which easily causes the problem of negative transfer. In addition, these methods forcibly reduce the distribution discrepancy between domains and do not take into account the interference of irrelevant target instances for distributional domain alignment, which leads to the problem of excessive alignment. To address the above issues, we propose a novel cross-domain code vulnerability detection framework named MN-CRI. Specifically, we introduce mutual nearest neighbor contrastive learning to align the source domain and target domain geometrically, which could align the common semantic characteristics of two domains and separate out the private semantic characteristics of each domain. Furthermore, we introduce an instance re-weighting scheme to alleviate the problem of excessive alignment. This scheme dynamically assign different weights to instances, reducing the contribution of irrelevant instances so as to achieve better domain alignment. Finally, extensive experiments demonstrate that MN-CRI significantly outperforms state-of-the-art cross-domain code vulnerability detection methods by a large margin.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
+            114,
+            804,
+            258,
+            819
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the development of the Internet, the number of vulnerabilities in software has increased rapidly, which leaves software to face huge security threats. There are multiple efforts (Lin et al., 2017; Grieco",
+        "bbox": [
+            112,
+            832,
+            489,
+            896
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "et al., 2016; Li et al., 2018; Zou et al., 2019; Zhou et al., 2019; Feng et al., 2020) have attempted to introduce deep learning and NLP techniques for automated vulnerability detection. Those deep learning-based detection methods mainly focus on in-domain code vulnerability detection. That is, the training and test datasets are assumed to be drawn from the same distribution (i.e., from the same software project). However, in practice, most software projects lack labeled vulnerability datasets. Labeling data is labor-intensive and expensive, which requires that the models trained on a label-rich source domain (i.e., a software project with abundant labeled data) are applied to a new target domain (i.e., a software project without labeled data). Owing to program style, application scenarios, and other factors, different software projects may obey different probability distributions. The models trained on the source domain suffer from severe performance loss on the target domain due to the obvious distribution discrepancy between two domains. To solve this problem, some research works have attempted to introduce domain adaptation to perform cross-domain code vulnerability detection. Domain adaptation is a technique that aims to eliminate distribution discrepancy and transfer knowledge from a labeled source domain to an unlabeled target domain (Ganin and Lempitsky, 2015). Lin et al. (2018) first proposed a function-level cross-domain code vulnerability detection framework. But they only hypothesize that the learned high-level representations are transferable, and they do not propose a method to explicitly eliminate the domain discrepancy. Lin et al. (2019) proposed a cross-domain detection framework that utilizes two LSTMs to learn two groups of transferable feature representations, and then combine both groups of feature representations to train a classifier. Nguyen et al. (2019) proposed a new code domain adaptation framework named SCDAN that incorporated conventional domain adaptation techniques such as",
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding authors.",
+        "bbox": [
+            136,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12791",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "footer",
+        "text": "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 12791-12800 December 6-10, 2023 ©2023 Association for Computational Linguistics",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/01f95eee71cd7758b7aa872365c274dc5f90771534d68a3ab1e00231ba03f477.jpg",
+        "image_caption": [
+            "Figure 1: The framework of MNCRI."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            131,
+            83,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018). CDVulD (Liu et al., 2020) employed a metric transfer learning framework (MTLF) (Xu et al., 2017) to learn cross-domain representations by minimizing the distribution divergence between the source domain and the target domain. Lastly, Li et al. (2023) proposed a detection framework called VulGDA that utilized a graph embedding method to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing Maximum Mean Discrepancy (MMD).",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although the above-mentioned research works achieve considerable performance improvements, there still exist two problems that restrict further performance improvements: (1) In practice, different domains (i.e., different software projects) share common semantic characteristics and while having their own private semantic characteristics due to different application scenarios, coding style, and code implementation, etc. Previous studies reduce the domain discrepancy by forcibly minimizing divergence of the entire source domain and the target domain. They ignore semantic differences between two domains and allow samples with private semantic characteristics to participate in domain alignment, which is prone to the problem of negative transfer. Eliminating the domain discrepancy should be constrained on only aligning the common semantic characteristics (also known as the common knowledge) between two domains",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "and the respective private semantic characteristics should be separated simultaneously. (2) There will always exist some target instances that are not relevant to source instances. Current methods treat the instances equally when conducting statistical distribution domain alignment. Intuitively, the relevant instances should be given larger weights, and irrelevant instances should be assigned smaller weights so as to decrease their importance and contribution to domain alignment. Ignoring the relevance of instances will make models learn suboptimal cross-domain representations. To address these issues, we propose a novel cross-domain code vulnerability detection framework named MNCRI (as illustrated in Figure 1) based on mutual nearest neighbor contrastive learning and the instance re-weighting scheme, which jointly achieves geometric domain alignment and statistical domain alignment. First, we argue that geometric domain alignment should follow a principle: semantically consistent instances should be geometrically adjacent to each other, whether within or across domains. Based on this principle, we introduce mutual nearest neighbor contrastive learning to achieve the alignment of common semantic characteristics. Specifically, we construct mutual nearest neighbor pairs across the source domain and the target domain by leveraging the mutual neighbor rule. Then we introduce a contrastive loss function that aims at reducing the feature discrepancy of mutual nearest neighbor pairs. By minimizing this contrastive loss, we achieve the alignment of",
+        "bbox": [
+            505,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "12792",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "common semantic characteristics across domains and separate out private semantic characteristics of each domain. Second, to alleviate the problem of excessive alignment, we introduce the instance re-weighting scheme that assigns different weights to different target domain instances based on the relevance with source domain instances. In this way, the effect of some target domain instances that are irrelevant to source domain instances is reduced and the effect of some relevant target domain instances is highlighted, which is beneficial for reducing the distribution discrepancy. Finally, we conduct extensive experiments to verify the effectiveness of our proposed method. The experimental results show that the proposed method outperforms current baseline methods by a large margin.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In summary, our contributions are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel cross-domain code vulnerability detection framework named MNCRI, which reduces the domain discrepancy from two perspectives of geometries and statistical distributions by exploiting the mutual nearest neighbor contrastive learning and the instance re-weighting scheme.",
+            "- We introduce mutual nearest neighbors contrastive learning to solve the problem of negative transfer, which explores instances relationships between domains and achieves the domain alignment geometrically.",
+            "- We incorporate an instance re-weighting scheme into the statistical domain alignment, which dynamically weights different instances according to the relevance between instances to eliminate the negative effect of irrelevant instances for domain alignment.",
+            "- We conduct extensive experiments to verify the effectiveness of MNCRI. Experimental results show that MNCRI outperforms current cross-domain detection methods and obtain obvious performance improvements."
+        ],
+        "bbox": [
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+            370,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
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+            790,
+            268,
+            806
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 Cross-domain Code Vulnerability Detection",
+        "text_level": 1,
+        "bbox": [
+            112,
+            816,
+            423,
+            848
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Since different software projects have different code styles, application scenarios and other factors, they may obey different distributions. Therefore, when a code vulnerability detection model",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "trained on a label-rich project dataset is applied to a new no-label project, its performance drop sharply. To address this issue, researchers have attempted to introduce domain-adaptation techniques into cross-domain code vulnerability detection tasks. Nam et al. (2013) utilized migration component analysis to map software metrics in the source and target domains to the same feature space. Hellendoorn et al. (2020) attempted to utilize local syntactic features and global semantic features to perform file-level cross-domain vulnerability detection. Lin et al. (2018) first proposed a cross-domain code vulnerability detection framework at the function-level, which extracts features from abstract syntax trees (ASTs) of functions and then feeds extracted features into a long short-term memory recurrent neural network (LSTM) to learn higher-level representations. But they only hypothesize that the learned high-level representations are transferable, and they do not propose an effective method to explicitly eliminate the discrepancy between the source domain and the target domain. Lin et al. (2019) presented a cross-domain detection framework that employed two LSTMs to learn two groups of transferable feature representations. These representations were then combined to train a classifier. Nguyen et al. (2019) proposed a novel code domain adaptation network called SCDAN. SCDAN incorporated conventional domain adaptation network techniques such as DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018) to eliminate distribution divergence. To further tackle the distribution divergence, CD-VulD (Liu et al., 2020) deployed the metric transfer learning framework (MTLF) (Xu et al., 2017) to learn domain-invariant representations by minimizing Mahalanobis distance. Li et al. (2023) proposed a cross-domain detection framework called VulGDA, which employed a graph embedding approach to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing the domain discrepancy.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 Contrastive Learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Contrastive learning in the latent space has recently shown great promise, which aims to make the representation of a given anchor data to be similar to its positive pairs and dissimilar to its negative pairs (Tian et al., 2020; Chen et al., 2020; Khosla et al., 2020). Many state-of-the-art methods for represent-",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "12793",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "tation learning tasks are based on the contrastive learning framework (Chen and He, 2021). Previous studies construct positive samples by augmenting original samples. In this paper, we utilize mutual nearest neighbors as positive pairs to achieve feature alignment between domains.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 Methodology",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 1, the architecture of MN-CRI contains two main components: 1) the mutual nearest neighbor contrastive learning module, which performs contrastive learning based on mutual nearest neighbors for better geometric domain alignment; 2) the statistical distribution domain alignment module equipped with the instance weighting scheme, which reduces the distribution discrepancy and achieves the domain alignment statistically. Below we elaborate the details of MN-CRI.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We formalize vulnerability detection as a binary classification problem. In cross-domain vulnerability detection, given a labeled source domain set  $D_{s} = \\{(x_{i}^{s},y_{i}^{s})\\}_{i = 1}^{n_{s}}$  including  $n_s$  instances  $x_{i}^{s}$ , it aims to predict the label  $y_{i}^{t}$  of the target sample  $x_{i}^{t}$  in an unlabeled target domain set  $D_{t} = \\{(x_{i}^{t})\\}_{i = 1}^{n_{t}}$  where  $y_{i}^{s}\\in \\{0,1\\}$  and  $y_{i}^{t}\\in \\{0,1\\}$  (1 means the sample is vulnerable and 0 means the sample is non-vulnerable).  $n_s$  and  $n_t$  are the number of the source domain set and the target domain set, respectively. As illustrated in Figure 1, our model consists of two basic modules: (1) a feature extractor  $f(\\cdot)$  that maps the code sample  $x_{i}$  into the embedding representation  $z_{i}$  ( $z_{i} = f(x_{i})$ ). (2) a classifier  $g(\\cdot)$  to classify the class  $y_{i}$  of the sample  $x_{i}$  ( $y_{i} = g(f(x_{i}))$ ).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Geometric Domain Alignment by Mutual Nearest Neighbor Contrastive Learning Paradigm",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In supervised learning scenarios, the cross-entropy loss on the source domain is defined as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {C E} = - \\frac {1}{n _ {s}} \\sum_ {i = 1} ^ {n _ {s}} y _ {i} ^ {s} \\log \\left(g \\left(f \\left(x _ {i} ^ {s}\\right)\\right)\\right) + \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n(1 - y _ {i} ^ {s}) \\log (1 - g (f (x _ {i} ^ {s})))\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            841,
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+            858
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Due to the domain discrepancy between the source domain and the target domain, the performance drops sharply when transfer the model trained on",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "source domain to the target domain. Previous methods mainly focus on minimizing the global distribution divergence between domains to achieve the domain alignment, such as Maximum Mean Discrepancy (MMD) (Yan et al., 2017; Li et al., 2023). In practice, the target domain may preserve its own private semantic characteristics that do not appear in the source domain. Previous methods do not consider domain private semantic characteristics and forcefully align the global distributions of two domains, which may cause the problem of negative transfer. In manifold learning (McInnes et al., 2018; Chen et al., 2022), the concept of geometric nearest neighbors is commonly used to describe the similarities of semantic characteristics. For different domains, the geometrically nearest neighbors can be viewed as the most similar samples that contain the same semantic characteristics. Therefore, to align the common semantic characteristics between domains and separate out private semantic characteristics of each domain, we introduce mutual nearest neighbors contrastive learning.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically, for a target domain sample  $x_{i}^{t}$ , we retrieve its corresponding  $k$  nearest neighbors  $\\mathcal{N}\\mathcal{N}_{i}^{s}$  in the source domain. In the same way, for a source domain sample  $x_{j}^{s}$ , we can also obtain its corresponding  $k$  nearest neighbors  $\\mathcal{N}\\mathcal{N}_{j}^{t}$  in the target domain. Then mutual nearest neighbors can be constructed by following the rule: if the source sample  $x_{j}^{s}$  and the target sample  $x_{i}^{t}$  are contained in each other's nearest neighbors, they are regarded as mutual nearest neighbors. After that, we build a relationship matrix to describe the mutual nearest neighbor relationship between source domain samples and target domain samples. Formally, the relationship matrix is defined as:  $M^{st} \\in \\mathbb{R}^{n_s \\times n_t}$  where  $M_{i,j}^{st} = 1$  if only  $x_{i}^{t}$  and  $x_{j}^{s}$  is the mutual nearest neighbor pair; otherwise  $M_{i,j}^{st} = 0$ . Besides, to fully utilize supervised information of the source domain and learn better discriminative features for classification, we also build in-domain relationship matrix  $M^{ss}$  according to ground-truth labels of the source domain.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In geometric domain alignment, we hope that built mutual nearest neighbor pairs can be closer to each other in the feature space, while non-geometrically samples should be far away from each other. In this paper, we introduce an contrastive learning loss to achieve this goal.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For each training sample  $x_{i}$ , its positive sample sets  $P_{i}$  and negative sample sets  $N_{i}$  in the memory",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12794",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "bank can be obtained by relationship matrices  $M^{ss}$  and  $M^{st}$ . The contrastive loss is formulated by:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C o n} = - \\sum_ {i = 1} ^ {n _ {s} + n _ {t}} \\sum_ {j \\in P _ {i}} \\log \\varphi_ {i, j} \\\\ \\log \\varphi_ {i, j} = \\frac {\\exp \\left(z _ {i} z _ {j} / \\tau\\right)}{\\sum_ {p \\in P _ {i}} \\exp \\left(z _ {i} z _ {p} / \\tau\\right) + \\sum_ {q \\in N _ {i}} \\exp \\left(z _ {i} z _ {q} / \\tau\\right)} \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            137,
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+            216
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  is a temperature parameter. By optimizing the contrastive loss, it makes the model learn geometric neighbor relationships between the source domain and the target domain and makes the feature representations of samples with common semantic characteristics closer in the feature space.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 Statistical Domain Alignment by Instance Re-weighting Scheme",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As depicted in Section 3.2, the mutual nearest neighbors contrastive learning could reduce the geometrical domain discrepancy and achieve better geometrical domain alignment. In practice, reducing the distributional divergence between domains and achieving the statistical domain alignment are also important for cross-domain code vulnerability detection. MMD (Gretton et al., 2008)) is a popular estimator to calculate the degree of statistical alignment of data distribution between two domains, and it is defined as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {M M D} = \\left\\| \\frac {1}{U ^ {2}} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) - \\frac {2}{U W} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {W} k (z _ {i} ^ {s}, z _ {j} ^ {t}) \\right. \\\\ + \\frac {1}{W ^ {2}} \\sum_ {i = 1} ^ {W} \\sum_ {j = 1} ^ {W} k \\left(z _ {i} ^ {t}, z _ {j} ^ {t}\\right) \\| _ {\\mathcal {H}} \\tag {3} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            117,
+            557,
+            485,
+            644
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Previous studies (Liu et al., 2020; Li et al., 2023) perform statistical domain alignment by minimizing Maximum Mean Discrepancy (MMD). However, there will always exist some instances that are not relevant to the source instances. Previous methods forcefully reduce the global distributional divergence between domains and ignore the negative effect of irrelevant instances, which easily leads to the problem of excessive alignment. Ideally, relevant target instances should be assigned large weights and irrelevant instances should be assigned small weights during the domain alignment. Thus, in order to achieve this goal, we propose to introduce the instance re-weighting scheme into the statistical domain alignment. Specifically, we adopt the prediction confidence of the classifier trained on the source domain for target instances",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "as the weights of target instances during statistical domain alignment. This process can be formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {M M D - I R} = \\Vert \\frac {1}{U ^ {2}} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) \\\\ - \\frac {2}{U W} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {W} f \\left(z _ {j} ^ {t}\\right) k \\left(z _ {i} ^ {s}, z _ {j} ^ {t}\\right) + \\frac {1}{W ^ {2}} \\sum_ {i = 1} ^ {W} \\sum_ {j = 1} ^ {W} k \\left(z _ {i} ^ {t}, z _ {j} ^ {t}\\right) \\| _ {\\mathcal {H}} \\\\ f \\left(z _ {j} ^ {t}\\right) = 2 * \\left| \\operatorname {P r o b} \\left(y _ {j} ^ {t} = 1 \\mid z _ {j} ^ {t}\\right) - 0. 5 \\right| \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $Prob(y_{j}^{t} = 1|z_{j}^{t})$  denotes the prediction probability that the classifier predicts the target instance  $x_{i}^{t}$  is vulnerable. Introducing the instance re-weighting scheme degrades the impact of some target instances that are not relevant to source instances, which is helpful for reducing the distributional divergence between domains and achieving better statistical domain alignment.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 Overall Objective",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "MNCRI is proposed to jointly minimize the cross entropy loss of the source domain instances and reduce the divergence between the source domain and target domain. The total objective function in MNCRI is formulated as:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {C E} + \\lambda \\mathcal {L} _ {C o n} + \\mu \\mathcal {L} _ {M M D - I R} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            559,
+            527,
+            880,
+            545
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{CE}$  denotes source supervised loss using source labels, and  $\\mathcal{L}_{Con}$  denotes the geometric domain alignment loss based on the mutual nearest neighbor contrastive learning, and  $\\mathcal{L}_{MMD-IR}$  denotes the statistical domain alignment loss using instance re-weighting scheme.  $\\lambda$  and  $\\mu$  are two trade-off parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct extensive experiments to evaluate the effectiveness of the proposed framework (MNCRI).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 Experimental Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1.1 Dataset",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In our work, we conduct experiments on three open-source software project datasets: FFmpeg, QEMU (Zhou et al., 2019) and ReVe (Chakraborty et al., 2021). There are several reasons for choosing the above datasets as experimental datasets. The first one is that they are manually labeled so that they could provide accurate supervised information.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12795",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Second, the number of samples of these datasets is abundant to support model training. The implementation details can be found in Appendix A.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1.2 Baselines",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The state-of-the-art cross-domain code vulnerability detection methods include: VulDeePecker (Li et al., 2018), SySeVr (Li et al., 2021), Devign (Zhou et al., 2019), CodeBERT (Feng et al., 2020), GraphCodeBERT (Guo et al., 2020), CodeT5 (Wang et al., 2021), SCDAN (Nguyen et al., 2019), CD-VulD (Liu et al., 2020), and VulGDA (Li et al., 2023).",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1.3 Evaluation Metric",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In general, F1-score is a widely used metric to evaluate the performance of vulnerability detection systems. Let  $TP$  be the number of vulnerable samples that are predicted correctly,  $FP$  be the number of truly non-vulnerable samples that are predicted as vulnerable and  $FN$  be the number of truly vulnerable samples that are predicted as non-vulnerable. Precision ( $P = \\frac{TP}{TP + FP}$ ) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all samples predicted as vulnerable. Recall ( $R = \\frac{TP}{TP + FN}$ ) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all truly vulnerable samples. The F1-score ( $F1 = \\frac{2 \\times P \\times R}{P + R}$ ) is the harmonic mean of precision and recall. It is clear that the higher F1-score represents better classification performance. Besides, vulnerability detection tasks also focus on TPR (True Positive Rate) performance (as known as Recall) of detectors. Because the higher TPR represents that the more vulnerable samples are discriminated correctly, it is crucial for the performance evaluation of detectors. Therefore, in our experiments, we adopt TPR (True Positive Rate) and F1-score as our evaluation metrics.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct extensive experiments to verify the effectiveness of the proposed framework (MNCRI). Experimental results are shown in Table 1. Our proposed framework MNCRI (CodeT5) achieves the best performances on all cross-domain code vulnerability detection tasks, and outperforms all baseline methods. For instance, in the FFmpeg-to-QEMU  $(\\mathrm{F} \\rightarrow \\mathrm{Q})$  cross-domain detection task, MNCRI (CodeT5) achieves an F1-score of  $58.21\\%$ , outperforming the current state-of-the-art cross-domain detection method VulGDA by",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.41%. Meanwhile, MNCRI (CodeT5) obtains a TPR gain of 9.18% compared to VulGDA. Moreover, our framework equipped with CodeBERT, GCBERT (GraphCodeBERT) also can obtain significant performance improvements compared to baseline methods. This demonstrates that the proposed framework has good generalization performance and it does not rely on the specific code feature extractor and can be adapted to various feature extractors. Since CodeT5 adopts more effective pre-training mechanisms compared to CodeBERT and GCBERT (GraphCodeBERT), MNCRI using CodeT5 as the feature extractor obtains the largest performance improvements. This demonstrates that a power feature extractor is helpful for improving cross-domain vulnerability detection performance. To make the comparison with VulGDA, MNCRI (VulGDA-f) uses the same feature extractor as VulGDA. We can observe that MNCRI (VulGDA-f) consistently outperforms VulGDA. We can conclude that the performance improvements can be attributed to the proposed domain adaptation strategies.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "By analyzing experimental results, we can observe that MNCRI could significantly improve TPR (True Positive Rate) of the detector compared to other cross-domain vulnerability detection methods. This observation shows that mutual nearest neighbor contrastive learning and the instance reweighting scheme are conducive to reducing domain discrepancy by jointly conducting geometric domain alignment and statistical domain alignment. Besides, compared to the detectors CD-VulD, VulGDA, and MNCRI exploiting domain adaptation techniques, traditional detectors VulDeePecker, SySeVr and Devign have the worse performance in cross-domain detection tasks. This is because traditional detectors do not consider the domain gap between domains. The comparison results indicate the importance of domain adaptation in cross-domain code vulnerability detection tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In order to more intuitively demonstrate the classification performance of MNCRI in cross-domain vulnerability detection tasks, we plot the histogram distributions of softmax-based prediction confidence on the target domain dataset (see Figure 2). We can see that the prediction confidence scores of VulGDA are mainly distributed around 0.5 (see Figure 2(a)). This phenomenon indicates that VulGDA has no discriminative ability for a large number of target instances and is unable to judge whether",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12796",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5b2ce55b4170f4f51f4c82dc36672777a6da8e1567424a8e1958116966da1fce.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">F → Q</td><td colspan=\"2\">F → R</td><td colspan=\"2\">Q → F</td><td colspan=\"2\">Q → R</td><td colspan=\"2\">R → F</td><td colspan=\"2\">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>VulDeePecker</td><td>64.82</td><td>41.31</td><td>12.59</td><td>12.47</td><td>34.85</td><td>32.04</td><td>33.98</td><td>12.04</td><td>35.57</td><td>29.01</td><td>16.57</td><td>13.88</td></tr><tr><td>SySeVr</td><td>66.98</td><td>43.22</td><td>12.73</td><td>13.19</td><td>35.57</td><td>33.22</td><td>35.77</td><td>12.96</td><td>37.28</td><td>30.05</td><td>17.65</td><td>14.36</td></tr><tr><td>Devign</td><td>68.92</td><td>45.61</td><td>14.58</td><td>13.31</td><td>37.99</td><td>35.91</td><td>39.82</td><td>13.55</td><td>35.56</td><td>31.35</td><td>18.97</td><td>16.28</td></tr><tr><td>CodeBert</td><td>53.22</td><td>46.66</td><td>10.66</td><td>11.22</td><td>37.44</td><td>38.15</td><td>30.02</td><td>12.97</td><td>30.66</td><td>33.59</td><td>15.21</td><td>18.34</td></tr><tr><td>GCBERT</td><td>55.34</td><td>47.14</td><td>10.79</td><td>11.30</td><td>39.40</td><td>38.60</td><td>31.09</td><td>13.68</td><td>30.97</td><td>33.98</td><td>16.88</td><td>18.77</td></tr><tr><td>CodeT5</td><td>58.57</td><td>49.50</td><td>11.23</td><td>12.11</td><td>38.80</td><td>39.42</td><td>33.70</td><td>15.02</td><td>31.77</td><td>35.73</td><td>18.22</td><td>20.39</td></tr><tr><td>SCDAN</td><td>70.30</td><td>52.32</td><td>13.99</td><td>12.68</td><td>40.78</td><td>43.30</td><td>43.29</td><td>17.65</td><td>38.92</td><td>37.05</td><td>15.29</td><td>22.21</td></tr><tr><td>CD-VulD</td><td>73.21</td><td>51.24</td><td>13.88</td><td>14.06</td><td>48.80</td><td>46.68</td><td>48.80</td><td>20.10</td><td>40.25</td><td>40.17</td><td>18.71</td><td>25.78</td></tr><tr><td>VulGDA</td><td>76.76</td><td>52.80</td><td>15.22</td><td>14.37</td><td>47.96</td><td>47.72</td><td>50.52</td><td>20.98</td><td>40.68</td><td>42.86</td><td>19.88</td><td>26.35</td></tr><tr><td>MNCRI (VulGDA-f)</td><td>81.37</td><td>54.95</td><td>16.21</td><td>15.44</td><td>50.39</td><td>50.99</td><td>51.39</td><td>22.37</td><td>41.38</td><td>45.92</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (CodeBERT)</td><td>84.55</td><td>56.57</td><td>17.11</td><td>16.68</td><td>53.22</td><td>53.96</td><td>53.88</td><td>23.10</td><td>42.56</td><td>48.10</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (GCBERT)</td><td>84.92</td><td>57.09</td><td>17.92</td><td>17.02</td><td>54.10</td><td>54.11</td><td>54.74</td><td>24.97</td><td>44.74</td><td>49.83</td><td>22.28</td><td>30.10</td></tr><tr><td>MNCRI (CodeT5)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.70</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1: Results on cross-domain code vulnerability detection tasks. For simplicity, GCBERT denotes the Graph-CodeBERT (Guo et al., 2020) model. MNCRI (VulGDA-f) denote that MNCRI use the same feature extractor as VulGDA. MNCRI (CodeT5) denotes that our framework MNCRI uses CodeT5 as the feature extractor. F denotes the FFmpeg project dataset, and Q denotes the QEMU project dataset, and R denotes the Reveal project dataset. F  $\\rightarrow$  Q represents the source domain is the FFmpeg project dataset and the target domain is the QEMU dataset.",
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+    {
+        "type": "image",
+        "img_path": "images/9f3f0239c98d09101658422a6cb289b97a82f4ee9b8f910e802fe947fece01a4.jpg",
+        "image_caption": [
+            "(a) VulGDA"
+        ],
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+    },
+    {
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+        "img_path": "images/c4346c9a86c29ce40f20c9af0df74751e69a7ef4b0a3e47f312479ec4c7ace1f.jpg",
+        "image_caption": [
+            "(b) MNCRI",
+            "Figure 2: Histogram of softmax-based prediction confidence on the target domain test dataset. (a) is the prediction confidence score of VulGDA; (b) is the prediction confidence score of MNCRI. x-axis coordinate represents the prediction confidence score from 0 to 1 and y-axis coordinate represents the corresponding counts."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "target instances are vulnerable or non-vulnerable. In contrast, our proposed framework MNCRI overcomes this phenomenon (see Figure 2(b)). We can observe that there are few prediction confidence distributed around 0.5, which shows that MNCRI learns the more accurate vulnerable patterns across domains and has the superior discriminative ability for target instances.",
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+    {
+        "type": "text",
+        "text": "Overall, the promising performance of MNCRI can be attributed to the mutual nearest neighbor-based contrastive learning and the instance weighting scheme.",
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+    {
+        "type": "text",
+        "text": "4.3 Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To analyze the impact of different components in our proposed MNCRI on the performance, we conduct an ablation study on all cross-domain vulnerability detection tasks and report the results in Table 2.",
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+    {
+        "type": "text",
+        "text": "Effect of Mutual Nearest Neighbors Contrastive Learning. From the results reported in Table 2, we can observe that the removal of the mutual nearest neighbors contrastive learning (\"w/o  $\\mathcal{L}_{Con}$ ) sharply reduces the performance in all evaluation metrics (TPR and F1). This indicates that contrastive learning based on mutual nearest neighbors guarantees geometric domain alignment by pulling mutual nearest neighbors pairs closer to each other and pulling away non-geometrically close samples. Furthermore, we remove the memory bank mechanism (\"w/o MB\") in the contrastive learning training stage and record its results. We can find that removing the memory bank mechanism would degrade performance. This indicates that the global semantic information containing in the memory bank is conducive to achieving more accurate domain alignment.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effect of Instance Re-weighting Scheme. To evaluate the contribution of the instance reweighting scheme, we abandon it and report its results in Table 2. We can see that the removal of the instance re-weighting scheme (\"w/o IR\") leads to performance degradation. This implies that assigning different weights to different instances according to relevance is helpful for reducing distributional divergence between domains, which en",
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+    },
+    {
+        "type": "page_number",
+        "text": "12797",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a0c410323ae2c9a11405c12f5f15f147ec32e76129f0526b315cf7688e9a250d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">F → Q</td><td colspan=\"2\">F → R</td><td colspan=\"2\">Q → F</td><td colspan=\"2\">Q → R</td><td colspan=\"2\">R → F</td><td colspan=\"2\">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>MNCRI (Full)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.7</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr><tr><td>MNCRI (w/o LCon)</td><td>79.74</td><td>54.30</td><td>16.92</td><td>15.29</td><td>49.99</td><td>49.37</td><td>52.69</td><td>22.13</td><td>42.72</td><td>45.35</td><td>20.61</td><td>28.17</td></tr><tr><td>MNCRI (w/o MB)</td><td>83.49</td><td>55.76</td><td>17.24</td><td>16.66</td><td>53.85</td><td>52.28</td><td>55.37</td><td>23.48</td><td>43.92</td><td>48.50</td><td>23.69</td><td>30.22</td></tr><tr><td>MNCRI (w/o IR)</td><td>84.87</td><td>56.87</td><td>18.04</td><td>16.65</td><td>55.12</td><td>54.39</td><td>56.21</td><td>24.71</td><td>45.98</td><td>49.74</td><td>24.01</td><td>30.85</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/333a170dc5370df3436b273792e839f0b06ab32c51524988919f7eb8360b4863.jpg",
+        "image_caption": [
+            "(a) Neighbors number  $k$"
+        ],
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+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/fe630837fc4c27c7797044c7a680e79d169b51a9b01503e300ca52ba95005743.jpg",
+        "image_caption": [
+            "(b) Loss weights  $\\lambda$  and  $\\mu$",
+            "Figure 3: (a) Varying nearest neighbors number  $k$ . (b) Varying loss weights  $\\lambda$  and  $\\mu$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            307,
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+    },
+    {
+        "type": "text",
+        "text": "ables the model to derive better cross-domain representations, and thus leads to improved MNCRI performance.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 Sensitivity to hyper-parameter",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Impact of the nearest neighbors number  $k$ . To show the sensitivity of MNCRI to the nearest neighbors number  $k$ , we conduct the experiments on the  $\\mathrm{F} \\rightarrow \\mathrm{Q}$  cross-domain vulnerability detection task, and show the results in Figure 3(a). We observe that the F1-score increases with the increasing value of  $k$  and peaks at  $\\mathrm{k} = 20$ . Further increasing the values of  $k$  results in worse performance. The F1-score varies slightly within a wide range of  $k$ , demonstrating that MNCRI is robust to the choices of  $k$ .",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Impact of loss weights  $\\lambda$  and  $\\mu$ . To show the sensitivity of MNCRI to the loss weights  $\\lambda$  and  $\\mu$ , we conduct control experiments on the  $\\mathrm{F} \\rightarrow \\mathrm{Q}$  cross-domain vulnerability detection task. The results are illustrated in Figure 3(b). We can observe that MNCRI achieves the best performance when  $\\lambda$  is set to 0.2. Within a wide range of  $\\lambda$ , the performance of MNCRI changes very little, validating that MNCRI is stable to the choices of  $\\lambda$ . Similarly, MNCRI varies slightly with  $\\mu \\in [0.01, 0.3]$ , showing that MNCRI is robust to the selection of  $\\mu$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.5 Analysis of Few-Shot Condition",
+        "text_level": 1,
+        "bbox": [
+            112,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the generalizability of MNCRI in few-shot vulnerability detection, we also evaluate MN-CRI in the few-shot condition on the  $\\mathrm{F}\\rightarrow \\mathrm{Q}$  cross",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "domain vulnerability detection task. From the experimental results shown in Table 3, we can see that MNCRI outperforms all baseline methods under the few-shot condition. This verifies the effectiveness and generalizability of MNCRI in dealing with both zero-shot and few-shot vulnerability detection.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/0879476d9d89c6868684712cd45b64baa52341ab996cc758074ba916d038894f.jpg",
+        "table_caption": [
+            "Table 2: Experimental results of ablation study."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>TPR</td><td>f1</td></tr><tr><td>SCDAN</td><td>74.51</td><td>52.67</td></tr><tr><td>CD-VulD</td><td>79.32</td><td>53.45</td></tr><tr><td>VulGDA</td><td>79.05</td><td>54.88</td></tr><tr><td>MNCRI</td><td>86.33</td><td>59.89</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Experimental results of few-shot condition with  $20\\%$  target domain labeled samples for training.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.6 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel cross-domain code vulnerability detection framework named MNCRI to achieve domain alignment. On the one hand, we introduce mutual nearest neighbors contrastive learning to learn geometric relationships between source domain samples and target domain samples, so as to achieve geometric domain alignment. On the other hand, we introduce the instance re-weighting scheme to reduce distributional divergence between domains and achieve statistical domain alignment. Finally, we conduct extensive experiments to verify the effectiveness of our proposed framework.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
+            509,
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+    },
+    {
+        "type": "text",
+        "text": "Here we summarize the limitations for further discussion and investigation of the community. Our proposed  $k$ -nearest neighbor mechanism requires manually setting the optimal  $k^{*}$  to achieve the best cross-domain detection performance, which is inefficient. A better solution is to design an adaptive  $k$ -nearest neighbor mechanism which could adaptively seek optimal neighbor samples according to the semantic information of training samples.",
+        "bbox": [
+            507,
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "12798",
+        "bbox": [
+            477,
+            927,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            115,
+            84,
+            213,
+            98
+        ],
+        "page_idx": 8
+    },
+    {
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+            "Van Nguyen, Trung Le, Tue Le, Khanh Nguyen, Olivier DeVel, Paul Montague, Lizhen Qu, and Dinh Phung. 2019. Deep domain adaptation for vulnerable code function identification. In 2019 international joint conference on neural networks (IJCNN), pages 1-8. IEEE."
+        ],
+        "bbox": [
+            510,
+            85,
+            882,
+            917
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "12799",
+        "bbox": [
+            477,
+            928,
+            524,
+            940
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Rui Shu, Hung H Bui, Hirokazu Narui, and Stefano Ermon. 2018. A dirt-t approach to unsupervised domain adaptation. arXiv preprint arXiv:1802.08735.",
+            "Yonglong Tian, Dilip Krishnan, and Phillip Isola. 2020. Contrastive multiview coding. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XI 16, pages 776-794. Springer.",
+            "Yue Wang, Weishi Wang, Shafiq Joty, and Steven CH Hoi. 2021. Codet5: Identifier-aware unified pre-trained encoder-decoder models for code understanding and generation. arXiv preprint arXiv:2109.00859.",
+            "Yonghui Xu, Sinno Jialin Pan, Hui Xiong, Qingyao Wu, Ronghua Luo, Huaqing Min, and Hengjie Song. 2017. A unified framework for metric transfer learning. IEEE Transactions on Knowledge and Data Engineering, 29(6):1158-1171.",
+            "Hongliang Yan, Yukang Ding, Peihua Li, Qilong Wang, Yong Xu, and Wangmeng Zuo. 2017. Mind the class weight bias: Weighted maximum mean discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2272-2281.",
+            "Y. Zhou, S. Liu, J. Siow, X. Du, and Y. Liu. 2019. Devign: Effective vulnerability identification by learning comprehensive program semantics via graph neural networks.",
+            "Deqing Zou, Sujuan Wang, Shouhuai Xu, Zhen Li, and Hai Jin. 2019.  $\\mu$ vuldeepecker: A deep learning-based system for multiclass vulnerability detection. IEEE Transactions on Dependable and Secure Computing."
+        ],
+        "bbox": [
+            115,
+            85,
+            489,
+            580
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            115,
+            593,
+            354,
+            608
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We use CodeBERT, GraphCodeBERT, CodeT5 as the feature extractor, respectively. We use cross-entropy to calculate the classification loss. The classifier is a 2-layer full connected layers with 256-dimensional output, and uses MMD to measure the distributional domain discrepancy. The initial learning rate is set to 5e-4. We split source and target samples into different mini-batches with size 36. The total training epoch is 10. The temperature parameter  $\\tau$  is set to 0.05.",
+        "bbox": [
+            115,
+            618,
+            487,
+            777
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "12800",
+        "bbox": [
+            478,
+            928,
+            524,
+            940
+        ],
+        "page_idx": 9
+    }
+]

2023/Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection/6ae8c7ae-1073-4cd9-abf5-6e298cc47b67_model.json

@@ -0,0 +1,1716 @@
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+            "angle": 0,
+            "content": "Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Qianjin Du\\(^{1}\\), Shiji Zhou\\(^{2}\\), Xiaohui Kuang\\(^{3}\\), Gang Zhao\\(^{3*}\\), Jidong Zhai\\(^{1*}\\)"
+        },
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+            "content": "\\(^{1}\\)Department of Computer Science and Technology, Tsinghua University"
+        },
+        {
+            "type": "text",
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+            "content": "\\(^{2}\\)Department of Automation, Tsinghua University"
+        },
+        {
+            "type": "text",
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+            "content": "\\(^{3}\\)National Key Laboratory of Science and Technology on Information System Security"
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+            "content": "dqj20@mails.tsinghua.edu.cn;zhaijidong@tsinghua.edu.cn"
+        },
+        {
+            "type": "text",
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+            "content": "zhoushiji00@gmail.com"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "xhkuang@bupt.edu.cn; bisezhaog@163.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.261,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.145,
+                0.282,
+                0.461,
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+            ],
+            "angle": 0,
+            "content": "In code vulnerability detection tasks, a detector trained on a label-rich source domain fails to provide accurate prediction on new or unseen target domains due to the lack of labeled training data on target domains. Previous studies mainly utilize domain adaptation to perform cross-domain vulnerability detection. But they ignore the negative effect of private semantic characteristics of the target domain for domain alignment, which easily causes the problem of negative transfer. In addition, these methods forcibly reduce the distribution discrepancy between domains and do not take into account the interference of irrelevant target instances for distributional domain alignment, which leads to the problem of excessive alignment. To address the above issues, we propose a novel cross-domain code vulnerability detection framework named MN-CRI. Specifically, we introduce mutual nearest neighbor contrastive learning to align the source domain and target domain geometrically, which could align the common semantic characteristics of two domains and separate out the private semantic characteristics of each domain. Furthermore, we introduce an instance re-weighting scheme to alleviate the problem of excessive alignment. This scheme dynamically assign different weights to instances, reducing the contribution of irrelevant instances so as to achieve better domain alignment. Finally, extensive experiments demonstrate that MN-CRI significantly outperforms state-of-the-art cross-domain code vulnerability detection methods by a large margin."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
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+            ],
+            "angle": 0,
+            "content": "1 Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.833,
+                0.49,
+                0.897
+            ],
+            "angle": 0,
+            "content": "With the development of the Internet, the number of vulnerabilities in software has increased rapidly, which leaves software to face huge security threats. There are multiple efforts (Lin et al., 2017; Grieco"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.253,
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+            "angle": 0,
+            "content": "et al., 2016; Li et al., 2018; Zou et al., 2019; Zhou et al., 2019; Feng et al., 2020) have attempted to introduce deep learning and NLP techniques for automated vulnerability detection. Those deep learning-based detection methods mainly focus on in-domain code vulnerability detection. That is, the training and test datasets are assumed to be drawn from the same distribution (i.e., from the same software project). However, in practice, most software projects lack labeled vulnerability datasets. Labeling data is labor-intensive and expensive, which requires that the models trained on a label-rich source domain (i.e., a software project with abundant labeled data) are applied to a new target domain (i.e., a software project without labeled data). Owing to program style, application scenarios, and other factors, different software projects may obey different probability distributions. The models trained on the source domain suffer from severe performance loss on the target domain due to the obvious distribution discrepancy between two domains. To solve this problem, some research works have attempted to introduce domain adaptation to perform cross-domain code vulnerability detection. Domain adaptation is a technique that aims to eliminate distribution discrepancy and transfer knowledge from a labeled source domain to an unlabeled target domain (Ganin and Lempitsky, 2015). Lin et al. (2018) first proposed a function-level cross-domain code vulnerability detection framework. But they only hypothesize that the learned high-level representations are transferable, and they do not propose a method to explicitly eliminate the domain discrepancy. Lin et al. (2019) proposed a cross-domain detection framework that utilizes two LSTMs to learn two groups of transferable feature representations, and then combine both groups of feature representations to train a classifier. Nguyen et al. (2019) proposed a new code domain adaptation framework named SCDAN that incorporated conventional domain adaptation techniques such as"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "*Corresponding authors."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "12791"
+        },
+        {
+            "type": "footer",
+            "bbox": [
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+            "angle": 0,
+            "content": "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 12791-12800 December 6-10, 2023 ©2023 Association for Computational Linguistics"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.132,
+                0.084,
+                0.874,
+                0.343
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.37,
+                0.355,
+                0.626,
+                0.37
+            ],
+            "angle": 0,
+            "content": "Figure 1: The framework of MNCRI."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.394,
+                0.49,
+                0.604
+            ],
+            "angle": 0,
+            "content": "DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018). CDVulD (Liu et al., 2020) employed a metric transfer learning framework (MTLF) (Xu et al., 2017) to learn cross-domain representations by minimizing the distribution divergence between the source domain and the target domain. Lastly, Li et al. (2023) proposed a detection framework called VulGDA that utilized a graph embedding method to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing Maximum Mean Discrepancy (MMD)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.614,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Although the above-mentioned research works achieve considerable performance improvements, there still exist two problems that restrict further performance improvements: (1) In practice, different domains (i.e., different software projects) share common semantic characteristics and while having their own private semantic characteristics due to different application scenarios, coding style, and code implementation, etc. Previous studies reduce the domain discrepancy by forcibly minimizing divergence of the entire source domain and the target domain. They ignore semantic differences between two domains and allow samples with private semantic characteristics to participate in domain alignment, which is prone to the problem of negative transfer. Eliminating the domain discrepancy should be constrained on only aligning the common semantic characteristics (also known as the common knowledge) between two domains"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.394,
+                0.885,
+                0.911
+            ],
+            "angle": 0,
+            "content": "and the respective private semantic characteristics should be separated simultaneously. (2) There will always exist some target instances that are not relevant to source instances. Current methods treat the instances equally when conducting statistical distribution domain alignment. Intuitively, the relevant instances should be given larger weights, and irrelevant instances should be assigned smaller weights so as to decrease their importance and contribution to domain alignment. Ignoring the relevance of instances will make models learn suboptimal cross-domain representations. To address these issues, we propose a novel cross-domain code vulnerability detection framework named MNCRI (as illustrated in Figure 1) based on mutual nearest neighbor contrastive learning and the instance re-weighting scheme, which jointly achieves geometric domain alignment and statistical domain alignment. First, we argue that geometric domain alignment should follow a principle: semantically consistent instances should be geometrically adjacent to each other, whether within or across domains. Based on this principle, we introduce mutual nearest neighbor contrastive learning to achieve the alignment of common semantic characteristics. Specifically, we construct mutual nearest neighbor pairs across the source domain and the target domain by leveraging the mutual neighbor rule. Then we introduce a contrastive loss function that aims at reducing the feature discrepancy of mutual nearest neighbor pairs. By minimizing this contrastive loss, we achieve the alignment of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12792"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.49,
+                0.341
+            ],
+            "angle": 0,
+            "content": "common semantic characteristics across domains and separate out private semantic characteristics of each domain. Second, to alleviate the problem of excessive alignment, we introduce the instance re-weighting scheme that assigns different weights to different target domain instances based on the relevance with source domain instances. In this way, the effect of some target domain instances that are irrelevant to source domain instances is reduced and the effect of some relevant target domain instances is highlighted, which is beneficial for reducing the distribution discrepancy. Finally, we conduct extensive experiments to verify the effectiveness of our proposed method. The experimental results show that the proposed method outperforms current baseline methods by a large margin."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.133,
+                0.344,
+                0.471,
+                0.358
+            ],
+            "angle": 0,
+            "content": "In summary, our contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.137,
+                0.372,
+                0.49,
+                0.484
+            ],
+            "angle": 0,
+            "content": "- We propose a novel cross-domain code vulnerability detection framework named MNCRI, which reduces the domain discrepancy from two perspectives of geometries and statistical distributions by exploiting the mutual nearest neighbor contrastive learning and the instance re-weighting scheme."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.137,
+                0.497,
+                0.49,
+                0.577
+            ],
+            "angle": 0,
+            "content": "- We introduce mutual nearest neighbors contrastive learning to solve the problem of negative transfer, which explores instances relationships between domains and achieves the domain alignment geometrically."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.137,
+                0.59,
+                0.49,
+                0.686
+            ],
+            "angle": 0,
+            "content": "- We incorporate an instance re-weighting scheme into the statistical domain alignment, which dynamically weights different instances according to the relevance between instances to eliminate the negative effect of irrelevant instances for domain alignment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.137,
+                0.699,
+                0.49,
+                0.778
+            ],
+            "angle": 0,
+            "content": "- We conduct extensive experiments to verify the effectiveness of MNCRI. Experimental results show that MNCRI outperforms current cross-domain detection methods and obtain obvious performance improvements."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.137,
+                0.372,
+                0.49,
+                0.778
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.791,
+                0.27,
+                0.807
+            ],
+            "angle": 0,
+            "content": "2 Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.818,
+                0.424,
+                0.849
+            ],
+            "angle": 0,
+            "content": "2.1 Cross-domain Code Vulnerability Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.855,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Since different software projects have different code styles, application scenarios and other factors, they may obey different distributions. Therefore, when a code vulnerability detection model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.887,
+                0.78
+            ],
+            "angle": 0,
+            "content": "trained on a label-rich project dataset is applied to a new no-label project, its performance drop sharply. To address this issue, researchers have attempted to introduce domain-adaptation techniques into cross-domain code vulnerability detection tasks. Nam et al. (2013) utilized migration component analysis to map software metrics in the source and target domains to the same feature space. Hellendoorn et al. (2020) attempted to utilize local syntactic features and global semantic features to perform file-level cross-domain vulnerability detection. Lin et al. (2018) first proposed a cross-domain code vulnerability detection framework at the function-level, which extracts features from abstract syntax trees (ASTs) of functions and then feeds extracted features into a long short-term memory recurrent neural network (LSTM) to learn higher-level representations. But they only hypothesize that the learned high-level representations are transferable, and they do not propose an effective method to explicitly eliminate the discrepancy between the source domain and the target domain. Lin et al. (2019) presented a cross-domain detection framework that employed two LSTMs to learn two groups of transferable feature representations. These representations were then combined to train a classifier. Nguyen et al. (2019) proposed a novel code domain adaptation network called SCDAN. SCDAN incorporated conventional domain adaptation network techniques such as DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018) to eliminate distribution divergence. To further tackle the distribution divergence, CD-VulD (Liu et al., 2020) deployed the metric transfer learning framework (MTLF) (Xu et al., 2017) to learn domain-invariant representations by minimizing Mahalanobis distance. Li et al. (2023) proposed a cross-domain detection framework called VulGDA, which employed a graph embedding approach to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing the domain discrepancy."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.798,
+                0.725,
+                0.813
+            ],
+            "angle": 0,
+            "content": "2.2 Contrastive Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.823,
+                0.886,
+                0.92
+            ],
+            "angle": 0,
+            "content": "Contrastive learning in the latent space has recently shown great promise, which aims to make the representation of a given anchor data to be similar to its positive pairs and dissimilar to its negative pairs (Tian et al., 2020; Chen et al., 2020; Khosla et al., 2020). Many state-of-the-art methods for represent-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12793"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.49,
+                0.182
+            ],
+            "angle": 0,
+            "content": "tation learning tasks are based on the contrastive learning framework (Chen and He, 2021). Previous studies construct positive samples by augmenting original samples. In this paper, we utilize mutual nearest neighbors as positive pairs to achieve feature alignment between domains."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.195,
+                0.264,
+                0.212
+            ],
+            "angle": 0,
+            "content": "3 Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.221,
+                0.491,
+                0.397
+            ],
+            "angle": 0,
+            "content": "As illustrated in Figure 1, the architecture of MN-CRI contains two main components: 1) the mutual nearest neighbor contrastive learning module, which performs contrastive learning based on mutual nearest neighbors for better geometric domain alignment; 2) the statistical distribution domain alignment module equipped with the instance weighting scheme, which reduces the distribution discrepancy and achieves the domain alignment statistically. Below we elaborate the details of MN-CRI."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.411,
+                0.332,
+                0.425
+            ],
+            "angle": 0,
+            "content": "3.1 Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.432,
+                0.49,
+                0.691
+            ],
+            "angle": 0,
+            "content": "We formalize vulnerability detection as a binary classification problem. In cross-domain vulnerability detection, given a labeled source domain set \\(D_{s} = \\{(x_{i}^{s},y_{i}^{s})\\}_{i = 1}^{n_{s}}\\) including \\(n_s\\) instances \\(x_{i}^{s}\\), it aims to predict the label \\(y_{i}^{t}\\) of the target sample \\(x_{i}^{t}\\) in an unlabeled target domain set \\(D_{t} = \\{(x_{i}^{t})\\}_{i = 1}^{n_{t}}\\) where \\(y_{i}^{s}\\in \\{0,1\\}\\) and \\(y_{i}^{t}\\in \\{0,1\\}\\) (1 means the sample is vulnerable and 0 means the sample is non-vulnerable). \\(n_s\\) and \\(n_t\\) are the number of the source domain set and the target domain set, respectively. As illustrated in Figure 1, our model consists of two basic modules: (1) a feature extractor \\(f(\\cdot)\\) that maps the code sample \\(x_{i}\\) into the embedding representation \\(z_{i}\\) (\\(z_{i} = f(x_{i})\\)). (2) a classifier \\(g(\\cdot)\\) to classify the class \\(y_{i}\\) of the sample \\(x_{i}\\) (\\(y_{i} = g(f(x_{i}))\\))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.702,
+                0.486,
+                0.75
+            ],
+            "angle": 0,
+            "content": "3.2 Geometric Domain Alignment by Mutual Nearest Neighbor Contrastive Learning Paradigm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.757,
+                0.488,
+                0.787
+            ],
+            "angle": 0,
+            "content": "In supervised learning scenarios, the cross-entropy loss on the source domain is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.166,
+                0.799,
+                0.486,
+                0.839
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {C E} = - \\frac {1}{n _ {s}} \\sum_ {i = 1} ^ {n _ {s}} y _ {i} ^ {s} \\log \\left(g \\left(f \\left(x _ {i} ^ {s}\\right)\\right)\\right) + \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.221,
+                0.842,
+                0.425,
+                0.859
+            ],
+            "angle": 0,
+            "content": "\\[\n(1 - y _ {i} ^ {s}) \\log (1 - g (f (x _ {i} ^ {s})))\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.872,
+                0.489,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Due to the domain discrepancy between the source domain and the target domain, the performance drops sharply when transfer the model trained on"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.885,
+                0.439
+            ],
+            "angle": 0,
+            "content": "source domain to the target domain. Previous methods mainly focus on minimizing the global distribution divergence between domains to achieve the domain alignment, such as Maximum Mean Discrepancy (MMD) (Yan et al., 2017; Li et al., 2023). In practice, the target domain may preserve its own private semantic characteristics that do not appear in the source domain. Previous methods do not consider domain private semantic characteristics and forcefully align the global distributions of two domains, which may cause the problem of negative transfer. In manifold learning (McInnes et al., 2018; Chen et al., 2022), the concept of geometric nearest neighbors is commonly used to describe the similarities of semantic characteristics. For different domains, the geometrically nearest neighbors can be viewed as the most similar samples that contain the same semantic characteristics. Therefore, to align the common semantic characteristics between domains and separate out private semantic characteristics of each domain, we introduce mutual nearest neighbors contrastive learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.442,
+                0.885,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Specifically, for a target domain sample \\( x_{i}^{t} \\), we retrieve its corresponding \\( k \\) nearest neighbors \\( \\mathcal{N}\\mathcal{N}_{i}^{s} \\) in the source domain. In the same way, for a source domain sample \\( x_{j}^{s} \\), we can also obtain its corresponding \\( k \\) nearest neighbors \\( \\mathcal{N}\\mathcal{N}_{j}^{t} \\) in the target domain. Then mutual nearest neighbors can be constructed by following the rule: if the source sample \\( x_{j}^{s} \\) and the target sample \\( x_{i}^{t} \\) are contained in each other's nearest neighbors, they are regarded as mutual nearest neighbors. After that, we build a relationship matrix to describe the mutual nearest neighbor relationship between source domain samples and target domain samples. Formally, the relationship matrix is defined as: \\( M^{st} \\in \\mathbb{R}^{n_s \\times n_t} \\) where \\( M_{i,j}^{st} = 1 \\) if only \\( x_{i}^{t} \\) and \\( x_{j}^{s} \\) is the mutual nearest neighbor pair; otherwise \\( M_{i,j}^{st} = 0 \\). Besides, to fully utilize supervised information of the source domain and learn better discriminative features for classification, we also build in-domain relationship matrix \\( M^{ss} \\) according to ground-truth labels of the source domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.787,
+                0.884,
+                0.883
+            ],
+            "angle": 0,
+            "content": "In geometric domain alignment, we hope that built mutual nearest neighbor pairs can be closer to each other in the feature space, while non-geometrically samples should be far away from each other. In this paper, we introduce an contrastive learning loss to achieve this goal."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.888,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "For each training sample \\( x_{i} \\), its positive sample sets \\( P_{i} \\) and negative sample sets \\( N_{i} \\) in the memory"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12794"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.085,
+                0.487,
+                0.117
+            ],
+            "angle": 0,
+            "content": "bank can be obtained by relationship matrices \\( M^{ss} \\) and \\( M^{st} \\). The contrastive loss is formulated by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.129,
+                0.139,
+                0.487,
+                0.217
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C o n} = - \\sum_ {i = 1} ^ {n _ {s} + n _ {t}} \\sum_ {j \\in P _ {i}} \\log \\varphi_ {i, j} \\\\ \\log \\varphi_ {i, j} = \\frac {\\exp \\left(z _ {i} z _ {j} / \\tau\\right)}{\\sum_ {p \\in P _ {i}} \\exp \\left(z _ {i} z _ {p} / \\tau\\right) + \\sum_ {q \\in N _ {i}} \\exp \\left(z _ {i} z _ {q} / \\tau\\right)} \\tag {2} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.218,
+                0.489,
+                0.314
+            ],
+            "angle": 0,
+            "content": "where \\(\\tau\\) is a temperature parameter. By optimizing the contrastive loss, it makes the model learn geometric neighbor relationships between the source domain and the target domain and makes the feature representations of samples with common semantic characteristics closer in the feature space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.325,
+                0.487,
+                0.356
+            ],
+            "angle": 0,
+            "content": "3.3 Statistical Domain Alignment by Instance Re-weighting Scheme"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.362,
+                0.49,
+                0.537
+            ],
+            "angle": 0,
+            "content": "As depicted in Section 3.2, the mutual nearest neighbors contrastive learning could reduce the geometrical domain discrepancy and achieve better geometrical domain alignment. In practice, reducing the distributional divergence between domains and achieving the statistical domain alignment are also important for cross-domain code vulnerability detection. MMD (Gretton et al., 2008)) is a popular estimator to calculate the degree of statistical alignment of data distribution between two domains, and it is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.119,
+                0.558,
+                0.487,
+                0.645
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {M M D} = \\left\\| \\frac {1}{U ^ {2}} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) - \\frac {2}{U W} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {W} k (z _ {i} ^ {s}, z _ {j} ^ {t}) \\right. \\\\ + \\frac {1}{W ^ {2}} \\sum_ {i = 1} ^ {W} \\sum_ {j = 1} ^ {W} k \\left(z _ {i} ^ {t}, z _ {j} ^ {t}\\right) \\| _ {\\mathcal {H}} \\tag {3} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.647,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Previous studies (Liu et al., 2020; Li et al., 2023) perform statistical domain alignment by minimizing Maximum Mean Discrepancy (MMD). However, there will always exist some instances that are not relevant to the source instances. Previous methods forcefully reduce the global distributional divergence between domains and ignore the negative effect of irrelevant instances, which easily leads to the problem of excessive alignment. Ideally, relevant target instances should be assigned large weights and irrelevant instances should be assigned small weights during the domain alignment. Thus, in order to achieve this goal, we propose to introduce the instance re-weighting scheme into the statistical domain alignment. Specifically, we adopt the prediction confidence of the classifier trained on the source domain for target instances"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.883,
+                0.132
+            ],
+            "angle": 0,
+            "content": "as the weights of target instances during statistical domain alignment. This process can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.515,
+                0.154,
+                0.882,
+                0.257
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {M M D - I R} = \\Vert \\frac {1}{U ^ {2}} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) \\\\ - \\frac {2}{U W} \\sum_ {i = 1} ^ {U} \\sum_ {j = 1} ^ {W} f \\left(z _ {j} ^ {t}\\right) k \\left(z _ {i} ^ {s}, z _ {j} ^ {t}\\right) + \\frac {1}{W ^ {2}} \\sum_ {i = 1} ^ {W} \\sum_ {j = 1} ^ {W} k \\left(z _ {i} ^ {t}, z _ {j} ^ {t}\\right) \\| _ {\\mathcal {H}} \\\\ f \\left(z _ {j} ^ {t}\\right) = 2 * \\left| \\operatorname {P r o b} \\left(y _ {j} ^ {t} = 1 \\mid z _ {j} ^ {t}\\right) - 0. 5 \\right| \\tag {4} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.259,
+                0.884,
+                0.388
+            ],
+            "angle": 0,
+            "content": "where \\( Prob(y_{j}^{t} = 1|z_{j}^{t}) \\) denotes the prediction probability that the classifier predicts the target instance \\( x_{i}^{t} \\) is vulnerable. Introducing the instance re-weighting scheme degrades the impact of some target instances that are not relevant to source instances, which is helpful for reducing the distributional divergence between domains and achieving better statistical domain alignment."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.399,
+                0.696,
+                0.414
+            ],
+            "angle": 0,
+            "content": "3.4 Overall Objective"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.419,
+                0.882,
+                0.498
+            ],
+            "angle": 0,
+            "content": "MNCRI is proposed to jointly minimize the cross entropy loss of the source domain instances and reduce the divergence between the source domain and target domain. The total objective function in MNCRI is formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.529,
+                0.882,
+                0.546
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {C E} + \\lambda \\mathcal {L} _ {C o n} + \\mu \\mathcal {L} _ {M M D - I R} \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.558,
+                0.884,
+                0.671
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{CE}\\) denotes source supervised loss using source labels, and \\(\\mathcal{L}_{Con}\\) denotes the geometric domain alignment loss based on the mutual nearest neighbor contrastive learning, and \\(\\mathcal{L}_{MMD-IR}\\) denotes the statistical domain alignment loss using instance re-weighting scheme. \\(\\lambda\\) and \\(\\mu\\) are two trade-off parameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.683,
+                0.656,
+                0.699
+            ],
+            "angle": 0,
+            "content": "4 Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.708,
+                0.884,
+                0.756
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct extensive experiments to evaluate the effectiveness of the proposed framework (MNCRI)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.768,
+                0.731,
+                0.783
+            ],
+            "angle": 0,
+            "content": "4.1 Experimental Settings"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.789,
+                0.63,
+                0.802
+            ],
+            "angle": 0,
+            "content": "4.1.1 Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.807,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "In our work, we conduct experiments on three open-source software project datasets: FFmpeg, QEMU (Zhou et al., 2019) and ReVe (Chakraborty et al., 2021). There are several reasons for choosing the above datasets as experimental datasets. The first one is that they are manually labeled so that they could provide accurate supervised information."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12795"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.085,
+                0.49,
+                0.135
+            ],
+            "angle": 0,
+            "content": "Second, the number of samples of these datasets is abundant to support model training. The implementation details can be found in Appendix A."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.144,
+                0.248,
+                0.158
+            ],
+            "angle": 0,
+            "content": "4.1.2 Baselines"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.164,
+                0.491,
+                0.293
+            ],
+            "angle": 0,
+            "content": "The state-of-the-art cross-domain code vulnerability detection methods include: VulDeePecker (Li et al., 2018), SySeVr (Li et al., 2021), Devign (Zhou et al., 2019), CodeBERT (Feng et al., 2020), GraphCodeBERT (Guo et al., 2020), CodeT5 (Wang et al., 2021), SCDAN (Nguyen et al., 2019), CD-VulD (Liu et al., 2020), and VulGDA (Li et al., 2023)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.303,
+                0.319,
+                0.318
+            ],
+            "angle": 0,
+            "content": "4.1.3 Evaluation Metric"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.323,
+                0.49,
+                0.709
+            ],
+            "angle": 0,
+            "content": "In general, F1-score is a widely used metric to evaluate the performance of vulnerability detection systems. Let \\( TP \\) be the number of vulnerable samples that are predicted correctly, \\( FP \\) be the number of truly non-vulnerable samples that are predicted as vulnerable and \\( FN \\) be the number of truly vulnerable samples that are predicted as non-vulnerable. Precision (\\( P = \\frac{TP}{TP + FP} \\)) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all samples predicted as vulnerable. Recall (\\( R = \\frac{TP}{TP + FN} \\)) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all truly vulnerable samples. The F1-score (\\( F1 = \\frac{2 \\times P \\times R}{P + R} \\)) is the harmonic mean of precision and recall. It is clear that the higher F1-score represents better classification performance. Besides, vulnerability detection tasks also focus on TPR (True Positive Rate) performance (as known as Recall) of detectors. Because the higher TPR represents that the more vulnerable samples are discriminated correctly, it is crucial for the performance evaluation of detectors. Therefore, in our experiments, we adopt TPR (True Positive Rate) and F1-score as our evaluation metrics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.721,
+                0.219,
+                0.735
+            ],
+            "angle": 0,
+            "content": "4.2 Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.743,
+                0.49,
+                0.92
+            ],
+            "angle": 0,
+            "content": "We conduct extensive experiments to verify the effectiveness of the proposed framework (MNCRI). Experimental results are shown in Table 1. Our proposed framework MNCRI (CodeT5) achieves the best performances on all cross-domain code vulnerability detection tasks, and outperforms all baseline methods. For instance, in the FFmpeg-to-QEMU \\((\\mathrm{F} \\rightarrow \\mathrm{Q})\\) cross-domain detection task, MNCRI (CodeT5) achieves an F1-score of \\(58.21\\%\\), outperforming the current state-of-the-art cross-domain detection method VulGDA by"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.885,
+                0.456
+            ],
+            "angle": 0,
+            "content": "5.41%. Meanwhile, MNCRI (CodeT5) obtains a TPR gain of 9.18% compared to VulGDA. Moreover, our framework equipped with CodeBERT, GCBERT (GraphCodeBERT) also can obtain significant performance improvements compared to baseline methods. This demonstrates that the proposed framework has good generalization performance and it does not rely on the specific code feature extractor and can be adapted to various feature extractors. Since CodeT5 adopts more effective pre-training mechanisms compared to CodeBERT and GCBERT (GraphCodeBERT), MNCRI using CodeT5 as the feature extractor obtains the largest performance improvements. This demonstrates that a power feature extractor is helpful for improving cross-domain vulnerability detection performance. To make the comparison with VulGDA, MNCRI (VulGDA-f) uses the same feature extractor as VulGDA. We can observe that MNCRI (VulGDA-f) consistently outperforms VulGDA. We can conclude that the performance improvements can be attributed to the proposed domain adaptation strategies."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.462,
+                0.885,
+                0.752
+            ],
+            "angle": 0,
+            "content": "By analyzing experimental results, we can observe that MNCRI could significantly improve TPR (True Positive Rate) of the detector compared to other cross-domain vulnerability detection methods. This observation shows that mutual nearest neighbor contrastive learning and the instance reweighting scheme are conducive to reducing domain discrepancy by jointly conducting geometric domain alignment and statistical domain alignment. Besides, compared to the detectors CD-VulD, VulGDA, and MNCRI exploiting domain adaptation techniques, traditional detectors VulDeePecker, SySeVr and Devign have the worse performance in cross-domain detection tasks. This is because traditional detectors do not consider the domain gap between domains. The comparison results indicate the importance of domain adaptation in cross-domain code vulnerability detection tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.759,
+                0.887,
+                0.92
+            ],
+            "angle": 0,
+            "content": "In order to more intuitively demonstrate the classification performance of MNCRI in cross-domain vulnerability detection tasks, we plot the histogram distributions of softmax-based prediction confidence on the target domain dataset (see Figure 2). We can see that the prediction confidence scores of VulGDA are mainly distributed around 0.5 (see Figure 2(a)). This phenomenon indicates that VulGDA has no discriminative ability for a large number of target instances and is unable to judge whether"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12796"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.125,
+                0.082,
+                0.875,
+                0.266
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">F → Q</td><td colspan=\"2\">F → R</td><td colspan=\"2\">Q → F</td><td colspan=\"2\">Q → R</td><td colspan=\"2\">R → F</td><td colspan=\"2\">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>VulDeePecker</td><td>64.82</td><td>41.31</td><td>12.59</td><td>12.47</td><td>34.85</td><td>32.04</td><td>33.98</td><td>12.04</td><td>35.57</td><td>29.01</td><td>16.57</td><td>13.88</td></tr><tr><td>SySeVr</td><td>66.98</td><td>43.22</td><td>12.73</td><td>13.19</td><td>35.57</td><td>33.22</td><td>35.77</td><td>12.96</td><td>37.28</td><td>30.05</td><td>17.65</td><td>14.36</td></tr><tr><td>Devign</td><td>68.92</td><td>45.61</td><td>14.58</td><td>13.31</td><td>37.99</td><td>35.91</td><td>39.82</td><td>13.55</td><td>35.56</td><td>31.35</td><td>18.97</td><td>16.28</td></tr><tr><td>CodeBert</td><td>53.22</td><td>46.66</td><td>10.66</td><td>11.22</td><td>37.44</td><td>38.15</td><td>30.02</td><td>12.97</td><td>30.66</td><td>33.59</td><td>15.21</td><td>18.34</td></tr><tr><td>GCBERT</td><td>55.34</td><td>47.14</td><td>10.79</td><td>11.30</td><td>39.40</td><td>38.60</td><td>31.09</td><td>13.68</td><td>30.97</td><td>33.98</td><td>16.88</td><td>18.77</td></tr><tr><td>CodeT5</td><td>58.57</td><td>49.50</td><td>11.23</td><td>12.11</td><td>38.80</td><td>39.42</td><td>33.70</td><td>15.02</td><td>31.77</td><td>35.73</td><td>18.22</td><td>20.39</td></tr><tr><td>SCDAN</td><td>70.30</td><td>52.32</td><td>13.99</td><td>12.68</td><td>40.78</td><td>43.30</td><td>43.29</td><td>17.65</td><td>38.92</td><td>37.05</td><td>15.29</td><td>22.21</td></tr><tr><td>CD-VulD</td><td>73.21</td><td>51.24</td><td>13.88</td><td>14.06</td><td>48.80</td><td>46.68</td><td>48.80</td><td>20.10</td><td>40.25</td><td>40.17</td><td>18.71</td><td>25.78</td></tr><tr><td>VulGDA</td><td>76.76</td><td>52.80</td><td>15.22</td><td>14.37</td><td>47.96</td><td>47.72</td><td>50.52</td><td>20.98</td><td>40.68</td><td>42.86</td><td>19.88</td><td>26.35</td></tr><tr><td>MNCRI (VulGDA-f)</td><td>81.37</td><td>54.95</td><td>16.21</td><td>15.44</td><td>50.39</td><td>50.99</td><td>51.39</td><td>22.37</td><td>41.38</td><td>45.92</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (CodeBERT)</td><td>84.55</td><td>56.57</td><td>17.11</td><td>16.68</td><td>53.22</td><td>53.96</td><td>53.88</td><td>23.10</td><td>42.56</td><td>48.10</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (GCBERT)</td><td>84.92</td><td>57.09</td><td>17.92</td><td>17.02</td><td>54.10</td><td>54.11</td><td>54.74</td><td>24.97</td><td>44.74</td><td>49.83</td><td>22.28</td><td>30.10</td></tr><tr><td>MNCRI (CodeT5)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.70</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.113,
+                0.275,
+                0.885,
+                0.349
+            ],
+            "angle": 0,
+            "content": "Table 1: Results on cross-domain code vulnerability detection tasks. For simplicity, GCBERT denotes the Graph-CodeBERT (Guo et al., 2020) model. MNCRI (VulGDA-f) denote that MNCRI use the same feature extractor as VulGDA. MNCRI (CodeT5) denotes that our framework MNCRI uses CodeT5 as the feature extractor. F denotes the FFmpeg project dataset, and Q denotes the QEMU project dataset, and R denotes the Reveal project dataset. F \\(\\rightarrow\\) Q represents the source domain is the FFmpeg project dataset and the target domain is the QEMU dataset."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.195,
+                0.357,
+                0.407,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.262,
+                0.474,
+                0.341,
+                0.486
+            ],
+            "angle": 0,
+            "content": "(a) VulGDA"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.194,
+                0.497,
+                0.406,
+                0.609
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.261,
+                0.614,
+                0.338,
+                0.626
+            ],
+            "angle": 0,
+            "content": "(b) MNCRI"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.113,
+                0.629,
+                0.49,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Figure 2: Histogram of softmax-based prediction confidence on the target domain test dataset. (a) is the prediction confidence score of VulGDA; (b) is the prediction confidence score of MNCRI. x-axis coordinate represents the prediction confidence score from 0 to 1 and y-axis coordinate represents the corresponding counts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.723,
+                0.489,
+                0.852
+            ],
+            "angle": 0,
+            "content": "target instances are vulnerable or non-vulnerable. In contrast, our proposed framework MNCRI overcomes this phenomenon (see Figure 2(b)). We can observe that there are few prediction confidence distributed around 0.5, which shows that MNCRI learns the more accurate vulnerable patterns across domains and has the superior discriminative ability for target instances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.855,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Overall, the promising performance of MNCRI can be attributed to the mutual nearest neighbor-based contrastive learning and the instance weighting scheme."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.371,
+                0.674,
+                0.387
+            ],
+            "angle": 0,
+            "content": "4.3 Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.398,
+                0.884,
+                0.476
+            ],
+            "angle": 0,
+            "content": "To analyze the impact of different components in our proposed MNCRI on the performance, we conduct an ablation study on all cross-domain vulnerability detection tasks and report the results in Table 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.482,
+                0.884,
+                0.772
+            ],
+            "angle": 0,
+            "content": "Effect of Mutual Nearest Neighbors Contrastive Learning. From the results reported in Table 2, we can observe that the removal of the mutual nearest neighbors contrastive learning (\"w/o \\(\\mathcal{L}_{Con}\\)) sharply reduces the performance in all evaluation metrics (TPR and F1). This indicates that contrastive learning based on mutual nearest neighbors guarantees geometric domain alignment by pulling mutual nearest neighbors pairs closer to each other and pulling away non-geometrically close samples. Furthermore, we remove the memory bank mechanism (\"w/o MB\") in the contrastive learning training stage and record its results. We can find that removing the memory bank mechanism would degrade performance. This indicates that the global semantic information containing in the memory bank is conducive to achieving more accurate domain alignment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.775,
+                0.885,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Effect of Instance Re-weighting Scheme. To evaluate the contribution of the instance reweighting scheme, we abandon it and report its results in Table 2. We can see that the removal of the instance re-weighting scheme (\"w/o IR\") leads to performance degradation. This implies that assigning different weights to different instances according to relevance is helpful for reducing distributional divergence between domains, which en"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12797"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.129,
+                0.082,
+                0.872,
+                0.159
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">F → Q</td><td colspan=\"2\">F → R</td><td colspan=\"2\">Q → F</td><td colspan=\"2\">Q → R</td><td colspan=\"2\">R → F</td><td colspan=\"2\">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>MNCRI (Full)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.7</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr><tr><td>MNCRI (w/o LCon)</td><td>79.74</td><td>54.30</td><td>16.92</td><td>15.29</td><td>49.99</td><td>49.37</td><td>52.69</td><td>22.13</td><td>42.72</td><td>45.35</td><td>20.61</td><td>28.17</td></tr><tr><td>MNCRI (w/o MB)</td><td>83.49</td><td>55.76</td><td>17.24</td><td>16.66</td><td>53.85</td><td>52.28</td><td>55.37</td><td>23.48</td><td>43.92</td><td>48.50</td><td>23.69</td><td>30.22</td></tr><tr><td>MNCRI (w/o IR)</td><td>84.87</td><td>56.87</td><td>18.04</td><td>16.65</td><td>55.12</td><td>54.39</td><td>56.21</td><td>24.71</td><td>45.98</td><td>49.74</td><td>24.01</td><td>30.85</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.337,
+                0.168,
+                0.658,
+                0.182
+            ],
+            "angle": 0,
+            "content": "Table 2: Experimental results of ablation study."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.133,
+                0.207,
+                0.296,
+                0.298
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.138,
+                0.306,
+                0.289,
+                0.318
+            ],
+            "angle": 0,
+            "content": "(a) Neighbors number \\( k \\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.308,
+                0.211,
+                0.471,
+                0.299
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.311,
+                0.306,
+                0.468,
+                0.318
+            ],
+            "angle": 0,
+            "content": "(b) Loss weights \\(\\lambda\\) and \\(\\mu\\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.113,
+                0.334,
+                0.489,
+                0.363
+            ],
+            "angle": 0,
+            "content": "Figure 3: (a) Varying nearest neighbors number \\( k \\). (b) Varying loss weights \\( \\lambda \\) and \\( \\mu \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.389,
+                0.489,
+                0.436
+            ],
+            "angle": 0,
+            "content": "ables the model to derive better cross-domain representations, and thus leads to improved MNCRI performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.448,
+                0.402,
+                0.464
+            ],
+            "angle": 0,
+            "content": "4.4 Sensitivity to hyper-parameter"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.469,
+                0.489,
+                0.643
+            ],
+            "angle": 0,
+            "content": "Impact of the nearest neighbors number \\( k \\). To show the sensitivity of MNCRI to the nearest neighbors number \\( k \\), we conduct the experiments on the \\( \\mathrm{F} \\rightarrow \\mathrm{Q} \\) cross-domain vulnerability detection task, and show the results in Figure 3(a). We observe that the F1-score increases with the increasing value of \\( k \\) and peaks at \\( \\mathrm{k} = 20 \\). Further increasing the values of \\( k \\) results in worse performance. The F1-score varies slightly within a wide range of \\( k \\), demonstrating that MNCRI is robust to the choices of \\( k \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.647,
+                0.49,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Impact of loss weights \\(\\lambda\\) and \\(\\mu\\). To show the sensitivity of MNCRI to the loss weights \\(\\lambda\\) and \\(\\mu\\), we conduct control experiments on the \\(\\mathrm{F} \\rightarrow \\mathrm{Q}\\) cross-domain vulnerability detection task. The results are illustrated in Figure 3(b). We can observe that MNCRI achieves the best performance when \\(\\lambda\\) is set to 0.2. Within a wide range of \\(\\lambda\\), the performance of MNCRI changes very little, validating that MNCRI is stable to the choices of \\(\\lambda\\). Similarly, MNCRI varies slightly with \\(\\mu \\in [0.01, 0.3]\\), showing that MNCRI is robust to the selection of \\(\\mu\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.851,
+                0.409,
+                0.866
+            ],
+            "angle": 0,
+            "content": "4.5 Analysis of Few-Shot Condition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.871,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "To evaluate the generalizability of MNCRI in few-shot vulnerability detection, we also evaluate MN-CRI in the few-shot condition on the \\(\\mathrm{F}\\rightarrow \\mathrm{Q}\\) cross"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.208,
+                0.885,
+                0.304
+            ],
+            "angle": 0,
+            "content": "domain vulnerability detection task. From the experimental results shown in Table 3, we can see that MNCRI outperforms all baseline methods under the few-shot condition. This verifies the effectiveness and generalizability of MNCRI in dealing with both zero-shot and few-shot vulnerability detection."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.587,
+                0.319,
+                0.807,
+                0.405
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>TPR</td><td>f1</td></tr><tr><td>SCDAN</td><td>74.51</td><td>52.67</td></tr><tr><td>CD-VulD</td><td>79.32</td><td>53.45</td></tr><tr><td>VulGDA</td><td>79.05</td><td>54.88</td></tr><tr><td>MNCRI</td><td>86.33</td><td>59.89</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.508,
+                0.414,
+                0.882,
+                0.443
+            ],
+            "angle": 0,
+            "content": "Table 3: Experimental results of few-shot condition with \\(20\\%\\) target domain labeled samples for training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.478,
+                0.644,
+                0.492
+            ],
+            "angle": 0,
+            "content": "4.6 Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.502,
+                0.884,
+                0.71
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a novel cross-domain code vulnerability detection framework named MNCRI to achieve domain alignment. On the one hand, we introduce mutual nearest neighbors contrastive learning to learn geometric relationships between source domain samples and target domain samples, so as to achieve geometric domain alignment. On the other hand, we introduce the instance re-weighting scheme to reduce distributional divergence between domains and achieve statistical domain alignment. Finally, we conduct extensive experiments to verify the effectiveness of our proposed framework."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.729,
+                0.614,
+                0.744
+            ],
+            "angle": 0,
+            "content": "Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.759,
+                0.884,
+                0.904
+            ],
+            "angle": 0,
+            "content": "Here we summarize the limitations for further discussion and investigation of the community. Our proposed \\(k\\)-nearest neighbor mechanism requires manually setting the optimal \\(k^{*}\\) to achieve the best cross-domain detection performance, which is inefficient. A better solution is to design an adaptive \\(k\\)-nearest neighbor mechanism which could adaptively seek optimal neighbor samples according to the semantic information of training samples."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.478,
+                0.928,
+                0.526,
+                0.941
+            ],
+            "angle": 0,
+            "content": "12798"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.116,
+                0.085,
+                0.214,
+                0.099
+            ],
+            "angle": 0,
+            "content": "References"
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+            "content": "Deqing Zou, Sujuan Wang, Shouhuai Xu, Zhen Li, and Hai Jin. 2019. \\(\\mu\\)vuldeepecker: A deep learning-based system for multiclass vulnerability detection. IEEE Transactions on Dependable and Secure Computing."
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+            "content": "A Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "We use CodeBERT, GraphCodeBERT, CodeT5 as the feature extractor, respectively. We use cross-entropy to calculate the classification loss. The classifier is a 2-layer full connected layers with 256-dimensional output, and uses MMD to measure the distributional domain discrepancy. The initial learning rate is set to 5e-4. We split source and target samples into different mini-batches with size 36. The total training epoch is 10. The temperature parameter \\(\\tau\\) is set to 0.05."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "content": "12800"
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+    ]
+]

2023/Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection/6ae8c7ae-1073-4cd9-abf5-6e298cc47b67_origin.pdf

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2023/Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection/full.md

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+# Joint Geometrical and Statistical Domain Adaptation for Cross-domain Code Vulnerability Detection
+
+Qianjin Du $^{1}$ , Shiji Zhou $^{2}$ , Xiaohui Kuang $^{3}$ , Gang Zhao $^{3*}$ , Jidong Zhai $^{1*}$
+
+$^{1}$ Department of Computer Science and Technology, Tsinghua University
+
+$^{2}$ Department of Automation, Tsinghua University
+
+$^{3}$ National Key Laboratory of Science and Technology on Information System Security
+
+dqj20@mails.tsinghua.edu.cn;zhaijidong@tsinghua.edu.cn
+
+zhoushiji00@gmail.com
+
+xhkuang@bupt.edu.cn; bisezhaog@163.com
+
+# Abstract
+
+In code vulnerability detection tasks, a detector trained on a label-rich source domain fails to provide accurate prediction on new or unseen target domains due to the lack of labeled training data on target domains. Previous studies mainly utilize domain adaptation to perform cross-domain vulnerability detection. But they ignore the negative effect of private semantic characteristics of the target domain for domain alignment, which easily causes the problem of negative transfer. In addition, these methods forcibly reduce the distribution discrepancy between domains and do not take into account the interference of irrelevant target instances for distributional domain alignment, which leads to the problem of excessive alignment. To address the above issues, we propose a novel cross-domain code vulnerability detection framework named MN-CRI. Specifically, we introduce mutual nearest neighbor contrastive learning to align the source domain and target domain geometrically, which could align the common semantic characteristics of two domains and separate out the private semantic characteristics of each domain. Furthermore, we introduce an instance re-weighting scheme to alleviate the problem of excessive alignment. This scheme dynamically assign different weights to instances, reducing the contribution of irrelevant instances so as to achieve better domain alignment. Finally, extensive experiments demonstrate that MN-CRI significantly outperforms state-of-the-art cross-domain code vulnerability detection methods by a large margin.
+
+# 1 Introduction
+
+With the development of the Internet, the number of vulnerabilities in software has increased rapidly, which leaves software to face huge security threats. There are multiple efforts (Lin et al., 2017; Grieco
+
+et al., 2016; Li et al., 2018; Zou et al., 2019; Zhou et al., 2019; Feng et al., 2020) have attempted to introduce deep learning and NLP techniques for automated vulnerability detection. Those deep learning-based detection methods mainly focus on in-domain code vulnerability detection. That is, the training and test datasets are assumed to be drawn from the same distribution (i.e., from the same software project). However, in practice, most software projects lack labeled vulnerability datasets. Labeling data is labor-intensive and expensive, which requires that the models trained on a label-rich source domain (i.e., a software project with abundant labeled data) are applied to a new target domain (i.e., a software project without labeled data). Owing to program style, application scenarios, and other factors, different software projects may obey different probability distributions. The models trained on the source domain suffer from severe performance loss on the target domain due to the obvious distribution discrepancy between two domains. To solve this problem, some research works have attempted to introduce domain adaptation to perform cross-domain code vulnerability detection. Domain adaptation is a technique that aims to eliminate distribution discrepancy and transfer knowledge from a labeled source domain to an unlabeled target domain (Ganin and Lempitsky, 2015). Lin et al. (2018) first proposed a function-level cross-domain code vulnerability detection framework. But they only hypothesize that the learned high-level representations are transferable, and they do not propose a method to explicitly eliminate the domain discrepancy. Lin et al. (2019) proposed a cross-domain detection framework that utilizes two LSTMs to learn two groups of transferable feature representations, and then combine both groups of feature representations to train a classifier. Nguyen et al. (2019) proposed a new code domain adaptation framework named SCDAN that incorporated conventional domain adaptation techniques such as
+
+![](images/01f95eee71cd7758b7aa872365c274dc5f90771534d68a3ab1e00231ba03f477.jpg)  
+Figure 1: The framework of MNCRI.
+
+DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018). CDVulD (Liu et al., 2020) employed a metric transfer learning framework (MTLF) (Xu et al., 2017) to learn cross-domain representations by minimizing the distribution divergence between the source domain and the target domain. Lastly, Li et al. (2023) proposed a detection framework called VulGDA that utilized a graph embedding method to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing Maximum Mean Discrepancy (MMD).
+
+Although the above-mentioned research works achieve considerable performance improvements, there still exist two problems that restrict further performance improvements: (1) In practice, different domains (i.e., different software projects) share common semantic characteristics and while having their own private semantic characteristics due to different application scenarios, coding style, and code implementation, etc. Previous studies reduce the domain discrepancy by forcibly minimizing divergence of the entire source domain and the target domain. They ignore semantic differences between two domains and allow samples with private semantic characteristics to participate in domain alignment, which is prone to the problem of negative transfer. Eliminating the domain discrepancy should be constrained on only aligning the common semantic characteristics (also known as the common knowledge) between two domains
+
+and the respective private semantic characteristics should be separated simultaneously. (2) There will always exist some target instances that are not relevant to source instances. Current methods treat the instances equally when conducting statistical distribution domain alignment. Intuitively, the relevant instances should be given larger weights, and irrelevant instances should be assigned smaller weights so as to decrease their importance and contribution to domain alignment. Ignoring the relevance of instances will make models learn suboptimal cross-domain representations. To address these issues, we propose a novel cross-domain code vulnerability detection framework named MNCRI (as illustrated in Figure 1) based on mutual nearest neighbor contrastive learning and the instance re-weighting scheme, which jointly achieves geometric domain alignment and statistical domain alignment. First, we argue that geometric domain alignment should follow a principle: semantically consistent instances should be geometrically adjacent to each other, whether within or across domains. Based on this principle, we introduce mutual nearest neighbor contrastive learning to achieve the alignment of common semantic characteristics. Specifically, we construct mutual nearest neighbor pairs across the source domain and the target domain by leveraging the mutual neighbor rule. Then we introduce a contrastive loss function that aims at reducing the feature discrepancy of mutual nearest neighbor pairs. By minimizing this contrastive loss, we achieve the alignment of
+
+common semantic characteristics across domains and separate out private semantic characteristics of each domain. Second, to alleviate the problem of excessive alignment, we introduce the instance re-weighting scheme that assigns different weights to different target domain instances based on the relevance with source domain instances. In this way, the effect of some target domain instances that are irrelevant to source domain instances is reduced and the effect of some relevant target domain instances is highlighted, which is beneficial for reducing the distribution discrepancy. Finally, we conduct extensive experiments to verify the effectiveness of our proposed method. The experimental results show that the proposed method outperforms current baseline methods by a large margin.
+
+In summary, our contributions are as follows:
+
+- We propose a novel cross-domain code vulnerability detection framework named MNCRI, which reduces the domain discrepancy from two perspectives of geometries and statistical distributions by exploiting the mutual nearest neighbor contrastive learning and the instance re-weighting scheme.  
+- We introduce mutual nearest neighbors contrastive learning to solve the problem of negative transfer, which explores instances relationships between domains and achieves the domain alignment geometrically.  
+- We incorporate an instance re-weighting scheme into the statistical domain alignment, which dynamically weights different instances according to the relevance between instances to eliminate the negative effect of irrelevant instances for domain alignment.  
+- We conduct extensive experiments to verify the effectiveness of MNCRI. Experimental results show that MNCRI outperforms current cross-domain detection methods and obtain obvious performance improvements.
+
+# 2 Related Work
+
+# 2.1 Cross-domain Code Vulnerability Detection
+
+Since different software projects have different code styles, application scenarios and other factors, they may obey different distributions. Therefore, when a code vulnerability detection model
+
+trained on a label-rich project dataset is applied to a new no-label project, its performance drop sharply. To address this issue, researchers have attempted to introduce domain-adaptation techniques into cross-domain code vulnerability detection tasks. Nam et al. (2013) utilized migration component analysis to map software metrics in the source and target domains to the same feature space. Hellendoorn et al. (2020) attempted to utilize local syntactic features and global semantic features to perform file-level cross-domain vulnerability detection. Lin et al. (2018) first proposed a cross-domain code vulnerability detection framework at the function-level, which extracts features from abstract syntax trees (ASTs) of functions and then feeds extracted features into a long short-term memory recurrent neural network (LSTM) to learn higher-level representations. But they only hypothesize that the learned high-level representations are transferable, and they do not propose an effective method to explicitly eliminate the discrepancy between the source domain and the target domain. Lin et al. (2019) presented a cross-domain detection framework that employed two LSTMs to learn two groups of transferable feature representations. These representations were then combined to train a classifier. Nguyen et al. (2019) proposed a novel code domain adaptation network called SCDAN. SCDAN incorporated conventional domain adaptation network techniques such as DDAN, MMD, and DIRT-T (Ganin and Lempitsky, 2015; Long et al., 2015; Shu et al., 2018) to eliminate distribution divergence. To further tackle the distribution divergence, CD-VulD (Liu et al., 2020) deployed the metric transfer learning framework (MTLF) (Xu et al., 2017) to learn domain-invariant representations by minimizing Mahalanobis distance. Li et al. (2023) proposed a cross-domain detection framework called VulGDA, which employed a graph embedding approach to extract comprehensive vulnerability features and a feature generator to generate domain-invariant feature representations by minimizing the domain discrepancy.
+
+# 2.2 Contrastive Learning
+
+Contrastive learning in the latent space has recently shown great promise, which aims to make the representation of a given anchor data to be similar to its positive pairs and dissimilar to its negative pairs (Tian et al., 2020; Chen et al., 2020; Khosla et al., 2020). Many state-of-the-art methods for represent-
+
+tation learning tasks are based on the contrastive learning framework (Chen and He, 2021). Previous studies construct positive samples by augmenting original samples. In this paper, we utilize mutual nearest neighbors as positive pairs to achieve feature alignment between domains.
+
+# 3 Methodology
+
+As illustrated in Figure 1, the architecture of MN-CRI contains two main components: 1) the mutual nearest neighbor contrastive learning module, which performs contrastive learning based on mutual nearest neighbors for better geometric domain alignment; 2) the statistical distribution domain alignment module equipped with the instance weighting scheme, which reduces the distribution discrepancy and achieves the domain alignment statistically. Below we elaborate the details of MN-CRI.
+
+# 3.1 Problem Formulation
+
+We formalize vulnerability detection as a binary classification problem. In cross-domain vulnerability detection, given a labeled source domain set  $D_{s} = \{(x_{i}^{s},y_{i}^{s})\}_{i = 1}^{n_{s}}$  including  $n_s$  instances  $x_{i}^{s}$ , it aims to predict the label  $y_{i}^{t}$  of the target sample  $x_{i}^{t}$  in an unlabeled target domain set  $D_{t} = \{(x_{i}^{t})\}_{i = 1}^{n_{t}}$  where  $y_{i}^{s}\in \{0,1\}$  and  $y_{i}^{t}\in \{0,1\}$  (1 means the sample is vulnerable and 0 means the sample is non-vulnerable).  $n_s$  and  $n_t$  are the number of the source domain set and the target domain set, respectively. As illustrated in Figure 1, our model consists of two basic modules: (1) a feature extractor  $f(\cdot)$  that maps the code sample  $x_{i}$  into the embedding representation  $z_{i}$  ( $z_{i} = f(x_{i})$ ). (2) a classifier  $g(\cdot)$  to classify the class  $y_{i}$  of the sample  $x_{i}$  ( $y_{i} = g(f(x_{i}))$ ).
+
+# 3.2 Geometric Domain Alignment by Mutual Nearest Neighbor Contrastive Learning Paradigm
+
+In supervised learning scenarios, the cross-entropy loss on the source domain is defined as:
+
+$$
+\mathcal {L} _ {C E} = - \frac {1}{n _ {s}} \sum_ {i = 1} ^ {n _ {s}} y _ {i} ^ {s} \log \left(g \left(f \left(x _ {i} ^ {s}\right)\right)\right) + \tag {1}
+$$
+
+$$
+(1 - y _ {i} ^ {s}) \log (1 - g (f (x _ {i} ^ {s})))
+$$
+
+Due to the domain discrepancy between the source domain and the target domain, the performance drops sharply when transfer the model trained on
+
+source domain to the target domain. Previous methods mainly focus on minimizing the global distribution divergence between domains to achieve the domain alignment, such as Maximum Mean Discrepancy (MMD) (Yan et al., 2017; Li et al., 2023). In practice, the target domain may preserve its own private semantic characteristics that do not appear in the source domain. Previous methods do not consider domain private semantic characteristics and forcefully align the global distributions of two domains, which may cause the problem of negative transfer. In manifold learning (McInnes et al., 2018; Chen et al., 2022), the concept of geometric nearest neighbors is commonly used to describe the similarities of semantic characteristics. For different domains, the geometrically nearest neighbors can be viewed as the most similar samples that contain the same semantic characteristics. Therefore, to align the common semantic characteristics between domains and separate out private semantic characteristics of each domain, we introduce mutual nearest neighbors contrastive learning.
+
+Specifically, for a target domain sample  $x_{i}^{t}$ , we retrieve its corresponding  $k$  nearest neighbors  $\mathcal{N}\mathcal{N}_{i}^{s}$  in the source domain. In the same way, for a source domain sample  $x_{j}^{s}$ , we can also obtain its corresponding  $k$  nearest neighbors  $\mathcal{N}\mathcal{N}_{j}^{t}$  in the target domain. Then mutual nearest neighbors can be constructed by following the rule: if the source sample  $x_{j}^{s}$  and the target sample  $x_{i}^{t}$  are contained in each other's nearest neighbors, they are regarded as mutual nearest neighbors. After that, we build a relationship matrix to describe the mutual nearest neighbor relationship between source domain samples and target domain samples. Formally, the relationship matrix is defined as:  $M^{st} \in \mathbb{R}^{n_s \times n_t}$  where  $M_{i,j}^{st} = 1$  if only  $x_{i}^{t}$  and  $x_{j}^{s}$  is the mutual nearest neighbor pair; otherwise  $M_{i,j}^{st} = 0$ . Besides, to fully utilize supervised information of the source domain and learn better discriminative features for classification, we also build in-domain relationship matrix  $M^{ss}$  according to ground-truth labels of the source domain.
+
+In geometric domain alignment, we hope that built mutual nearest neighbor pairs can be closer to each other in the feature space, while non-geometrically samples should be far away from each other. In this paper, we introduce an contrastive learning loss to achieve this goal.
+
+For each training sample  $x_{i}$ , its positive sample sets  $P_{i}$  and negative sample sets  $N_{i}$  in the memory
+
+bank can be obtained by relationship matrices  $M^{ss}$  and  $M^{st}$ . The contrastive loss is formulated by:
+
+$$
+\begin{array}{l} \mathcal {L} _ {C o n} = - \sum_ {i = 1} ^ {n _ {s} + n _ {t}} \sum_ {j \in P _ {i}} \log \varphi_ {i, j} \\ \log \varphi_ {i, j} = \frac {\exp \left(z _ {i} z _ {j} / \tau\right)}{\sum_ {p \in P _ {i}} \exp \left(z _ {i} z _ {p} / \tau\right) + \sum_ {q \in N _ {i}} \exp \left(z _ {i} z _ {q} / \tau\right)} \tag {2} \\ \end{array}
+$$
+
+where  $\tau$  is a temperature parameter. By optimizing the contrastive loss, it makes the model learn geometric neighbor relationships between the source domain and the target domain and makes the feature representations of samples with common semantic characteristics closer in the feature space.
+
+# 3.3 Statistical Domain Alignment by Instance Re-weighting Scheme
+
+As depicted in Section 3.2, the mutual nearest neighbors contrastive learning could reduce the geometrical domain discrepancy and achieve better geometrical domain alignment. In practice, reducing the distributional divergence between domains and achieving the statistical domain alignment are also important for cross-domain code vulnerability detection. MMD (Gretton et al., 2008)) is a popular estimator to calculate the degree of statistical alignment of data distribution between two domains, and it is defined as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {M M D} = \left\| \frac {1}{U ^ {2}} \sum_ {i = 1} ^ {U} \sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) - \frac {2}{U W} \sum_ {i = 1} ^ {U} \sum_ {j = 1} ^ {W} k (z _ {i} ^ {s}, z _ {j} ^ {t}) \right. \\ + \frac {1}{W ^ {2}} \sum_ {i = 1} ^ {W} \sum_ {j = 1} ^ {W} k \left(z _ {i} ^ {t}, z _ {j} ^ {t}\right) \| _ {\mathcal {H}} \tag {3} \\ \end{array}
+$$
+
+Previous studies (Liu et al., 2020; Li et al., 2023) perform statistical domain alignment by minimizing Maximum Mean Discrepancy (MMD). However, there will always exist some instances that are not relevant to the source instances. Previous methods forcefully reduce the global distributional divergence between domains and ignore the negative effect of irrelevant instances, which easily leads to the problem of excessive alignment. Ideally, relevant target instances should be assigned large weights and irrelevant instances should be assigned small weights during the domain alignment. Thus, in order to achieve this goal, we propose to introduce the instance re-weighting scheme into the statistical domain alignment. Specifically, we adopt the prediction confidence of the classifier trained on the source domain for target instances
+
+as the weights of target instances during statistical domain alignment. This process can be formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {M M D - I R} = \Vert \frac {1}{U ^ {2}} \sum_ {i = 1} ^ {U} \sum_ {j = 1} ^ {U} k (z _ {i} ^ {s}, z _ {j} ^ {s}) \\ - \frac {2}{U W} \sum_ {i = 1} ^ {U} \sum_ {j = 1} ^ {W} f \left(z _ {j} ^ {t}\right) k \left(z _ {i} ^ {s}, z _ {j} ^ {t}\right) + \frac {1}{W ^ {2}} \sum_ {i = 1} ^ {W} \sum_ {j = 1} ^ {W} k \left(z _ {i} ^ {t}, z _ {j} ^ {t}\right) \| _ {\mathcal {H}} \\ f \left(z _ {j} ^ {t}\right) = 2 * \left| \operatorname {P r o b} \left(y _ {j} ^ {t} = 1 \mid z _ {j} ^ {t}\right) - 0. 5 \right| \tag {4} \\ \end{array}
+$$
+
+where  $Prob(y_{j}^{t} = 1|z_{j}^{t})$  denotes the prediction probability that the classifier predicts the target instance  $x_{i}^{t}$  is vulnerable. Introducing the instance re-weighting scheme degrades the impact of some target instances that are not relevant to source instances, which is helpful for reducing the distributional divergence between domains and achieving better statistical domain alignment.
+
+# 3.4 Overall Objective
+
+MNCRI is proposed to jointly minimize the cross entropy loss of the source domain instances and reduce the divergence between the source domain and target domain. The total objective function in MNCRI is formulated as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {C E} + \lambda \mathcal {L} _ {C o n} + \mu \mathcal {L} _ {M M D - I R} \tag {5}
+$$
+
+where  $\mathcal{L}_{CE}$  denotes source supervised loss using source labels, and  $\mathcal{L}_{Con}$  denotes the geometric domain alignment loss based on the mutual nearest neighbor contrastive learning, and  $\mathcal{L}_{MMD-IR}$  denotes the statistical domain alignment loss using instance re-weighting scheme.  $\lambda$  and  $\mu$  are two trade-off parameters.
+
+# 4 Experiments
+
+In this section, we conduct extensive experiments to evaluate the effectiveness of the proposed framework (MNCRI).
+
+# 4.1 Experimental Settings
+
+# 4.1.1 Dataset
+
+In our work, we conduct experiments on three open-source software project datasets: FFmpeg, QEMU (Zhou et al., 2019) and ReVe (Chakraborty et al., 2021). There are several reasons for choosing the above datasets as experimental datasets. The first one is that they are manually labeled so that they could provide accurate supervised information.
+
+Second, the number of samples of these datasets is abundant to support model training. The implementation details can be found in Appendix A.
+
+# 4.1.2 Baselines
+
+The state-of-the-art cross-domain code vulnerability detection methods include: VulDeePecker (Li et al., 2018), SySeVr (Li et al., 2021), Devign (Zhou et al., 2019), CodeBERT (Feng et al., 2020), GraphCodeBERT (Guo et al., 2020), CodeT5 (Wang et al., 2021), SCDAN (Nguyen et al., 2019), CD-VulD (Liu et al., 2020), and VulGDA (Li et al., 2023).
+
+# 4.1.3 Evaluation Metric
+
+In general, F1-score is a widely used metric to evaluate the performance of vulnerability detection systems. Let  $TP$  be the number of vulnerable samples that are predicted correctly,  $FP$  be the number of truly non-vulnerable samples that are predicted as vulnerable and  $FN$  be the number of truly vulnerable samples that are predicted as non-vulnerable. Precision ( $P = \frac{TP}{TP + FP}$ ) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all samples predicted as vulnerable. Recall ( $R = \frac{TP}{TP + FN}$ ) represents the ratio of vulnerable samples that are correctly predicted as vulnerable out of all truly vulnerable samples. The F1-score ( $F1 = \frac{2 \times P \times R}{P + R}$ ) is the harmonic mean of precision and recall. It is clear that the higher F1-score represents better classification performance. Besides, vulnerability detection tasks also focus on TPR (True Positive Rate) performance (as known as Recall) of detectors. Because the higher TPR represents that the more vulnerable samples are discriminated correctly, it is crucial for the performance evaluation of detectors. Therefore, in our experiments, we adopt TPR (True Positive Rate) and F1-score as our evaluation metrics.
+
+# 4.2 Results
+
+We conduct extensive experiments to verify the effectiveness of the proposed framework (MNCRI). Experimental results are shown in Table 1. Our proposed framework MNCRI (CodeT5) achieves the best performances on all cross-domain code vulnerability detection tasks, and outperforms all baseline methods. For instance, in the FFmpeg-to-QEMU  $(\mathrm{F} \rightarrow \mathrm{Q})$  cross-domain detection task, MNCRI (CodeT5) achieves an F1-score of  $58.21\%$ , outperforming the current state-of-the-art cross-domain detection method VulGDA by
+
+5.41%. Meanwhile, MNCRI (CodeT5) obtains a TPR gain of 9.18% compared to VulGDA. Moreover, our framework equipped with CodeBERT, GCBERT (GraphCodeBERT) also can obtain significant performance improvements compared to baseline methods. This demonstrates that the proposed framework has good generalization performance and it does not rely on the specific code feature extractor and can be adapted to various feature extractors. Since CodeT5 adopts more effective pre-training mechanisms compared to CodeBERT and GCBERT (GraphCodeBERT), MNCRI using CodeT5 as the feature extractor obtains the largest performance improvements. This demonstrates that a power feature extractor is helpful for improving cross-domain vulnerability detection performance. To make the comparison with VulGDA, MNCRI (VulGDA-f) uses the same feature extractor as VulGDA. We can observe that MNCRI (VulGDA-f) consistently outperforms VulGDA. We can conclude that the performance improvements can be attributed to the proposed domain adaptation strategies.
+
+By analyzing experimental results, we can observe that MNCRI could significantly improve TPR (True Positive Rate) of the detector compared to other cross-domain vulnerability detection methods. This observation shows that mutual nearest neighbor contrastive learning and the instance reweighting scheme are conducive to reducing domain discrepancy by jointly conducting geometric domain alignment and statistical domain alignment. Besides, compared to the detectors CD-VulD, VulGDA, and MNCRI exploiting domain adaptation techniques, traditional detectors VulDeePecker, SySeVr and Devign have the worse performance in cross-domain detection tasks. This is because traditional detectors do not consider the domain gap between domains. The comparison results indicate the importance of domain adaptation in cross-domain code vulnerability detection tasks.
+
+In order to more intuitively demonstrate the classification performance of MNCRI in cross-domain vulnerability detection tasks, we plot the histogram distributions of softmax-based prediction confidence on the target domain dataset (see Figure 2). We can see that the prediction confidence scores of VulGDA are mainly distributed around 0.5 (see Figure 2(a)). This phenomenon indicates that VulGDA has no discriminative ability for a large number of target instances and is unable to judge whether
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">F → Q</td><td colspan="2">F → R</td><td colspan="2">Q → F</td><td colspan="2">Q → R</td><td colspan="2">R → F</td><td colspan="2">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>VulDeePecker</td><td>64.82</td><td>41.31</td><td>12.59</td><td>12.47</td><td>34.85</td><td>32.04</td><td>33.98</td><td>12.04</td><td>35.57</td><td>29.01</td><td>16.57</td><td>13.88</td></tr><tr><td>SySeVr</td><td>66.98</td><td>43.22</td><td>12.73</td><td>13.19</td><td>35.57</td><td>33.22</td><td>35.77</td><td>12.96</td><td>37.28</td><td>30.05</td><td>17.65</td><td>14.36</td></tr><tr><td>Devign</td><td>68.92</td><td>45.61</td><td>14.58</td><td>13.31</td><td>37.99</td><td>35.91</td><td>39.82</td><td>13.55</td><td>35.56</td><td>31.35</td><td>18.97</td><td>16.28</td></tr><tr><td>CodeBert</td><td>53.22</td><td>46.66</td><td>10.66</td><td>11.22</td><td>37.44</td><td>38.15</td><td>30.02</td><td>12.97</td><td>30.66</td><td>33.59</td><td>15.21</td><td>18.34</td></tr><tr><td>GCBERT</td><td>55.34</td><td>47.14</td><td>10.79</td><td>11.30</td><td>39.40</td><td>38.60</td><td>31.09</td><td>13.68</td><td>30.97</td><td>33.98</td><td>16.88</td><td>18.77</td></tr><tr><td>CodeT5</td><td>58.57</td><td>49.50</td><td>11.23</td><td>12.11</td><td>38.80</td><td>39.42</td><td>33.70</td><td>15.02</td><td>31.77</td><td>35.73</td><td>18.22</td><td>20.39</td></tr><tr><td>SCDAN</td><td>70.30</td><td>52.32</td><td>13.99</td><td>12.68</td><td>40.78</td><td>43.30</td><td>43.29</td><td>17.65</td><td>38.92</td><td>37.05</td><td>15.29</td><td>22.21</td></tr><tr><td>CD-VulD</td><td>73.21</td><td>51.24</td><td>13.88</td><td>14.06</td><td>48.80</td><td>46.68</td><td>48.80</td><td>20.10</td><td>40.25</td><td>40.17</td><td>18.71</td><td>25.78</td></tr><tr><td>VulGDA</td><td>76.76</td><td>52.80</td><td>15.22</td><td>14.37</td><td>47.96</td><td>47.72</td><td>50.52</td><td>20.98</td><td>40.68</td><td>42.86</td><td>19.88</td><td>26.35</td></tr><tr><td>MNCRI (VulGDA-f)</td><td>81.37</td><td>54.95</td><td>16.21</td><td>15.44</td><td>50.39</td><td>50.99</td><td>51.39</td><td>22.37</td><td>41.38</td><td>45.92</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (CodeBERT)</td><td>84.55</td><td>56.57</td><td>17.11</td><td>16.68</td><td>53.22</td><td>53.96</td><td>53.88</td><td>23.10</td><td>42.56</td><td>48.10</td><td>21.69</td><td>29.32</td></tr><tr><td>MNCRI (GCBERT)</td><td>84.92</td><td>57.09</td><td>17.92</td><td>17.02</td><td>54.10</td><td>54.11</td><td>54.74</td><td>24.97</td><td>44.74</td><td>49.83</td><td>22.28</td><td>30.10</td></tr><tr><td>MNCRI (CodeT5)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.70</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr></table>
+
+Table 1: Results on cross-domain code vulnerability detection tasks. For simplicity, GCBERT denotes the Graph-CodeBERT (Guo et al., 2020) model. MNCRI (VulGDA-f) denote that MNCRI use the same feature extractor as VulGDA. MNCRI (CodeT5) denotes that our framework MNCRI uses CodeT5 as the feature extractor. F denotes the FFmpeg project dataset, and Q denotes the QEMU project dataset, and R denotes the Reveal project dataset. F  $\rightarrow$  Q represents the source domain is the FFmpeg project dataset and the target domain is the QEMU dataset.
+
+![](images/9f3f0239c98d09101658422a6cb289b97a82f4ee9b8f910e802fe947fece01a4.jpg)  
+(a) VulGDA
+
+![](images/c4346c9a86c29ce40f20c9af0df74751e69a7ef4b0a3e47f312479ec4c7ace1f.jpg)  
+(b) MNCRI  
+Figure 2: Histogram of softmax-based prediction confidence on the target domain test dataset. (a) is the prediction confidence score of VulGDA; (b) is the prediction confidence score of MNCRI. x-axis coordinate represents the prediction confidence score from 0 to 1 and y-axis coordinate represents the corresponding counts.
+
+target instances are vulnerable or non-vulnerable. In contrast, our proposed framework MNCRI overcomes this phenomenon (see Figure 2(b)). We can observe that there are few prediction confidence distributed around 0.5, which shows that MNCRI learns the more accurate vulnerable patterns across domains and has the superior discriminative ability for target instances.
+
+Overall, the promising performance of MNCRI can be attributed to the mutual nearest neighbor-based contrastive learning and the instance weighting scheme.
+
+# 4.3 Ablation Study
+
+To analyze the impact of different components in our proposed MNCRI on the performance, we conduct an ablation study on all cross-domain vulnerability detection tasks and report the results in Table 2.
+
+Effect of Mutual Nearest Neighbors Contrastive Learning. From the results reported in Table 2, we can observe that the removal of the mutual nearest neighbors contrastive learning ("w/o  $\mathcal{L}_{Con}$ ) sharply reduces the performance in all evaluation metrics (TPR and F1). This indicates that contrastive learning based on mutual nearest neighbors guarantees geometric domain alignment by pulling mutual nearest neighbors pairs closer to each other and pulling away non-geometrically close samples. Furthermore, we remove the memory bank mechanism ("w/o MB") in the contrastive learning training stage and record its results. We can find that removing the memory bank mechanism would degrade performance. This indicates that the global semantic information containing in the memory bank is conducive to achieving more accurate domain alignment.
+
+Effect of Instance Re-weighting Scheme. To evaluate the contribution of the instance reweighting scheme, we abandon it and report its results in Table 2. We can see that the removal of the instance re-weighting scheme ("w/o IR") leads to performance degradation. This implies that assigning different weights to different instances according to relevance is helpful for reducing distributional divergence between domains, which en
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">F → Q</td><td colspan="2">F → R</td><td colspan="2">Q → F</td><td colspan="2">Q → R</td><td colspan="2">R → F</td><td colspan="2">R → Q</td></tr><tr><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td><td>TPR</td><td>F1</td></tr><tr><td>MNCRI (Full)</td><td>85.94</td><td>58.21</td><td>18.66</td><td>17.51</td><td>56.7</td><td>55.42</td><td>57.09</td><td>25.65</td><td>46.60</td><td>50.22</td><td>24.41</td><td>31.50</td></tr><tr><td>MNCRI (w/o LCon)</td><td>79.74</td><td>54.30</td><td>16.92</td><td>15.29</td><td>49.99</td><td>49.37</td><td>52.69</td><td>22.13</td><td>42.72</td><td>45.35</td><td>20.61</td><td>28.17</td></tr><tr><td>MNCRI (w/o MB)</td><td>83.49</td><td>55.76</td><td>17.24</td><td>16.66</td><td>53.85</td><td>52.28</td><td>55.37</td><td>23.48</td><td>43.92</td><td>48.50</td><td>23.69</td><td>30.22</td></tr><tr><td>MNCRI (w/o IR)</td><td>84.87</td><td>56.87</td><td>18.04</td><td>16.65</td><td>55.12</td><td>54.39</td><td>56.21</td><td>24.71</td><td>45.98</td><td>49.74</td><td>24.01</td><td>30.85</td></tr></table>
+
+![](images/333a170dc5370df3436b273792e839f0b06ab32c51524988919f7eb8360b4863.jpg)  
+(a) Neighbors number  $k$
+
+![](images/fe630837fc4c27c7797044c7a680e79d169b51a9b01503e300ca52ba95005743.jpg)  
+(b) Loss weights  $\lambda$  and  $\mu$  
+Figure 3: (a) Varying nearest neighbors number  $k$ . (b) Varying loss weights  $\lambda$  and  $\mu$ .
+
+ables the model to derive better cross-domain representations, and thus leads to improved MNCRI performance.
+
+# 4.4 Sensitivity to hyper-parameter
+
+Impact of the nearest neighbors number  $k$ . To show the sensitivity of MNCRI to the nearest neighbors number  $k$ , we conduct the experiments on the  $\mathrm{F} \rightarrow \mathrm{Q}$  cross-domain vulnerability detection task, and show the results in Figure 3(a). We observe that the F1-score increases with the increasing value of  $k$  and peaks at  $\mathrm{k} = 20$ . Further increasing the values of  $k$  results in worse performance. The F1-score varies slightly within a wide range of  $k$ , demonstrating that MNCRI is robust to the choices of  $k$ .
+
+Impact of loss weights  $\lambda$  and  $\mu$ . To show the sensitivity of MNCRI to the loss weights  $\lambda$  and  $\mu$ , we conduct control experiments on the  $\mathrm{F} \rightarrow \mathrm{Q}$  cross-domain vulnerability detection task. The results are illustrated in Figure 3(b). We can observe that MNCRI achieves the best performance when  $\lambda$  is set to 0.2. Within a wide range of  $\lambda$ , the performance of MNCRI changes very little, validating that MNCRI is stable to the choices of  $\lambda$ . Similarly, MNCRI varies slightly with  $\mu \in [0.01, 0.3]$ , showing that MNCRI is robust to the selection of  $\mu$ .
+
+# 4.5 Analysis of Few-Shot Condition
+
+To evaluate the generalizability of MNCRI in few-shot vulnerability detection, we also evaluate MN-CRI in the few-shot condition on the  $\mathrm{F}\rightarrow \mathrm{Q}$  cross
+
+domain vulnerability detection task. From the experimental results shown in Table 3, we can see that MNCRI outperforms all baseline methods under the few-shot condition. This verifies the effectiveness and generalizability of MNCRI in dealing with both zero-shot and few-shot vulnerability detection.
+
+Table 2: Experimental results of ablation study.  
+
+<table><tr><td>Methods</td><td>TPR</td><td>f1</td></tr><tr><td>SCDAN</td><td>74.51</td><td>52.67</td></tr><tr><td>CD-VulD</td><td>79.32</td><td>53.45</td></tr><tr><td>VulGDA</td><td>79.05</td><td>54.88</td></tr><tr><td>MNCRI</td><td>86.33</td><td>59.89</td></tr></table>
+
+Table 3: Experimental results of few-shot condition with  $20\%$  target domain labeled samples for training.
+
+# 4.6 Conclusion
+
+In this paper, we propose a novel cross-domain code vulnerability detection framework named MNCRI to achieve domain alignment. On the one hand, we introduce mutual nearest neighbors contrastive learning to learn geometric relationships between source domain samples and target domain samples, so as to achieve geometric domain alignment. On the other hand, we introduce the instance re-weighting scheme to reduce distributional divergence between domains and achieve statistical domain alignment. Finally, we conduct extensive experiments to verify the effectiveness of our proposed framework.
+
+# Limitations
+
+Here we summarize the limitations for further discussion and investigation of the community. Our proposed  $k$ -nearest neighbor mechanism requires manually setting the optimal  $k^{*}$  to achieve the best cross-domain detection performance, which is inefficient. A better solution is to design an adaptive  $k$ -nearest neighbor mechanism which could adaptively seek optimal neighbor samples according to the semantic information of training samples.
+
+# References
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+
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+
+# A Implementation Details
+
+We use CodeBERT, GraphCodeBERT, CodeT5 as the feature extractor, respectively. We use cross-entropy to calculate the classification loss. The classifier is a 2-layer full connected layers with 256-dimensional output, and uses MMD to measure the distributional domain discrepancy. The initial learning rate is set to 5e-4. We split source and target samples into different mini-batches with size 36. The total training epoch is 10. The temperature parameter  $\tau$  is set to 0.05.

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+        "text": "Henry Peng Zou Cornelia Caragea",
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+        "text": "Computer Science University of Illinois Chicago pzou3@uic.edu cornelia@uic.edu",
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+        "text": "Semi-supervised text classification (SSTC) has gained increasing attention due to its ability to leverage unlabeled data. However, existing approaches based on pseudo-labeling suffer from the issues of pseudo-label bias and error accumulation. In this paper, we propose JointMatch, a holistic approach for SSTC that addresses these challenges by unifying ideas from recent semi-supervised learning and the task of learning with noise. JointMatch adaptively adjusts classwise thresholds based on the learning status of different classes to mitigate model bias towards current easy classes. Additionally, JointMatch alleviates error accumulation by utilizing two differently initialized networks to teach each other in a cross-labeling manner. To maintain divergence between the two networks for mutual learning, we introduce a strategy that weighs more disagreement data while also allowing the utilization of high-quality agreement data for training. Experimental results on benchmark datasets demonstrate the superior performance of JointMatch, achieving a significant  $5.13\\%$  improvement on average. Notably, JointMatch delivers impressive results even in the extremely-scarce-label setting, obtaining  $86\\%$  accuracy on AG News with only 5 labels per class. We make our code available at https://github.com/HenryPengZou/JointMatch.",
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+        "text": "1 Introduction",
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+        "text": "The success of deep learning models often heavily depends on the availability of large amounts of labeled data (He et al., 2016; Vaswani et al., 2017). However, the labeled data for many tasks are often expensive, difficult, and time-consuming to obtain. By contrast, acquiring unlabeled data is more cost-effective and convenient in many scenarios. This has led to a surge of interest in semi-supervised learning, which aims to enhance learning performance with limited labeled samples by leveraging",
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+        "text": "large amounts of unlabeled data (Berthelot et al., 2019; Sohn et al., 2020).",
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+        "text": "Recently, the combination of pseudo-labeling and consistency regularization has become a popular paradigm for semi-supervised learning (Sohn et al., 2020; Zhang et al., 2021; Sosea and Caragea, 2022). Pseudo-labeling (Lee et al., 2013) uses a fixed threshold to select the model's high-confidence predictions as pseudo-labels for further training, whereas consistency regularization (Sajjadi et al., 2016) enforces the model to make similar predictions for perturbed versions of the same data. For example, UDA (Xie et al., 2020) applies strong data augmentations, such as back-translation, to unlabeled data and minimizes the divergence between model predictions of input and its augmented views. FixMatch (Sohn et al., 2020) uses the pseudo-label generated from weakly-augmented unlabeled data to supervise the strongly augmented version of the same data. SAT (Chen et al., 2022) improves FixMatch by training a meta-learner to re-rank different augmentations based on their similarities with the original data. These methods require a pre-defined high-confidence threshold to generate high-quality pseudo-labels for good performance. However, there are some potential limitations: (1) Setting a fixed threshold for pseudo-label selection neglects the varied difficulties of learning different classes (Zhang et al., 2021; Wang et al., 2023b,a). This can cause the model bias toward easy classes, as more pseudo-labels will be generated for current easy classes (see Figure 1a); and (2) If these pseudo-labels are incorrect and used to train the model, the model can be worse and produce more inaccurate pseudo-labels, progressively accumulating its error and degenerating its performance (see Figure 1c) (Arazo et al., 2020).",
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+        "text": "To address these issues, we propose JointMatch, a diverse and collaborative pseudo-labeling approach for semi-supervised text classification (SSTC). JointMatch is a holistic framework that",
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+        "text": "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 7290-7301 December 6-10, 2023 ©2023 Association for Computational Linguistics",
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+        "img_path": "images/122c5d928600c62e8f94e6ab0a531459b9c88b7b96cac42f91a74784cc2a1f09.jpg",
+        "image_caption": [
+            "(a) FixMatch"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/afde5150bd3d088cf5304a84cd30a8da550adf31084740d38b4f3fa8c155841d.jpg",
+        "image_caption": [
+            "(b) JointMatch",
+            "Figure 1: Number of pseudo labels (a, b) and validation accuracy (c) of FixMatch and JointMatch on AG News with 10 labels per category. Pseudo-labeling approaches that use a fixed threshold, such as FixMatch, suffer from pseudo-label bias towards easy classes and error accumulation along the training. In contrast, JointMatch effectively balances pseudo-labels and avoids degenerated performance caused by error accumulation."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/1fb2ae51672a9ce23e5961046c250eaa6b7863b01ba1bbe010324e30595e41b5.jpg",
+        "image_caption": [
+            "(c) Error Accumulation"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            628,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "unifies ideas from recent semi-supervised learning and the task of learning with noise for SSTC. Inspired by FlexMatch (Zhang et al., 2021) and FreeMatch (Wang et al., 2023b), we adaptively adjust classwise thresholds based on the estimated learning status for different classes at different times. This enables difficult classes at the current iteration to have lower local thresholds, thereby facilitating more pseudo-labels to be produced and used for learning these classes (see Figure 1b). Following the idea of co-training (Blum and Mitchell, 1998), JointMatch simultaneously trains two differently initialized networks and uses them to teach each other in a cross-labeling manner to alleviate error accumulation, as different networks can filter different types of noise.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Nevertheless, with the increase of training iterations, those networks will slowly converge and reduce to one network and thus will again suffer from the issue of error accumulation. Inspired by Co-Teaching+ (Yu et al., 2019) and Decoupling (Malach and Shalev-Shwartz, 2017), we propose to give more weight to disagreement data to keep the two networks diverged while also allowing the utilization of high-quality agreement data for training. The relationship and difference between our JointMatch and related techniques are discussed in detail in Section 2.5.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We evaluate the proposed JointMatch on three commonly studied SSTC benchmark datasets. Experimental results indicate the superior performance of JointMatch, obtaining a significant  $5.13\\%$  average improvement over the latest work SAT. We also analyze the performance of JointMatch with varying numbers of labeled data. The results show that JointMatch can deliver impressive results even",
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+    {
+        "type": "text",
+        "text": "in the extremely-scarce-labels setting, achieving  $86\\%$  accuracy on AG News with only 5 labels per class. We provide comprehensive ablation studies and analysis to understand each part of JointMatch.",
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+    {
+        "type": "text",
+        "text": "2 JointMatch",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1 Overview",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we introduce our proposed Joint-Match for semi-supervised text classification. Joint-Match is a unified approach that integrates ideas and components from recent semi-supervised learning and the task of learning with noise. Specifically, we utilize three key techniques, i.e., (i) adaptive local thresholding; (ii) cross-labeling; (iii) weighted disagreement & agreement update, to address the limitations we have identified: (a) bias towards easy classes; (b) error accumulation; (c) tradeoff between divergence & consensus.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The main pipeline for JointMatch is shown in Figure 2. For each batch of unlabeled data  $\\mathcal{U}$ , we first apply both weak data augmentation  $\\alpha(\\cdot)$  and strong data augmentation  $A(\\cdot)$ , such as synonym replacement and back translation, respectively. The weakly augmented data are then forwarded to two differently initialized models  $f$  and  $g$  to make predictions. High-confidence predictions that pass the adaptive local threshold  $\\tau_t(c)$  are selected as pseudo-labels. Especially, the pseudo-labels generated by one model are used to teach its peer network, i.e., cross-labeling. The unlabeled loss  $\\mathcal{L}_u$  is computed between generated pseudo-labels and model predictions of strongly augmented data. Here, we weigh more disagreement data (where both networks have different label predictions) to keep the two networks diverged but also allow the utilization of agreement data that are more likely",
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+    {
+        "type": "page_number",
+        "text": "7291",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "image",
+        "img_path": "images/d4b8b3662497b17d3cacf5e68e8f60fe49f584f2b5f4b31b15ecdf07a90a6c3d.jpg",
+        "image_caption": [
+            "Figure 2: Pipeline of JointMatch. Unlabeled data undergo both weak and strong data augmentation. Weakly augmented data are first fed into two differently initialized models. Predictions with confidence surpassing adaptive local thresholds are selected as pseudo labels for training. Notably, pseudo labels from one model are used to teach its peer network, i.e., cross-labeling. Unlabeled data loss is then computed between pseudo labels from weakly-augmented data and model predictions from strongly augmented data. Here, we weigh more disagreement data to keep the two models diverged for effective mutual learning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "to be correct. A complete algorithm for JointMatch is presented in Algorithm 1. Next, we explain our key components in detail.",
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+    },
+    {
+        "type": "text",
+        "text": "2.2 Adaptive Local Thresholding",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Pseudo-labeling-based semi-supervised text classification algorithms use a fixed threshold to select high-confidence unlabeled data as pseudo-labels for training. However, this ignores the varied difficulties of learning different classes at different time steps, and may result in that easier classes can generate more pseudo-labels than hard classes for learning and can cause increasing model bias along training (see Figure 1a). Inspired by FlexMatch (Zhang et al., 2021) and FreeMatch (Wang et al., 2023b), instead of using a fixed threshold, our JointMatch estimates the learning status of different classes and adaptively adjusts the local thresholds for different classes to produce more diversified pseudo-labels (see Figure 1b). Specifically, at each time step  $t$ , we first estimate the classwise learning status  $\\tilde{p}_t = [\\tilde{p}_t(1),\\tilde{p}_t(2),\\dots,\\tilde{p}_t(C)]$  via the exponential moving average of model's predicted probability on unlabeled data:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {p} _ {t} = \\lambda \\tilde {p} _ {t - 1} + (1 - \\lambda) \\frac {1}{\\mu B} \\sum_ {b = 1} ^ {\\mu B} q _ {b} \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{p}_0 = [1 / C, 1 / C, \\dots, 1 / C]$ ,  $C$  is the number of classes,  $B$  is the batch size of labeled data,  $\\mu$  is the ratio of unlabeled data to labeled data,  $\\lambda \\in (0, 1)$  is the momentum parameter,  $q_b = p_m(\\alpha(u_b))$  denotes model's predicted class distribution on weak-augmented unlabeled data. Then we normalize the estimated learning status and adjust the local threshold for each class  $c$  from the pre-defined threshold  $\\tau$ :",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tau_ {t} (c) = \\operatorname {M a x N o r m} \\left(\\tilde {p} _ {t} (c)\\right) \\cdot \\tau = \\frac {\\tilde {p} _ {t} (c)}{\\max  _ {c} \\left(\\tilde {p} _ {t} (c) \\right.} \\cdot \\tau \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "By doing this, difficult classes at the current iteration will have lower local thresholds, encouraging more pseudo-labels to be generated and utilized for training these classes.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 Cross-Labeling",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Another issue of pseudo-labeling, or more generally, self-training, is error accumulation: If the generated predictions are incorrect and the model is trained on them, the model can become worse and worse, continually producing more noisy pseudo-labels and accumulating its error (see Figure 1c). Inspired by Co-Training (Blum and Mitchell, 1998), our JointMatch involves the simultaneous training of two networks with different initializations. These networks are utilized to mutually instruct each other through cross-labeling. This strategy mitigates error accumulation because different networks can filter out different noises.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "More formally, given two differently initialized networks  $f$  and  $g$ , each network first selects its own high-confidence predictions of unlabeled data as pseudo-labels for the other network. The selected pseudo-labels are then used to compute unlabeled data loss  $\\mathcal{L}_u$  to update the parameters for its peer network:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {f} = \\frac {1}{\\mu B} \\sum_ {b = 1} ^ {\\mu B} \\mathbb {1} (\\max  (q _ {b} ^ {g}) \\geq \\\\ \\tau_ {t} ^ {g} (\\arg \\max (q _ {b} ^ {g}))) \\mathcal {H} (\\hat {q} _ {b} ^ {g}, Q _ {b} ^ {f}) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {g} = \\frac {1}{\\mu B} \\sum_ {b = 1} ^ {\\mu B} \\mathbb {1} \\left(\\max  \\left(q _ {b} ^ {f}\\right) \\geq \\right. \\\\ \\tau_ {t} ^ {f} \\left(\\arg \\max  \\left(q _ {b} ^ {f}\\right)\\right)) \\mathcal {H} \\left(\\hat {q} _ {b} ^ {f}, Q _ {b} ^ {g}\\right) \\tag {3} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "page_number",
+        "text": "7292",
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+    {
+        "type": "text",
+        "text": "Algorithm 1 JointMatch algorithm.",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1: Input: Differently initialized model  $f$ ,  $g$ , number of classes  $C$ , labeled batch  $\\mathcal{X} = \\{(x_b, y_b) : b \\in (1, 2, \\ldots, B)\\}$ , unlabeled batch  $\\mathcal{U} = \\{u_b : b \\in (1, 2, \\ldots, \\mu B)\\}$ , where  $B$  is the batch size of labeled data,  $\\mu$  is the ratio of unlabeled data to labeled data, unsupervised loss weight  $w_u$ , EMA decay  $\\lambda$ , fixed threshold  $\\tau$ , disagreement weight  $\\delta$ , weak and strong data augmentations  $\\alpha(\\cdot)$ ,  $A(\\cdot)$ .",
+        "bbox": [
+            124,
+            103,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "2: for model  $f, g$  do",
+            "3:  $\\mathcal{L}_s = \\frac{1}{B}\\sum_{b = 1}^B\\mathcal{H}(y_b,p_m(\\alpha (x_b)))$  {Compute loss for labeled data,  $p_m(\\cdot)$  denotes for model prediction}",
+            "4:  $\\tilde{p}_t = \\lambda \\tilde{p}_{t-1} + (1 - \\lambda) \\frac{1}{\\mu B} \\sum_{b=1}^{\\mu B} q_b$  {Estimate learning status for different classes,  $q_b$  is an abbreviation of  $p_m(\\alpha(u_b))$ }",
+            "5: for  $c = 1$  to  $C$  do",
+            "6:  $\\tau_{t}(c) = \\mathrm{MaxNorm}(\\tilde{p}_{t}(c))\\cdot \\tau$  {Adjust the local threshold for each class based on its learning status}",
+            "7: end for",
+            "8: end for",
+            "9: for  $b = 1$  to  $\\mu B$  do"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "10:  $w_{b} = \\delta \\mathbb{1}(\\hat{q}_{b}^{f}\\neq \\hat{q}_{b}^{g}) + (1 - \\delta)\\mathbb{1}(\\hat{q}_{b}^{f} = \\hat{q}_{b}^{g})$  {Compute sample weight based on prediction disagreement,  $\\hat{q}_b$  denotes the generated hard label}",
+            "11: end for",
+            "12:  $\\mathcal{L}_u^f = \\frac{1}{\\mu B}\\sum_{b = 1}^{\\mu B}w_b\\mathbb{1}\\left(\\max \\left(q_b^g\\right)\\geq \\tau_t^g (\\arg \\max \\left(q_b^g\\right))\\right)\\mathcal{H}(\\hat{q}_b^g,Q_b^f)$"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "\\(\\mathcal{L}_u^g = \\frac{1}{\\mu B}\\sum_{b = 1}^{\\mu B}w_b\\mathbb{1}\\left(\\max \\left(q_b^f\\right)\\geq \\tau_t^f (\\arg \\max \\left(q_b^f\\right))\\right)\\mathcal{H}(\\hat{q}_b^f,Q_b^g)\\) {Compute loss for unlabeled data, the pseudo-label generated by one network is used to supervise another network, \\(Q_{b}\\) is an abbreviation of \\(p_m(A(u_b))\\})",
+        "bbox": [
+            144,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "13: Return:  $\\mathcal{L}_s^f + w_u\\mathcal{L}_u^f$ ,  $\\mathcal{L}_s^g + w_u\\mathcal{L}_u^g$",
+        "bbox": [
+            119,
+            420,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $q_{b}$  and  $Q_{b}$  denote model's predicted class distributions on weakly and strongly augmented data, respectively,  $\\hat{q}_{b}$  is the one-hot label that is converted from  $q_{b}$ , and  $\\mathcal{H}$  refers to cross-entropy loss. Compared to self-training, this approach displays a zigzag-shaped error flow, which helps to avoid direct error accumulation within a single network.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.4 Weighted Disagreement & Agreement Update",
+        "text_level": 1,
+        "bbox": [
+            112,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Two differently initialized networks can have varied learning abilities to filter different types of error in the initial training stage, allowing them to learn from its peer. However, as the training goes on, those networks will gradually converge, and the co-training approach will degenerate to self-training and thus again suffer from error accumulation. To address this problem, Decoupling (Malach and Shalev-Shwartz, 2017) and Co-Teaching+ (Yu et al., 2019) propose to update networks only by data with disagreed network predictions and find that this strategy is effective in keeping two networks diverged. Nevertheless, their approaches completely ignore the agreement data, where both networks have the same prediction. We argue that those agreement data are a valuable learning signal, as they are more likely to receive correct pseudo",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "labels and should also be utilized. To this end, we propose to compute a loss weight  $w_{b}$  for each unlabeled data  $u_{b}$  that weighs more disagreement data to keep two networks diverged while also allowing the utilization of agreement data:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {b} = \\delta \\mathbb {1} (\\hat {q} _ {b} ^ {f} \\neq \\hat {q} _ {b} ^ {g}) + (1 - \\delta) \\mathbb {1} (\\hat {q} _ {b} ^ {f} = \\hat {q} _ {b} ^ {g}) \\quad (4)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\delta \\in (0.5,1)$  is the disagreement weight. The unlabeled data loss  $\\mathcal{L}_u$  thus becomes:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {f} = \\frac {1}{\\mu B} \\sum_ {b = 1} ^ {\\mu B} w _ {b} \\mathbb {1} (\\max  (q _ {b} ^ {g}) \\geq \\\\ \\tau_ {t} ^ {g} (\\arg \\max  \\left(q _ {b} ^ {g}\\right))) \\mathcal {H} (\\hat {q} _ {b} ^ {g}, Q _ {b} ^ {f}) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            510,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {g} = \\frac {1}{\\mu B} \\sum_ {b = 1} ^ {\\mu B} w _ {b} \\mathbb {1} (\\max  (q _ {b} ^ {f}) \\geq \\\\ \\tau_ {t} ^ {f} \\left(\\arg \\max  \\left(q _ {b} ^ {f}\\right)\\right)) \\mathcal {H} \\left(\\hat {q} _ {b} ^ {f}, Q _ {b} ^ {g}\\right) \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Our experiment result in Section 4.2 shows that this approach is more effective than the method using (i) only disagreement data; (2) only agreement data; (3) weighting both kinds of data equally. Note that this method can be further improved by adaptively adjusting the disagreement weight based on the disagreement degree of two networks or based on",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "7293",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "table",
+        "img_path": "images/dbd0c72c619015ed8c01462507cae1db11bd9d6f896d7471cc51d2c6219c7535.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">Semi-Supervised</td><td colspan=\"2\">Fully-Supervised</td><td>SSTC</td></tr><tr><td></td><td>FixMatch/ SAT</td><td>FlexMatch/ FreeMatch</td><td>Co-Training</td><td>Decoupling</td><td>Co-Teaching+</td><td>JointMatch</td></tr><tr><td>Pseudo-Labeling</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td></tr><tr><td>Weak-Strong Augmentation</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td></tr><tr><td>Adaptive Local Threshold</td><td>✗</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td></tr><tr><td>Double Networks</td><td>✗</td><td>✗</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Cross Labeling</td><td>✗</td><td>✗</td><td>✓</td><td>✗</td><td>✓</td><td>✓</td></tr><tr><td>Disagreement Update</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Weighted Disagree &amp; Agree Update</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Comparison of closely related techniques with our JointMatch approach. In the first column, \"Pseudo-Labeling\": select high-confidence predictions as pseudo-labels for training; \"Weak-Strong Augmentation\": use the pseudo-labels generated by weakly-augmented sample to supervise the strongly-augmented sample; \"Disagreement Update\": update networks by only samples receives different pseudo-label from the two networks.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "different time steps for curriculum learning. However, this topic is outside the focus and scope of this paper, and we leave it to interested researchers for future exploration.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The overall objective for training one network in JointMatch is:",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {s} + w _ {u} \\mathcal {L} _ {u} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $w_{u}$  represents the loss weight for unlabeled data loss  $\\mathcal{L}_u$  and the supervised loss  $\\mathcal{L}_s$  is given by:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s} = \\frac {1}{B} \\sum_ {b = 1} ^ {B} \\mathcal {H} \\left(y _ {b}, p _ {m} (\\alpha (x _ {b}))\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2.5 Relation to Other Approaches",
+        "text_level": 1,
+        "bbox": [
+            112,
+            607,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our JointMatch algorithm with closely related approaches in Table 1. Our goal is to identify the connections among them and point out the key techniques that make JointMatch effective in semi-supervised text classification. FixMatch (Sohn et al., 2020) and SAT (Chen et al., 2022) employ the consistency regularization between weak and strong augmentation with pseudo-labeling to leverage unlabeled data. However, this approach uses a fixed threshold for pseudo-labeling, and often suffers from model bias towards easy class and error accumulation along their training. FlexMatch (Zhang et al., 2021) and FreeMatch (Wang et al., 2023b) propose to adaptively adjust local thresholds based on the estimated learning status of each class, which alleviates the bias towards easy classes. To address the issue of error accumulation, Co-Training (Blum and Mitchell,",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1998) trains two networks simultaneously and supervises each network by the generated pseudolabels from its peer network.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Decoupling (Malach and Shalev-Shwartz, 2017) and Co-Teaching+ (Yu et al., 2019) observe that update by disagreement data can make two networks in Co-Training diverged and thus more effective. However, when updating their network, they completely ignore agreement data, which is also more likely to receive correct pseudo-labels in semi-supervised learning. Therefore, we propose utilizing both disagreement and agreement data for training, but weighting disagreement data higher to keep the two networks diverged while also exploiting the high-quality pseudo-labels from agreement data.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our JoinMatch framework unifies ideas from the approaches described above into a single, effective framework for semi-supervised text classification. The three key techniques in JointMatch are: (i) adaptive local thresholding; (ii) cross-labeling; and (iii) weighted disagreement & agreement update.",
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+    {
+        "type": "text",
+        "text": "3 Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1 Experimental Setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets and Metrics. We evaluate JointMatch on three standard semi-supervised text classification benchmarks: AG News (Zhang et al., 2015), Yahoo! Answers (Chang et al., 2008) and IMDB (Maas et al., 2011). Following (Chen et al., 2022, 2020; Li et al., 2021), we use the original test set and randomly sample from the training set to construct our training unlabeled set and validation set. Table 2 presents the dataset statistics and split information. We report the mean and standard",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "7294",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/385b3b2912f8213d62d665d0d8214ae0def9d1a856a30fe5ce932ea4f3f80a1b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Label Type</td><td># Classes</td><td># Unlabeled</td><td># Validation</td><td># Test</td></tr><tr><td>AG News</td><td>News Topic</td><td>4</td><td>5000</td><td>2000</td><td>1900</td></tr><tr><td>Yahoo! Answer</td><td>AQ Topic</td><td>10</td><td>5000</td><td>2000</td><td>6000</td></tr><tr><td>IMDB</td><td>Review Sentiment</td><td>2</td><td>5000</td><td>1000</td><td>12500</td></tr></table>",
+        "bbox": [
+            208,
+            82,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/a459bd2425fec0754dc8c687bb77dfc18dd93fb7309d8781fb1eddb504a5ca8e.jpg",
+        "table_caption": [
+            "Table 2: Dataset statistics and split information. The number of unlabeled data, validation data and test data in the table means the number of data per class."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">AG News (c=4)</td><td colspan=\"2\">Yahoo! (c=10)</td><td colspan=\"2\">IMDB (c=2)</td><td></td></tr><tr><td>Methods</td><td>Accuracy</td><td>Macro-F1</td><td>Accuracy</td><td>Macro-F1</td><td>Accuracy</td><td>Macro-F1</td><td>Average</td></tr><tr><td>BERT</td><td>69.18 ± 3.7</td><td>68.27 ± 3.5</td><td>58.11 ± 1.6</td><td>57.38 ± 1.9</td><td>63.16 ± 1.4</td><td>62.93 ± 1.6</td><td>63.17</td></tr><tr><td>UDA</td><td>76.69 ± 3.2</td><td>76.51 ± 3.0</td><td>59.32 ± 2.0</td><td>58.47 ± 2.3</td><td>64.88 ± 1.7</td><td>64.57 ± 1.5</td><td>66.74</td></tr><tr><td>MixText</td><td>78.07 ± 2.8</td><td>77.23 ± 3.5</td><td>59.93 ± 1.9</td><td>59.24 ± 1.8</td><td>65.22 ± 1.1</td><td>65.78 ± 1.2</td><td>67.58</td></tr><tr><td>FixMatch</td><td>80.22 ± 2.4</td><td>78.98 ± 2.1</td><td>60.17 ± 1.7</td><td>59.86 ± 1.5</td><td>64.52 ± 1.6</td><td>64.31 ± 1.4</td><td>68.18</td></tr><tr><td>SAT</td><td>85.43 ± 1.2</td><td>85.30 ± 1.5</td><td>61.33 ± 1.5</td><td>60.96 ± 1.4</td><td>68.96 ± 1.7</td><td>68.92 ± 1.6</td><td>71.82</td></tr><tr><td>JointMatch (Ours)</td><td>87.68 ± 0.5</td><td>87.64 ± 0.5</td><td>66.58 ± 0.7</td><td>66.09 ± 0.8</td><td>76.91 ± 4.5</td><td>76.79 ± 4.6</td><td>76.95</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "deviation of accuracy and macro-F1 from five runs with different model parameter initialization.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare JointMatch with several popular and recent approaches: UDA (Xie et al., 2020), MixText (Chen et al., 2020), FixMatch (Sohn et al., 2020) and SAT (Chen et al., 2022). We also compare to the vanilla ensemble of FixMatch and FreeMatch (Wang et al., 2023b) to further demonstrate the effectiveness of JointMatch.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Following (Chen et al., 2022, 2020), we use the BERT-based-uncased model as our backbone model and the HuggingFace Transformers (Wolf et al., 2020) library for the implementation. We adopt the same data augmentation techniques for fair comparisons, i.e., synonym replacement for weak augmentation and back-translation for strong augmentation, in all baselines. In detail, for back translation, we translate texts into German and then translate them back into English; for synonym replacement, we randomly substitute  $30\\%$  of words with WordNet synonyms. A complete list of our hyper-parameters is provided in Appendix A, and our code is released.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 Comparison with Baselines",
+        "text_level": 1,
+        "bbox": [
+            112,
+            833,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We summarize the comparison with baselines on different text classification datasets in Table 3. Following SAT (Chen et al., 2022), we randomly sample  $N_{c}$  samples per class as labeled data for train-",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/48199bc9b034ae8a493ad00b6c3c50b66cbf08f09c14bac7239e732e39334bcf.jpg",
+        "table_caption": [
+            "Table 3: Performance (accuracy (\\%) and macro-F1 (\\%)) comparison with baselines on different text classification datasets. JointMatch delivers best results on all benchmark datasets, surpassing the latest work SAT (Chen et al., 2022) on SSTC by  $5.13\\%$  on average. The best results are shown in blue.  $c$ : number of classes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#Labels/Class</td><td>5</td><td>10</td><td>15</td><td>25</td><td>100</td><td>1000</td></tr><tr><td>FixMatch</td><td>56.13</td><td>59.81</td><td>65.07</td><td>63.85</td><td>68.07</td><td>68.81</td></tr><tr><td>FixMatch-Ensemble</td><td>57.08</td><td>61.62</td><td>66.52</td><td>65.92</td><td>68.40</td><td>70.42</td></tr><tr><td>JointMatch</td><td>64.08</td><td>65.52</td><td>67.51</td><td>67.24</td><td>69.74</td><td>71.39</td></tr></table>",
+        "bbox": [
+            509,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/7e3e4ee139ae2eb0ddec1716cb64ddea61a4e31cac82691b84328b66b155f205.jpg",
+        "table_caption": [
+            "Table 4: Accuracy on Yahoo! Answer with varying numbers of labeled data."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#Labels/Class</td><td>5</td><td>10</td><td>15</td><td>25</td><td>100</td><td>1000</td></tr><tr><td>FixMatch</td><td>70.29</td><td>80.25</td><td>82.32</td><td>85.96</td><td>87.79</td><td>89.57</td></tr><tr><td>FixMatch-Ensemble</td><td>72.01</td><td>80.86</td><td>84.14</td><td>85.33</td><td>86.86</td><td>88.61</td></tr><tr><td>FreeMatch-Ensemble</td><td>77.03</td><td>85.83</td><td>86.55</td><td>87.36</td><td>87.79</td><td>89.67</td></tr><tr><td>JointMatch</td><td>86.00</td><td>87.68</td><td>88.33</td><td>88.50</td><td>89.07</td><td>90.29</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Accuracy on AG News with varying numbers of labeled data. JointMatch delivers significant improvements over FixMatch, especially for extremely low-shot settings, indicating its effectiveness in leveraging unlabeled data.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b17e9b88cec4553a12de9a054c313f621eceda20e82db3e1b847d7c4b1d84c49.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Empathetic Dialogues</td><td>Go Emotions</td><td>Hurricane</td><td>Average Accuracy</td></tr><tr><td># Classes</td><td>32</td><td>27</td><td>8</td><td>-</td></tr><tr><td>BERT (2019)</td><td>21.63</td><td>28.86</td><td>71.72</td><td>40.74</td></tr><tr><td>FixMatch (2020)</td><td>24.40</td><td>30.06</td><td>73.44</td><td>42.63</td></tr><tr><td>SAT (2022)</td><td>29.25</td><td>30.36</td><td>74.06</td><td>44.56</td></tr><tr><td>FreeMatch (2023)</td><td>30.15</td><td>32.74</td><td>77.03</td><td>46.64</td></tr><tr><td>SoftMatch (2023)</td><td>29.96</td><td>31.84</td><td>74.38</td><td>45.39</td></tr><tr><td>JointMatch (Ours)</td><td>34.67</td><td>38.40</td><td>78.98</td><td>50.68</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 6: Accuracy results on diverse datasets with a larger number of classes. JointMatch consistently outperforms other methods, showing that our approach also works well in settings with a larger number of classes.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ing.  $N_{c}$  is set to 10 for both the AG News and IMDB datasets, and 20 for the Yahoo! dataset.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "7295",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/320089263910ea7312c9a27548b9bb4ebd175bc4be95f202587310f55ea74f25.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td># Classes</td><td>Total</td><td>Train</td><td>Val</td><td>Test</td></tr><tr><td>Empathetic Dialogues</td><td>32</td><td>24,850</td><td>19,533</td><td>2,770</td><td>2,547</td></tr><tr><td>GoEmotions</td><td>27</td><td>29,425</td><td>23,485</td><td>2,956</td><td>2,984</td></tr><tr><td>Hurricane</td><td>8</td><td>12,800</td><td>10,240</td><td>1,280</td><td>1,280</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "The results are averaged over 5 runs with different model parameter initialization. We observe that our JointMatch consistently demonstrates the best performances across all 3 datasets, surpassing the best baseline by  $5.13\\%$  on average. On the most challenging Yahoo! Answer dataset, JointMatch also significantly outperforms the best baseline by  $5.25\\%$  accuracy and  $5.13\\%$  macro-F1. These substantial improvements indicate the effectiveness of our diverse and collaborative pseudo-labeling framework JoinMatch. We further provide detailed ablation studies and analysis in the next section.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3 Varying the Number of Labeled Data",
+        "text_level": 1,
+        "bbox": [
+            112,
+            426,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also conduct experiments with varying numbers of labeled data to demonstrate the accuracy improvement of our JointMatch over FixMatch on Yahoo! Answers and AG News datasets. To ensure a fair comparison, we also include the performance of the vanilla ensemble of FixMatch, where we train two FixMatch models with different initializations and average their predicted probability distributions to obtain the result for the ensemble model. As shown in Table 4 and Table 5, JointMatch outperforms the vanilla ensemble of FixMatch with different numbers of labeled data on both datasets. This indicates that our improvement does not come simply from the model ensemble. Noteworthy is that, JointMatch offers remarkable improvements over this vanilla ensemble model, especially with extremely limited labeled data:  $7\\%$  on Yahoo! Answer with 5 labels per class and surprisingly  $13.99\\%$  on AG News with 5 labels per class. This further validates the effectiveness of JointMatch in utilizing unlabeled data and demonstrates its capability and potential to be used in real-world scenarios.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.4 Generalizability Results",
+        "text_level": 1,
+        "bbox": [
+            112,
+            832,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To show the generalizability of JointMatch, we add experiments on three datasets with a larger number of classes ( $c = 32$ , 27, 8). Table 6 summarizes the accuracy results in the 10-shot setting. We also",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2e8fbaad94580eb4cde730796c1565a3954a44ab869a17de9274adad6445f957.jpg",
+        "table_caption": [
+            "Table 7: Statistics and split information of the added datasets. All numbers shown here are the total number of data in all classes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AG News</td><td>Yahoo!</td></tr><tr><td>JointMatch</td><td>88.39</td><td>68.32</td></tr><tr><td>- Adaptive Threshold</td><td>82.97</td><td>66.42</td></tr><tr><td>- Cross Labeling</td><td>82.84</td><td>65.62</td></tr><tr><td>- Disagree Weights</td><td>87.89</td><td>67.47</td></tr><tr><td>- All (FixMatch)</td><td>80.25</td><td>63.80</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 8: Accuracy after removing different parts of JointMatch on AG News with 10 labels per class, Yahoo! Answer with 30 labels per class.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "include one more recently published and competitive semi-supervised learning method SoftMatch (Chen et al., 2023) for comparison. JointMatch consistently delivers improvement over other methods, indicating that our approach also works well in settings with a larger number of classes. Table 7 provides the statistics and split information of the added datasets. We provide short descriptions of these datasets in Appendix C.",
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+    },
+    {
+        "type": "text",
+        "text": "4 Ablation Study and Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 Effectiveness of Each Component",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To show the effectiveness of each component in JointMatch, we also measure the accuracy performance of JointMatch after removing different parts in Table 8. We observe that the performance decreases after stripping each component, suggesting that all components in JointMatch contribute to the final performance. The performance of JointMatch drops most significantly after removing cross-labeling on both datasets, justifying the benefits of two models teaching each other and its help in alleviating error accumulation. Adaptive local thresholding performs a similarly vital role in the final performance of JointMatch. This indicates the effectiveness of adjusting local thresholds based on current classwise learning status.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Removing disagree weights, i.e., weighted disagreement and agreement updates, also gives a performance drop, although smaller compared to the other two components. We hypothesize that the reason for this is that the current fixed disagreement weights are not optimal. They should be adaptively adjusted based on the degree of disagreement between the two networks at different times. This topic is outside the focus and scope of this paper and we leave it for future exploration. Despite this, we show the benefit of disagreement weights and provide an ablation study on its values in the next section.",
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+    },
+    {
+        "type": "page_number",
+        "text": "7296",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/3b10002113cb883e46343842783589e4fbbb02bdb665ae820fd9435095e208b3.jpg",
+        "image_caption": [
+            "(a) Quantity"
+        ],
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+        "bbox": [
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+        "img_path": "images/e20087e89ef5d618ff631cb1ad0a2e4ece3130079c41bd106ab3c2a6dbffbc75.jpg",
+        "image_caption": [
+            "(b) Quality",
+            "Figure 3: The quantity and quality of pseudo labels on AG News with 10 labels per class. Ratio refers to the fraction of pseudo-labeled data that participate in the current training iteration. JointMatch improves the quantity of pseudo labels at the early training stage, while maintaining a high quality of pseudo labels throughout the whole training process."
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/18f4b2d6e5315641fee1003366b4c3adfff878dba421c33ada2636b1691370a3.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 9: Accuracy on AG News with 10 labels per class and various disagreement weights. Updating networks by only agreement samples  $(\\delta = 0)$  and only disagreement samples  $(\\delta = 1)$  perform worse than updating by both types of data. Weighting more disagreement samples further delivers better results."
+        ],
+        "table_body": "<table><tr><td>δ</td><td>0</td><td>0.3</td><td>0.5</td><td>0.7</td><td>0.9</td><td>1</td></tr><tr><td>Accuracy</td><td>87.22</td><td>87.55</td><td>87.89</td><td>88.22</td><td>88.39</td><td>87.71</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 Influence of Disagreement Weights",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We now analyze the benefits of the weighted disagreement & agreement update. Table 9 shows how our approach performs with different disagreement weights  $\\delta$  on AG News with 10 labels per class. Note that (1)  $\\delta = 0$  means updating networks by only agreement samples,  $\\delta = 1$  means updating by only disagreement samples and  $\\delta = 0.5$  means updating by both types of samples and weighting them equally; (2) All samples used for updating networks are firstly high confidence samples.",
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+    {
+        "type": "text",
+        "text": "We observe that updating by either only agreement samples or only disagreement samples performs worse than updating by both kinds of samples. This validates our assumption both agreement samples and disagreement samples are beneficial for training, as agreement samples provide high-quality pseudo-labels while disagreement samples offer sample diversity and keep the two networks diverse. In addition, weighting more disagreement samples can obtain better results than equal weighting, which emphasizes the importance of keeping the two networks diverged and thus enabling them",
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+    {
+        "type": "text",
+        "text": "to learn from each other.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3 Quantity & Quality of Pseudo Labels",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "JointMatch improves both the quality and quantity of pseudo labels used for training. As shown in Figure 3a, FixMatch gradually leverages more pseudo labels as training advances, ultimately utilizing about  $80\\%$  of the available pseudo labels. However, the cost is that the accuracy of pseudo labels keeps dropping, eventually falling below  $40\\%$ , as indicated in Figure 3b. This is consistent with our motivation in Section 2.3 that directly using noisy pseudo labels will cause models to accumulate errors and gradually produce even more noisy pseudo labels. On the contrary, JointMatch maintains a high accuracy of pseudo labels throughout the entire training process (Figure 3b), which validates the effectiveness of cross-labeling in preventing error accumulation. Furthermore, JoinMatch generates a greater number of pseudo labels than FixMatch during the early stages of training (Figure 3a) without sacrificing their quality.",
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+    {
+        "type": "text",
+        "text": "5 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Semi-Supervised Text Classification. Semi-supervised learning has attracted a lot of attention in the field of text classification due to its ability to leverage large amounts of unlabeled data with limited labels. UDA (Xie et al., 2020) introduces strong data augmentation and proposes a consistency loss to minimize the distance of predicted distributions between differently perturbed data. MixText (Chen et al., 2020) leverages Mixup",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "7297",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(Zhang et al., 2018) to interpolate unlabeled data and labeled data in hidden space to avoid overfitting the limited labeled data. S2TC-BDD (Li et al., 2021) notices the margin bias issue and addresses it by balancing label angle variances. PCM (Xu et al., 2022) exploits the inherent semantic matching capability inside pre-trained language models to benefit SSTC. AUM-ST (Sosea and Caragea, 2022) builds on self-training and uses Area Under the Margin (Pleiss et al., 2020) to filter possibly inaccurate pseudo-labels. Hosseini and Caragea (2023) combine two models in a co-training fashion, one being trained using unsupervised domain adaptation from a source to a target domain and the other using semi-supervised learning in the target domain where the two models iteratively teach each other by interchanging their high confident predictions. CrisisMatch (Zou et al., 2023) studies several popular semi-supervised components and integrates Mixup with pseudo-labeling (Lee et al., 2013) for disaster tweet classification. Building upon the idea of FixMatch (Sohn et al., 2020) that uses pseudo-labels generated by weakly-augmented data to teach strongly-augmented data, the recent work SAT (Chen et al., 2022) proposes to re-rank different weak and strong augmentations according to their similarity with the original input. However, these works ignore the difficulties of learning different classes at different time steps. Inspired by recent FlexMatch (Zhang et al., 2021) and FreeMatch (Wang et al., 2023b), our Joint-Match introduces adaptive thresholding to SSTC to dynamically adjust classwise thresholds based on the learning status of each class.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Learning with Noise. The task of learning with noise aims to train robust networks against label noise. Co-Teaching (Han et al., 2018) proposes to simultaneously train two networks and mutually select small-loss instances to teach its peer, thus avoiding direct error accumulation within one network. Nevertheless, as the training goes on, the two networks may converge, reduce to one identical network, and the problem of error accumulation resurfaces. Decoupling (Malach and Shalev-Shwartz, 2017) proposes to update models only by the data receiving different predictions from the two networks. Co-Teaching+ (Yu et al., 2019) observes that this strategy can keep the two networks diverged and further boost the performance of CoTeaching. While these approaches are originally designed for fully supervised settings, our Joint",
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+    {
+        "type": "text",
+        "text": "Match integrates their ideas into semi-supervised text classification. We provide a comprehensive comparison between closely related approaches with our JointMatch in Table 1.",
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+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose JointMatch, a semisupervised text classification approach that integrates ideas from recent semi-supervised learning and learning with noise. Our method is motivated by observed problems in semi-supervised text classification (SSTC): model bias towards easy classes and error accumulation. JointMatch utilizes adaptive thresholding, cross-labeling, and weighted disagreement & agreement updates to address these issues effectively. Through extensive experiments on three standard SSTC benchmark datasets, we found that JointMatch significantly outperforms previous works on all datasets and demonstrates surprising improvement over FixMatch on an extremely scarce label setting. We also show that JointMatch can generalize well to datasets that have a large number of classes.",
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+    },
+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "There are several limitations to our work. First, our method trains two networks simultaneously, resulting in a higher computational cost and longer training time. For example, each experiment on AG News takes approximately 2.5 hours on an A5000 GPU for JointMatch, while FixMatch only requires 1.25 hours. However, the additional computational cost is not a significant issue in low-resource settings, as experiments in such settings typically do not take much time. Second, our weighted disagreement & agreement update could be further improved by adaptively adjusting the disagreement weight based on the degree of mutual agreement among networks and their confidence at different times. This will be explored in the future.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            512,
+            764,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This research is partially supported by National Science Foundation (NSF) grants IIS-1912887, IIS-2107487, and ITE-2137846. Any opinions, findings, and conclusions expressed here are those of the authors and do not necessarily reflect the views of NSF. We thank our reviewers for their insightful feedback and comments which helped improve the quality of our paper.",
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+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "7298",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+            98
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+        "page_idx": 9
+    },
+    {
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+        ],
+        "bbox": [
+            510,
+            85,
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+            365
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "7300",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A Hyperparameters",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A complete list of JointMatch hyperparameters on all evaluated datasets are provided in Table 10.",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/d6869bd4412f5d2ff389e31f6904d0b3a5a4b028b41753b30ff525b5f1d90a0c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>AG News</td><td>Yahoo! Answer</td><td>IMDB</td></tr><tr><td>Batch Size B</td><td>8</td><td>4</td><td>4</td></tr><tr><td>Learning Rate lr</td><td>1e-5</td><td>2e-5</td><td>2e-5</td></tr><tr><td>Unsupervised Loss Weight wU</td><td>1</td><td>1</td><td>0.05</td></tr><tr><td>EMA decay λ</td><td colspan=\"3\">0.9</td></tr><tr><td>Fixed Threshold τ</td><td colspan=\"3\">0.98</td></tr><tr><td>Disagreement Weight δ</td><td colspan=\"3\">0.9</td></tr><tr><td>Unlabeled Data Ratio μ</td><td colspan=\"3\">10</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "B Additional Ablation Study Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This section provides additional ablation study results on several hyperparameters as complementary to the main paper. All experimental results here are obtained from JointMatch on AG News with 10 labels per class.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "B.1 EMA Decay",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 11 shows the result of JointMatch with different EMA decay  $\\lambda$  for estimating classwise learning status. Note that  $\\lambda = 1$  means the estimated learning status for all classes always equals their initial value  $1 / C$  and not adjusting local thresholds ( $C$  is the number of classes). We observe that adjusting local thresholds based on estimated learning ( $\\lambda \\in [0,1)$ ) is significantly better than not adjusting local thresholds ( $\\lambda = 1$ ).",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fdda21dab18666e7360046365ec041a005c8b99ca94ec185e1aa6e98b128acf6.jpg",
+        "table_caption": [
+            "Table 10: Complete list of JointMatch hyperparameters on AG News, Yahoo! Answer, IMDB."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>EMA Decay</td><td>Accuracy</td><td>Macro-F1</td></tr><tr><td>0</td><td>87.13</td><td>87.06</td></tr><tr><td>0.25</td><td>86.93</td><td>86.95</td></tr><tr><td>0.5</td><td>87.61</td><td>87.59</td></tr><tr><td>0.9</td><td>88.39</td><td>88.32</td></tr><tr><td>0.99</td><td>87.28</td><td>87.28</td></tr><tr><td>1</td><td>83.68</td><td>83.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "B.2 Fixed Confidence Threshold",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In Table 12, we show the performance of Joint-Match with varying fixed confidence threshold  $\\tau$ . It can be seen that setting a threshold higher than 0.75 is generally beneficial for good performance, but setting it to a too high value will lead to some",
+        "bbox": [
+            112,
+            838,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/961e54a8d1bd9372052d9e9ffe0d6373e37bdb50376295b4d601a04c09775ba8.jpg",
+        "table_caption": [
+            "Table 11: Ablation study on EMA decay."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Fixed Threshold</td><td>Accuracy</td><td>Macro-F1</td></tr><tr><td>0</td><td>83.13</td><td>83.32</td></tr><tr><td>0.25</td><td>83.13</td><td>83.32</td></tr><tr><td>0.5</td><td>85.21</td><td>85.13</td></tr><tr><td>0.75</td><td>87.32</td><td>87.37</td></tr><tr><td>0.9</td><td>87.47</td><td>87.49</td></tr><tr><td>0.95</td><td>87.37</td><td>87.3</td></tr><tr><td>0.98</td><td>88.39</td><td>88.32</td></tr><tr><td>0.99</td><td>87.84</td><td>87.82</td></tr></table>",
+        "bbox": [
+            536,
+            80,
+            857,
+            244
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "performance drop, as less number of unlabeled can be utilized.",
+        "bbox": [
+            507,
+            293,
+            880,
+            323
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B.3 Unlabeled Data Ratio in MiniBatch",
+        "text_level": 1,
+        "bbox": [
+            507,
+            335,
+            836,
+            350
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In Table 13, we present the results of JointMatch with different unlabeled data to labeled data ratio  $\\mu$ . One can observe that using a large amount of unlabeled data can help increase performance. A very high value of  $\\mu$  is not encouraged since it slows down the training while just giving marginal improvements.",
+        "bbox": [
+            507,
+            355,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/4079396f1348ed15a14ef6be6509d28338c46cdee910e7953b567ea9dc574a4e.jpg",
+        "table_caption": [
+            "Table 12: Ablation study on the fixed threshold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Unlabeled Data Ratio</td><td>Accuracy</td><td>Macro-F1</td></tr><tr><td>1</td><td>86.43</td><td>86.39</td></tr><tr><td>3</td><td>86.74</td><td>86.71</td></tr><tr><td>5</td><td>88.08</td><td>88.04</td></tr><tr><td>10</td><td>88.39</td><td>88.32</td></tr><tr><td>15</td><td>88.22</td><td>88.22</td></tr><tr><td>20</td><td>88.45</td><td>88.46</td></tr><tr><td>30</td><td>88.49</td><td>88.50</td></tr></table>",
+        "bbox": [
+            521,
+            479,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 13: Ablation Study on Unlabeled Data to Labeled Data Ratio.",
+        "bbox": [
+            507,
+            634,
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+            663
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C Short Descriptions of Added Datasets",
+        "text_level": 1,
+        "bbox": [
+            507,
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+            701
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We provide a short description of these datasets here: (1) GoEmotions (Demszky et al., 2020) is a dataset of Reddit comments labeled with 27 emotions, such as amusement, fear, and gratitude. (2) Empathetic Dialogues (Rashkin et al., 2019) consists of conversations between a speaker and listener and is labeled with 32 fine-grained emotions. (3) Hurricane is a crisis tweet dataset sampled from HumAID (Alam et al., 2021). It contains human-labeled tweets collected during hurricane disasters and includes 8 crisis-related classes, such as infrastructure and utility damage, displaced people and evacuations.",
+        "bbox": [
+            507,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "7301",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 11
+    }
+]