A Multi-granularity Interaction Network for Relational Triple Extraction

# A Multi-granularity Interaction Network for Relational Triple Extraction
Source: [https://arxiv.org/html/2610.26952](https://arxiv.org/html/2610.26952)
††highlights:A multi\-granularity interaction network is proposed for relational triple extraction\. Word\-word, entity\-relation and head\-tail interactions are jointly leveraged\. The model handles entirely seen, partially seen and unseen relational triples\. Consistent improvements are observed on NYT\-R and WebNLG\-R datasets\.Yanping Chenypench@gmail\.comZaifu Zhanzhan8023@umn\.eduorganization=School of Computer Science and Technology,addressline=Soochow University, city=Suzhou, postcode=215006, state=Jiangsu, country=PR Chinaorganization=State Key Laboratory of Public Big Data, College of Computer Science and Technology, addressline=Guizhou University, city=Guiyang, postcode=550025, state=Guizhou, country=PR Chinaorganization=Department of Electrical and Computer Engineering,addressline=University of Minnesota, city=Minneapolis, postcode=55455, state=MN, country=USA

###### Abstract

Relational triple extraction identifies entity relations from raw sentences without depending on entity type information\. The performance of traditional methods is seriously degenerated by “unseen” entities, because these methods can’t build contextual dependencies relevant “unseen” entities\. This paper addresses this challenge by proposing a multi\-granularity interaction network that leverages word\-word, entity\-relation, and head\-tail interactions to capture deep semantic dependencies\. By incorporating multiple iterations, the multi\-granularity interaction network is effective to refine the representations corresponding to head and tail entities\. It enhances the global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps\. Strong and consistent performance is achieved by our method on two rearranged datasets, with a significant improvement in identifying relational triples, including those involving “unseen” named entities\. For example, our model improves F1\-score by 3\.1%/20\.5% over previous approaches on the NYT\-R/WebNLG\-R datasets in the Unseen metric\. Code:[https://github\.com/xiaocen\-luo/Interaction\-Network\.](https://github.com/xiaocen-luo/Interaction-Network)

###### keywords

Interaction network ,Small language model ,Multi\-granularity ,Relational triple extraction

††corresponding:Corresponding author## 1Introduction

The task of Relational Triple Extraction \(RTE\) involves both extracting entity pairs and recognizing their relation types from a raw sentence\. The output can be represented in the form of a 3\-tuple \(hh,rr,tt\) denoted to three parameters: ah​e​a​dheadentity, ar​e​l​a​t​i​o​nrelationtype and at​a​i​ltailentity\. Because relation triple extraction ignores semantic types of named entities, it is effective to retrieve semantic relations between all possible named entities and avoid the error propagation problem caused by classifying the semantic types of named entities\. In recent years, this task has received a lot of attention in the field of natural language processing\. Knowledge graph construction\([Dong et al\., 2014](https://arxiv.org/html/2610.26952#bib.bib31)\), information retrieval\([Sinha et al\., 2015](https://arxiv.org/html/2610.26952#bib.bib32)\), and text semantic analysis\([Hua et al\., 2015](https://arxiv.org/html/2610.26952#bib.bib34)\)are among the downstream tasks that commonly benefit from this technique\.

Large Language Models \(LLMs\)\([Achiam et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib39);[Team, 2024](https://arxiv.org/html/2610.26952#bib.bib38);[Dubey et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib37)\)have recently achieved impressive results in many natural language processing applications\. For instance, they work well for Question Answering\([Yona et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib41)\)and Code Generation\([Li et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib42)\)\. However, these same models tend to experience a notable performance decline when tackling information extraction tasks\. For instance, as reported by[Ding et al\. \(2024\)](https://arxiv.org/html/2610.26952#bib.bib40), LLMs are able to perform triple extraction from basic sentences\. This can be achieved through few\-shot learning or fine\-tuning, assuming appropriate instructions are provided\. Despite this capability, they frequently suffer from poor performance in NLP tasks relevant to complex sentence structures\. The performance drop stems from the fact that sentences often contain multiple entities simultaneously, particularly in the relational triple extraction\. Within the scope of relational triple extraction, all entities in a given sentence share overlapping contextual cues, leading to intricate semantic structures\. Standard practice for generative models is to convert a sentence into a dense vector, which hampers their ability to tell entities apart while decoding overlapping relational triples\.

Early works on relational triple extraction are usually based on a pipelined framework\([Zelenko et al\., 2003](https://arxiv.org/html/2610.26952#bib.bib1);[Chan and Roth, 2011](https://arxiv.org/html/2610.26952#bib.bib3)\), which decomposes the task into a two\-step process involving entity recognition followed by relation classification\. Because each incorrect entity will be paired with all entities for relation classification, the error propagation problem is very influential in the pipeline framework\. To address this problem, joint methods are widely adopted to extract entity pairs together with their relations via a unified approach\([Zheng et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib27);[Wei et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib26);[Li et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib28);[An et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib30)\)\. These methods demonstrate strong promise for tackling the relational triple extraction problem\.

In joint relational triple extraction, every relation triple is directly extracted without depends on any prior information about named entities\. Because the task imposes no limits about the types of named entities, all named entities can be used as candidates of a relation triple\. Therefore, to support this task, it is critical to identify relation triples composed of “unseen” named entities in the training process\. According to the “visibility” of triple parameters, relational triples in the testing dataset can be divided into three categories\([Lee et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib33)\):​e​n​t​i​r​e​l​y​s​e​e​n\\emph\{entirelyseen\}\(Entire\),​p​a​r​t​i​a​l​l​y​s​e​e​n\\emph\{partiallyseen\}\(Partial\),​u​n​s​e​e​n\\emph\{unseen\}\(Unseen\)\. The​e​n​t​i​r​e​l​y​s​e​e​n\\emph\{entirelyseen\}refers to relational triples with the same two entity parameters \(h​e​a​dheadandt​a​i​ltail\) that occurred within the training set as well as the testing set\. In a​p​a​r​t​i​a​l​l​y​s​e​e​n\\emph\{partiallyseen\}triple, either a tail entity or a head entity co\-occurred in training and testing datasets\. Table[1](https://arxiv.org/html/2610.26952#S1.T1)lists the statistical information about unseen relational triples in four evaluation datasets includingNYT\\mathrm\{NYT\},WebNLG\\mathrm\{WebNLG\}, along with their modified versionsNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\.

Table 1:The number \(ratio\) of triple types in the testing datasets\.DatasetEntirePartialUnseenWebNLG\\mathrm\{WebNLG\}756 \(85\.23%\{\\color\[rgb\]\{1,0,0\}\\mathbf\{85\.23\}\\%\}\)110 \(12\.40%\\%\)21 \(2\.37%\\%\)NYT\\mathrm\{NYT\}2672 \(77\.07%\{\\color\[rgb\]\{1,0,0\}\\mathbf\{77\.07\\%\}\}\)663 \(19\.12%\\%\)132 \(3\.81%\\%\)WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}439 \(44\.17%\\%\)338 \(34\.00%\\%\)217 \(21\.83%\\%\)NYT\\mathrm\{NYT\}\-R\\mathrm\{R\}823\(13\.81%\\%\)3985 \(66\.89%\\%\)1150 \(19\.30%\\%\)In the above table,NYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}are two public evaluations for relational triple extraction, where ‘Entire’ accounts for77\.07%\\mathbf\{77\.07\\%\}and85\.23%\\mathbf\{85\.23\\%\}on theNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}datasets, respectively\. As shown in this table, the two datasets only contain a small number of unseen relational triples\. To support practical applications of relational triple extraction,[Lee et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib33)rearranged the two datasets to generate theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets\. They contain a larger number of unseen triple, which makes the datasets closer to real applications\.

To show the influence of unseen relational triples in real applications, an experiment was conducted on the four datasetsNYT\\mathrm\{NYT\},WebNLG\\mathrm\{WebNLG\},NYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\. Three recent state\-of\-the\-art models such as CasRel\([Wei et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib26)\), TPLinker\([Wang et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib14)\), and PRGC\([Zheng et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib27)\)are implemented on the four datasets\. The result is shown in Table[2](https://arxiv.org/html/2610.26952#S1.T2)\.

Table 2:The F1 performance achieved by the current best\-performing model across four datasets\([Lee et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib33)\)\.ModelDatasetWebNLG\\mathrm\{WebNLG\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}NYT\\mathrm\{NYT\}NYT\\mathrm\{NYT\}\-R\\mathrm\{R\}CasRel88\.368\.6\(↓19\.7\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 19\.7\}\}\)90\.162\.9\(↓27\.2\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 27\.2\}\}\)TPLinker89\.069\.1\(↓19\.9\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 19\.9\}\}\)92\.464\.7\(↓27\.7\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 27\.7\}\}\)PRGC88\.061\.8\(↓26\.2\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 26\.2\}\}\)89\.162\.6\(↓26\.5\\mathbf\{\{\\color\[rgb\]\{1,0,0\}\\downarrow 26\.5\}\}\)The experiment showed that the performance is degenerated seriously when evaluated on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}andNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}\. This underscores that current methodologies excessively depend on the model’s memory capabilities while neglecting its generalization abilities, which is inefficient in real applications\.

Before giving the motivation of our method, an example is first given to show the characteristics of unseen relational triples\. A testing sentence “Bionico is a food found in Mexico, where Enrique Pena Nieto is the leader and Mexicans are the inhabitants\.”\. It contains four named entities \(“Bionico”, “Mexico”, “Enrique” and “Mexicans”\) and three relations \(“leaderName”, “country” and “demonym”\)\. They generate three relational triples, which is illustrated in Figure[1](https://arxiv.org/html/2610.26952#S1.F1)\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/reasoning_pattern.png)Figure 1:An example contains two types of relational triples\.As shown in the bottom of Figure[1](https://arxiv.org/html/2610.26952#S1.F1), there is another sentence in the training dataset “Bionico is a food found in Mexico\. Mexico’s currency is the Peso and a leader in Mexico is Enrique Pena Nieto”\. Therefore, the testing sentence contains two entirely seen tripes \(Mexico, leaderName, Enrique\) and \(Bionico, country, Mexico\), an unseen tripe \(Mexico, demonym, Mexicans\)\. Entirely seen relational triples tend to be easier to identify\. On the other hand, the unseen triple is more challenging\.

The motivation for developing multi\-granularity interaction networks stems from several observations\. First, entity pairs of unseen relational triples in the sentence can be inferred through interactions between head and tail\. For example, in Figure[1](https://arxiv.org/html/2610.26952#S1.F1), the entity pair of the unseen relational triple makes a new relational connection through the head entity “Mexico” and the tail entity “Mexicans”\. Second, the relation types of unseen relational triples may be obtained through entity\-relation interactions\. For example, in Figure[1](https://arxiv.org/html/2610.26952#S1.F1), the specific logical structure “one is the resident” aids determine the type of the triple of relations as “demonym”, which requires the interaction of a sufficient amount of semantic information\.

Motivated by the above observations, we introduce a multi\-granularity interaction network designed to jointly extract relational triples across three categories:*entirely seen*,*partially seen*, and*unseen*\. “multi\-granularity” refers to the model’s ability to integrate different levels of interaction \(or granularities\) to improve relational triple extraction\. Our model leverages the semantic interactions of word\-word interaction, entity\-relation interaction and head\-tail interaction\. The word\-word interaction reinforces the semantic features of elements within a 2D sentence encoding, which makes the use of relation and entity information\. The entity\-relation interaction captures long\-distance semantic dependencies between relations and entities, effectively filtering out the semantic features related to redundant relational triples\. The head\-tail interaction enhances the global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps\. By incorporating multiple iterations, the multi\-granularity interaction network is effective to progressively refine the representations corresponding to head and tail entities\. Evaluated on two rearranged datasets, our model consistently outperforms the compared baselines for relational triple extraction\. Our work makes the following contributions:

- 1\)A multi\-granularity interaction network is proposed for extracting relational triples, that makes full use of word\-word interactions, entity\-relation associations, and head\-tail interactions to extract entirely seen, partially seen, and unseen relational triples\.
- 2\)Extensive experiments are performed on two rearranged datasets, where our method achieves the best results among all compared baselines\. Further analytical results confirm the efficacy of our proposed approach for relational triple extraction\.

## 2Related Work

Early studies commonly adopted pipeline\-based approaches to support relational triples extraction\([Zelenko et al\., 2003](https://arxiv.org/html/2610.26952#bib.bib1);[Zhou et al\., 2005](https://arxiv.org/html/2610.26952#bib.bib2);[Chan and Roth, 2011](https://arxiv.org/html/2610.26952#bib.bib3)\)\. Pipeline methods split the RTE problem into independent components: entity extraction followed by relation classification\. These approaches have two main drawbacks\. First, it ignores the possible interplay between entity identification and relation categorization\. Second, it suffers from vulnerability to error propagation\.

To overcome pipeline limitations, researchers now prioritize joint extraction methods\([Sui et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib4);[Ning et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib5);[Zhang et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib6)\), which can extract entities and relations simultaneously\. Related works on joint relational triple extraction fall into three types: tagging\-based, Seq2Seq\-based, and table\-filling approaches\. Each of these categories is outlined below\.

### 2\.1Tagging based Methods

Tagging\-based methods involve assigning tags to every token within a sentence for identifying entity boundaries and their relations\. For instance,[Zhan et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib8)frames the relation extraction task as a multi\-label problem that iteratively processesn⁡\(n\+1\)/2n\(n\+1\)/2tokens\. For every distinct token pair, they incorporate bidirectional relations, utilizing dependency relations to capture directional information between entity pairs\.[Wang et al\. \(2023\)](https://arxiv.org/html/2610.26952#bib.bib9)introduced a relation\-aware sequence labeling decoder, which utilizes a filter\-attention mechanism to emphasize informative features\. Subsequently, an additional matrix is employed to integrate entity pair information\.[He et al\. \(2023\)](https://arxiv.org/html/2610.26952#bib.bib7)present a framework implementing taggers in two directions\. It enables triples extraction from subject to object and vice versa\. Tagging based methods have achieved good performance for identifying triples without overlapping\. Because they usually rely on semantic expressions associated with a pair of named entities within a triple, performance seriously degrades when identifying relational triples with “unseen” entities\.

### 2\.2Seq2Seq based Methods

Sequence\-to\-sequence approaches typically view a relational triple as a token sequence, thus casting the RTE problem as a generative task\. The goal is to generate relational triples in an autoregressive manner\. For example,[Zeng et al\. \(2018\)](https://arxiv.org/html/2610.26952#bib.bib10)tackle the issue of overlapping relational triples by employing a copy mechanism\. Meanwhile,[Zeng et al\. \(2019\)](https://arxiv.org/html/2610.26952#bib.bib11)incorporate reinforcement learning into their Seq2Seq framework and investigate the ordering issue in triple generation\. Furthermore,[Zeng et al\. \(2020\)](https://arxiv.org/html/2610.26952#bib.bib12)design a multi\-task learning architecture that utilizes a copy mechanism to address the difficulty posed by multi\-token entities\.[Nayak and Ng \(2020\)](https://arxiv.org/html/2610.26952#bib.bib13)present a new representation method that proves effective at extracting multiple triples containing overlapping entities, including those with multi\-token entities within a sentence\. The main problem of the Seq2Seq based approach is that these methods should compress sentences into dense representations, which leads to serious information loss\.

### 2\.3Table Filling based Methods

Approaches based on table filling convert the relational triple extraction problem into a table\-filling procedure\.[Wang et al\. \(2020\)](https://arxiv.org/html/2610.26952#bib.bib14)frames joint extraction as a problem of linking token pairs\. They propose a handshaking labeling strategy that matches the start and end tokens of entity pairs for each relation category\.[Shang et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib15)reformulates joint extraction as fine\-grained triple classification, enabling the task to simultaneously capture information pertaining to head entities, relations, and tail entities\.[Tang et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib16)propose an interaction graph constructed on top of standard self\-attention mechanisms to unify interaction modeling\. The table filling method is constrained by a fixed table size and may struggle to accommodate relational triple extraction in lengthy sentences\.

## 3Methodology

This section begins by presenting the task definition in Section[3\.1](https://arxiv.org/html/2610.26952#S3.SS1)\. Afterwards, we describe our model’s implementation in Section[3\.2](https://arxiv.org/html/2610.26952#S3.SS2)\.

### 3\.1Task Definition

Consider a sentenceS=\{w1,w2,…,wN\}S=\\\{w\_\{1\},w\_\{2\},\\ldots,w\_\{N\}\\\}with lengthNN\. The objective of relational triple extraction is to identify all possible relational triples𝒯=\{\(hi,ri,ti\)\}i=1μ\\mathcal\{T\}=\\\{\(h\_\{i\},r\_\{i\},t\_\{i\}\)\\\}^\{\\mu\}\_\{i=1\}contained inSS, whereμ\\murepresents the total number of triples\. Here,hi,ti∈Eh\_\{i\},t\_\{i\}\\in E, withEEdenoting the entity set withinSS\. Meanwhile,ri∈Rr\_\{i\}\\in R, andR=\{r1,…,r𝒦\}R=\\\{r\_\{1\},\\ldots,r\_\{\\mathcal\{K\}\}\\\}denotes the set of𝒦\\mathcal\{K\}predefined relation categories\.

Let𝒯t​r​a\\mathcal\{T\}\_\{tra\}be the relational triple set in a training dataset\. For a triple\(h,r,t\)\(h,r,t\)from the testing dataset, the three categories,*entirely seen*,*partially seen*and*unseen*, are specified below:

- •The triple\(h,r,t\)\(h,r,t\)is categorized as*entirely seen*type, when\(h,r,t\)∈𝒯t​r​a\(h,r,t\)\\in\\mathcal\{T\}\_\{tra\}\.
- •The triple\(h,r,t\)\(h,r,t\)fall into the*partially seen*type, if it satisfies either\(h,r,⋅\)∈𝒯t​r​a\(h,r,\\cdot\)\\in\\mathcal\{T\}\_\{tra\}or\(⋅,r,t\)∈𝒯t​r​a\(\\cdot,r,t\)\\in\\mathcal\{T\}\_\{tra\}\.
- •Otherwise, if\(h,r,t\)∉𝒯t​r​a\(h,r,t\)\\notin\\mathcal\{T\}\_\{tra\}and\(h,r,⋅\)∉𝒯t​r​a\(h,r,\\cdot\)\\notin\\mathcal\{T\}\_\{tra\}and\(⋅,r,t\)∉𝒯t​r​a\(\\cdot,r,t\)\\notin\\mathcal\{T\}\_\{tra\}, the triple is categorized as*unseen*\.

### 3\.2Interaction Network

Figure[2](https://arxiv.org/html/2610.26952#S3.F2)illustrates the architecture of our model designed for relational triple extraction\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/our-model.png)Figure 2:Model Architecture\.The proposed model consists of five primary components: an*Encoder*module, a*Word\-Word Interaction*\(WWI\) module, an*Entity\-Relation Interaction*\(ERI\) module, a*Head\-Tail Interaction*\(HTI\) module, and a*Triple Extraction \(TE\)*module\. The interaction network is composed by the three WWI, ERI, and HTI modules\.

Given an input, it is processed by the interaction network multiple times in an iterative manner to progressively refine the representations corresponding to head and tail entities\. Finally, the*TE*module builds the*Interaction Map*using these refined representations to extract all triples from a sentence\.

Comparing with existing models, our interaction network for extracting relational triples, aims to fully leverage all potential semantic interactions relevant to the parameters of a relational triple\. It enables the extraction of entirely seen, partially seen, and unseen relational triples\. Unlike existing table\-filling methods\([Wang et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib14);[Ren et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib29);[Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15);[Dai et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib36)\)that rely solely on head and tail entity semantics, our model integrates different levels of semantic interaction \(WWI, ERI, and HTI\)\. Traditional methods usually place excessive reliance on the model’s memory capabilities while overlooking its generalization abilities, making them inefficient in real\-world applications\. Our approach encompasses all types of relational triples, including entirely seen, partially seen, and unseen relational triples, making it more suitable for practical applications\.

#### 3\.2\.1Encoder

For an input sentenceS=\{w1,w2,…,wN\}S=\\\{w\_\{1\},w\_\{2\},\\ldots,w\_\{N\}\\\}along with a predefined relation setR=\{r1,…,r𝒦\}R=\\\{r\_\{1\},\\ldots,r\_\{\\mathcal\{K\}\}\\\}, to lean semantic features of tokens and build the semantic dependencies between them, a pre\-trained language model \(BERT\([Eberts and Ulges, 2020](https://arxiv.org/html/2610.26952#bib.bib18)\)\) is utilized to convert the sentence into a sequential abstract representation\. The process is formalized as follows:

=BERT​\(\[w1,…,wN,r1,…,r𝒦\]\)\\displaystyle=\\text\{BERT\}\\left\(\[w\_\{1\},\\ldots,w\_\{N\},r\_\{1\},\\ldots,r\_\{\\mathcal\{K\}\}\]\\right\)\(1\)or,H\\displaystyle\\text\{or\},\\ \\ H=BERT​\(S⊕R\)\\displaystyle=\\text\{BERT\}\\left\(S\\oplus R\\right\)where,⊕\\oplusdenotes the string concatenation operation, which indicates that all relation type labels are concatenated with the sentence\. It is effective to capture the semantic interplay between tokens and relation types\. The outputH=\[h1,…,hN\+𝒦\]∈ℝ\(N\+𝒦\)×deH=\[h\_\{1\},\\ldots,h\_\{N\+\\mathcal\{K\}\}\]\\in\\mathbb\{R\}^\{\(N\+\\mathcal\{K\}\)\\times d\_\{e\}\}is the abstract sentence representation\.

Then,HHis fed into two independent*Multilayer Perceptrons*\(MLP\) to generate the initial head and tail representations, denoted asIh\(1\)I\_\{h\}^\{\(1\)\}andIt\(1\)I\_\{t\}^\{\(1\)\}, respectively\. It is shown in the following equations:

Ih\(1\)\\displaystyle I\_\{h\}^\{\(1\)\}=Wh​H\+bh\\displaystyle=W\_\{h\}H\+b\_\{h\}\(2\)It\(1\)\\displaystyle I\_\{t\}^\{\(1\)\}=Wt​H\+bt\\displaystyle=W\_\{t\}H\+b\_\{t\}
whereWh/t∈ℝde×deW\_\{h/t\}\\in\\mathbb\{R\}^\{d\_\{e\}\\times d\_\{e\}\}andbh/t∈ℝdeb\_\{h/t\}\\in\\mathbb\{R\}^\{d\_\{e\}\}are trainable weights and biases, respectively\.

#### 3\.2\.2Word\-Word Interaction

The Word\-Word Interaction plays a vital role in capturing the contextual relationships between words within a sentence\. It is essential for capturing the overall semantics\. This interaction reinforces semantic features of elements in a two\-dimensional sentence representation, which makes the full use of relation and entity information\. By analyzing these word relationships, the model can discern subtle nuances in meaning, allowing it to identify relational triples more accurately\. This capability is particularly beneficial when dealing with relational triples unseen during training\.

To better learn the word\-word interaction information, the one\-dimensional head and tail representations are transformed into two two\-dimensional head and tail representations, denotedMh∈ℝ\(N\+𝒦\)×\(N\+𝒦\)×deM^\{h\}\\in\\mathbb\{R\}^\{\(N\+\\mathcal\{K\}\)\\times\(N\+\\mathcal\{K\}\)\\times d\_\{e\}\}andMt∈ℝ\(N\+𝒦\)×\(N\+𝒦\)×deM^\{t\}\\in\\mathbb\{R\}^\{\(N\+\\mathcal\{K\}\)\\times\(N\+\\mathcal\{K\}\)\\times d\_\{e\}\}, respectively\. The two\-dimensional representations are similar to the existing table filling method\([Wang et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib14);[Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15);[Ning et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib5)\)\. The cell\(wi,wj\)\(w\_\{i\},w\_\{j\}\)in each two\-dimensional representation,Mi,jϵM^\{\\epsilon\}\_\{i,j\}ϵ∈\{h,t\}\\epsilon\\in\\\{h,t\\\}is calculated as follows:

Mi,jϵ=R​e​L​U​\(Wc​\[hi;hj\]\+bc\)M^\{\\epsilon\}\_\{i,j\}=ReLU\(W\_\{c\}\[h\_\{i\};h\_\{j\}\]\+b\_\{c\}\)\\\\\(3\)
with1≤i,j≤N1\\leq i,j\\leq N, whereR​e​L​U​\(⋅\)ReLU\(\\cdot\)denotes the ReLU nonlinearity\([Agarap, 2018](https://arxiv.org/html/2610.26952#bib.bib19)\), and “;” represents the concatenation operation\.Wc∈ℝde×2​deW\_\{c\}\\in\\mathbb\{R\}^\{d\_\{e\}\\times 2d\_\{e\}\}andbc∈ℝdeb\_\{c\}\\in\\mathbb\{R\}^\{d\_\{e\}\}are trainable parameters\.

The dimensionality expansion process of the head and tail representations involves word\-to\-word interactions\. To further enhance word\-word interactions, we employ a tensor\-based transformation that derives the head\-tail semantic representation\.

For two cellszi,zj∈ℝdez\_\{i\},z\_\{j\}\\in\\mathbb\{R\}^\{d\_\{e\}\}in two\-dimensional head and tail representationsMh/tM^\{h/t\}, the tensor\-oriented operation is formulated as:

ℳ\(zi,zj;V\)=zi⊤V\[1:m\]zj\\mathcal\{M\}\\left\(z\_\{i\},z\_\{j\};V\\right\)=z\_\{i\}^\{\\top\}V^\{\[1:m\]\}z\_\{j\}\(4\)
whereV∈ℝde×de×mV\\in\\mathbb\{R\}^\{d\_\{e\}\\times d\_\{e\}\\times m\}is a tensor\. For each sliceV\[k\]∈ℝde×deV^\{\[k\]\}\\in\\mathbb\{R\}^\{d\_\{e\}\\times d\_\{e\}\}, this operation computes the dot product of two cell vectors in a given vector space:

ℳ​\(zi,zj,V\)k=zi⊤​V\[k\]​zj\\mathcal\{M\}\\left\(z\_\{i\},z\_\{j\};V\\right\)\_\{k\}=z\_\{i\}^\{\\top\}V^\{\[k\]\}z\_\{j\}\(5\)
Through the use of multiple vector spaces, the proposed tensor operation is capable of thoroughly capturing token\-token interactions\.

Finally, we construct a two\-dimensional entity\-relation representation through a nonlinear projection:

Me​r\\displaystyle M^\{er\}=f⁡\(Linear​\(\[Mh;Mh​t;Mt\]\)\)\\displaystyle=f\(\\text\{Linear\}\(\[M^\{h\};M^\{ht\};M^\{t\}\]\)\)\(6\)Mh​t\\displaystyle M^\{ht\}=ℳ⁡\(zi,zj,V\)∈ℝN×N×m\\displaystyle=\\mathcal\{M\}\\left\(z\_\{i\},z\_\{j\};V\\right\)\\in\\mathbb\{R\}^\{N\\times N\\times m\}
here,f⁡\(⋅\)f\(\\cdot\)represents the GELU nonlinearity\([Hendrycks and Gimpel, 2016](https://arxiv.org/html/2610.26952#bib.bib20)\)\. The dimension ofMe​rM^\{er\}is denoted asdrd\_\{r\},Me​r∈ℝN×N×drM^\{er\}\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}\.

#### 3\.2\.3Entity\-Relation Interaction

The entity\-relation interaction centers on how entities connect with various types of relations, which is crucial for contextualizing them within their specific relational frameworks\. This interaction captures long\-distance semantic dependencies between relations and entities, allowing the model to filter out the semantic features related to redundant relational triples\. By emphasizing these interactions, the model can effectively differentiate between similar entities that may have distinct relationships in different contexts, thus enhancing the precision of the extracted triples\.

There are potential dependencies between elements of an entity\-relation representationMe​rM^\{er\}\. For example, if an element in the Entity\-Entity region is labeled, it must be labeled correctly in both the Head\-Relation and the Relation\-Tail region\. Notably, we observed that the positions of the Entity\-Entity, Head\-Relation, and Relation\-Tail markers exhibit a criss\-crossing long\-distance semantic dependency\. To model these dependencies, we utilize the*Criss\-Cross Attention*\(CCA\)\([Huang et al\., 2019](https://arxiv.org/html/2610.26952#bib.bib22)\)to encode this entity\-relation representation matrix, as shown in Figure[3](https://arxiv.org/html/2610.26952#S3.F3)\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/cca.png)Figure 3:The details of Entity\-Relation Interaction\.Given an entity\-relation representationMe​r∈ℝN×N×drM^\{er\}\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}, unlike the*Criss\-Cross Attention*used by[Huang et al\. \(2019\)](https://arxiv.org/html/2610.26952#bib.bib22), two fully connection layers are first applied onMe​rM^\{er\}to produce a pair of feature mapsQQandKKwith\{Q,K\}∈ℝN×N×dr\\\{Q,K\\\}\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}\. The motivation for using1×11\\times 1filters instead of the traditional convolutional layer stems from the fact that the fully connected layer has strong nonlinear fitting capabilities for learning task\-relevant semantic features\.

After computingQQandKK, the𝐀𝐟𝐟𝐢𝐧𝐢𝐭𝐲\\mathbf\{Affinity\}operation yields an attention mapA∈ℝ\(N\+N−1\)×\(N×N\)A\\in\\mathbb\{R\}^\{\(N\+N\-1\)\\times\(N\\times N\)\}\. Eachuu\(spatial position inQQ\) gives a vectorQu∈ℝdrQ\_\{u\}\\in\\mathbb\{R\}^\{d\_\{r\}\}\. Simultaneously, a setΩu∈ℝ\(N\+N−1\)×dr\\Omega\_\{u\}\\in\\mathbb\{R\}^\{\(N\+N\-1\)\\times d\_\{r\}\}is derived via selecting feature vectors fromKKthat share the same row or column with positionuu\. Here,Ωi,u∈ℝdr\\Omega\_\{i,u\}\\in\\mathbb\{R\}^\{d\_\{r\}\}denotes theii\-th component ofΩu\\Omega\_\{u\}\. The𝐀𝐟𝐟𝐢𝐧𝐢𝐭𝐲\\mathbf\{Affinity\}operation is formulated as:

di,u=Qu​Ωi,u⊤/dr,d\_\{i,u\}=Q\_\{u\}\\Omega\_\{i,u\}^\{\\top\}/\\sqrt\{d\_\{r\}\},\(7\)
wheredi,ud\_\{i,u\}represents the correlation score betweenQuQ\_\{u\}andΩi,u\\Omega\_\{i,u\}\.iiranges from 1 toN\+N−1N\+N\-1, andD∈ℝ\(N\+N−1\)×\(N×N\)D\\in\\mathbb\{R\}^\{\(N\+N\-1\)\\times\(N\\times N\)\}\.

Then, a softmax function is performed overDDalong the channel axis to obtain the attention mapAA\.

An additional fully connected layer is applied toMe​rM^\{er\}to obtainV∈ℝN×N×drV\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}for feature adaptation\. At every spatial positionuuwithinVV, we extract a vectorVu∈ℝdrV\_\{u\}\\in\\mathbb\{R\}^\{d\_\{r\}\}along with a setΦu∈ℝ\(N\+N−1\)×dr\\Phi\_\{u\}\\in\\mathbb\{R\}^\{\(N\+N\-1\)\\times d\_\{r\}\}\.Φu\\Phi\_\{u\}consists of feature vectors fromVVlying on the same row or column with positionuu\. The surrounding information is then integrated via an𝐀𝐠𝐠𝐫𝐞𝐠𝐚𝐭𝐢𝐨𝐧\\mathbf\{Aggregation\}operation, which is defined as:

M^ue​r=∑i=0N\+N−1Ai,u​Φi,u\+Mue​r\\hat\{M\}^\{er\}\_\{u\}=\\sum\_\{i=0\}^\{N\+N\-1\}A\_\{i,u\}\\Phi\_\{i,u\}\+M^\{er\}\_\{u\}\(8\)
whereM^ue​r\\hat\{M\}^\{er\}\_\{u\}is the feature vector fromM^e​r∈ℝN×N×dr\\hat\{M\}^\{er\}\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}located at positionuu, andAi,uA\_\{i,u\}is the scalar entry inAAfor channeliiat the same position\. This allows the contextual information to be fused with the local featureMe​rM^\{er\}, thereby strengthening the semantic dependencies within the entity\-relation representation\. To fully utilize the potential of CCA, CCA unrolled into 2 loops\. For more details, please referred to[Huang et al\. \(2019\)](https://arxiv.org/html/2610.26952#bib.bib22)\.

Finally, we use concatenation operators and an MLP to produce an enhanced entity\-relation representation, which is defined in the following equation:

M^e​r\\displaystyle\\hat\{M\}^\{er\}=CCA​\(Me​r\)×1/2\\displaystyle=\\text\{CCA\}\(M^\{er\}\)\_\{\\times 1/2\}\(9\)M^e​r\\displaystyle\\hat\{M\}^\{er\}=We​r​\[M^e​r;Me​r\]\+be​r\\displaystyle=W\_\{er\}\[\\hat\{M\}^\{er\};M^\{er\}\]\+b\_\{er\}
where, “×1/2\\times 1/2” means CCA unrolled into 1 or 2 loops,\[⋅;⋅\]\[\\cdot;\\cdot\]is concatenation operators,We​r∈ℝdr×2​drW\_\{er\}\\in\\mathbb\{R\}^\{d\_\{r\}\\times 2d\_\{r\}\}andbe​r∈ℝdrb\_\{er\}\\in\\mathbb\{R\}^\{d\_\{r\}\}are trainable parameters\.

#### 3\.2\.4Head\-Tail Interaction

The head\-tail interaction is crucial for comprehending how relational triples are structurally composed, since it involves interpreting both head and tail entities in light of their relationship\. This interaction enhances the global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps\. Consequently, it ensures that the model can accurately associate the correct entities with their respective relations, especially in complex sentences where relationships may not adhere to straightforward patterns\.

The*Head\-Tail Interaction Module*is proposed to address the remediation of overlooked or omitted triples\. This module comprises two key components:*Self Interaction*and*Multi\-Object Interaction*\. The*Self Interaction*component can utilize either MLP or*Multi\-Head Self\-Attention \(MHA\)*, depending on the specific task requirements\. Meanwhile, the*Multi\-Object Interaction*component can employ either MLP or*Cross Attention \(CA\)*\. Specifically, MHA is a mechanism that allows the model to extract multiple relationships from the input through parallel attention processes, while CA is designed to align and relate information from diverse sources or modalities\. Finally, MLP is a robust technique for modeling complex, non\-linear interactions by leveraging fully connected layers\.

Assuming that the current iteration isll, after WWI and ERI, the entity\-relation representation contains rich information about the interactions linking entity pairs with their corresponding relations\. In this module, we first use a Maxpooling operation and an MLP forM^e​r\\hat\{M\}^\{er\}to generate the head\-refined representationIh​r\(l\)I\_\{hr\}^\{\(l\)\}and tail\-refined representationIt​r\(l\)I\_\{tr\}^\{\(l\)\}respectively, as shown in Equation[10](https://arxiv.org/html/2610.26952#S3.E10)\.

Ih​r\(l\)\\displaystyle I\_\{hr\}^\{\(l\)\}=Wh​r​Maxpoolh​r​\(M^e​r\)\+bh​r\\displaystyle=W\_\{hr\}\\text\{Maxpool\}\_\{hr\}\(\\hat\{M\}^\{er\}\)\+b\_\{hr\}\(10\)It​r\(l\)\\displaystyle I\_\{tr\}^\{\(l\)\}=Wt​r​Maxpoolt​r​\(M^e​r\)\+bt​r\\displaystyle=W\_\{tr\}\\text\{Maxpool\}\_\{tr\}\(\\hat\{M\}^\{er\}\)\+b\_\{tr\}
whereWh​r/t​r∈ℝdr×deW\_\{hr/tr\}\\in\\mathbb\{R\}^\{d\_\{r\}\\times d\_\{e\}\}denotes learnable weight matrices, andbh​r/t​r∈ℝdeb\_\{hr/tr\}\\in\\mathbb\{R\}^\{d\_\{e\}\}represents learnable bias vectors\.

Then, we employ the*Self Interaction*onIh/t\(l\)I\_\{h/t\}^\{\(l\)\}to extract interaction cues from the head\-relation and tail\-relation pairs\. The formula is as follows:

I~h​r/t​r\(l\)=Self\-Interactionε​\(Ih​r/t​r\(l\)\)\\tilde\{I\}\_\{hr/tr\}^\{\(l\)\}=\\text\{Self\-Interaction\}\_\{\\varepsilon\}\\left\(I\_\{hr/tr\}^\{\(l\)\}\\right\)\\\\\(11\)whereε∈\{MHA,MLP\}\\varepsilon\\in\\\{\\text\{MHA\},\\text\{MLP\}\\\}denotes the two strategies of the*Self Interaction*\. Each strategy has its advantages depending on the dataset and task\. However, MHA tends to perform poorly on long\-sentence, multi\-relation datasets, as shown in Section[5\.4](https://arxiv.org/html/2610.26952#S5.SS4)\. On the other hand, MLP, while simpler, can offer more stable performance on these datasets by processing information through fully connected layers, which helps to improve the performance on complex sentences\.

Next, to prevent the omission of certain global and local semantic details, we adopt the*Multi\-Object Interaction*approach to allow head\-refined representation and tail\-refined representation to interact withHH, so as to extract the information about the reasoning paths between relational triples\. The computation procedure is given below:

I~h​r/t​r\(l\+1\)\\displaystyle\\tilde\{I\}\_\{hr/tr\}^\{\(l\+1\)\}=MulObj\-Interactionδ​\(I~h​r/t​r\(l\),H\)\\displaystyle=\\text\{MulObj\-Interaction\}\_\{\\delta\}\\left\(\\tilde\{I\}\_\{hr/tr\}^\{\(l\)\},H\\right\)\(12\)=\{CrossAtt​\(I~h​r/t​r\(l\),H,H\)δ∈CAMLP​\(I~h​r/t​r\(l\),H\)δ∈MLP\\displaystyle=\\begin\{cases\}\\text\{CrossAtt\}\\left\(\\tilde\{I\}\_\{hr/tr\}^\{\(l\)\},H,H\\right\)&\\delta\\in\\text\{CA\}\\\\ \\text\{MLP\}\\left\(\\tilde\{I\}\_\{hr/tr\}^\{\(l\)\};H\\right\)&\\delta\\in\\text\{MLP\}\\end\{cases\}whereδ∈\{CA,MLP\}\\delta\\in\\\{\\text\{CA\},\\text\{MLP\}\\\}represents the two strategies for the Multi\-Object Interaction process\. In the first case, CA allows for interactions between the head and tail representations through attention mechanisms, leveraging the information fromHHfor deeper reasoning\. In the second case, MLP applies a simpler fully connected layer to combine the refined representations withHH, offering a more straightforward interaction mechanism\. Both approaches aim to improve the extraction of reasoning paths across relational triples, but their effectiveness depends on the specific dataset\.

Finally, we generate new head representationIh\(l\+1\)I\_\{h\}^\{\(l\+1\)\}and tail representationIt\(l\+1\)I\_\{t\}^\{\(l\+1\)\}with an MLP model\. These representations are fed back to WWI for the subsequent iteration\. It is worth noting that the network parameters are reused across all iterations\.

In summary, the new head and tail representations are formulated via the equation below[13](https://arxiv.org/html/2610.26952#S3.E13)\.

Ih/t\(l\+1\)\\displaystyle I\_\{h/t\}^\{\(l\+1\)\}=ReLU⁡\(I~h​r/t​r\(l\+1\)​W\+b\)\\displaystyle=\\operatorname\{ReLU\}\\left\(\\tilde\{I\}\_\{hr/tr\}^\{\(l\+1\)\}W\+b\\right\)\(13\)Ih/t\(l\+1\)\\displaystyle I\_\{h/t\}^\{\(l\+1\)\}=LN⁡\(Ih/t\(l\+1\)\+Ih/t\(l\)\)\\displaystyle=\\operatorname\{LN\}\\left\(I\_\{h/t\}^\{\(l\+1\)\}\+I\_\{h/t\}^\{\(l\)\}\\right\)
whereLN⁡\(⋅\)\\operatorname\{LN\}\(\\cdot\)is Layer Norm\([Ba et al\., 2016](https://arxiv.org/html/2610.26952#bib.bib21)\)\. A residual connection avoids gradient vanishing\.

#### 3\.2\.5Triple Extraction

In this module, an*Interaction Map*is generated through the interaction of head and tail representations\. Assuming that the number of final iterations of the interaction network isLL, the head representationIh\(L\)I\_\{h\}^\{\(L\)\}and the tail representationIt\(L\)I\_\{t\}^\{\(L\)\}are fed into the Biaffine\([Yu et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib17)\)for generating the*Interaction Map*\. The equation is given below:

ℐi​j=Ih\(L\)⊤​UB​It\(L\)\+WB​\(Ih\(L\),It\(L\)\)\+bB\\mathcal\{I\}\_\{ij\}=I\_\{h\}^\{\(L\)\{\\top\}\}U\_\{B\}I\_\{t\}^\{\(L\)\}\+W\_\{B\}\(I\_\{h\}^\{\(L\)\};I\_\{t\}^\{\(L\)\}\)\+b\_\{B\}\\\\\(14\)
where,ℐ∈ℝ\(N\+𝒦\)×\(N\+𝒦\)\\mathcal\{I\}\\in\\mathbb\{R\}^\{\(N\+\\mathcal\{K\}\)\\times\(N\+\\mathcal\{K\}\)\}\.UBU\_\{B\}is ade×1×ded\_\{e\}\\times 1\\times d\_\{e\}tensor,WBW\_\{B\}is a2​de×12d\_\{e\}\\times 1matrix andbBb\_\{B\}is the bias\.

The*Interaction Map*strategy\([Tang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib16)\)stems from its narrowed prediction space, estimated atO⁡\(\(N\+𝒦\)2\)O\(\(N\+\\mathcal\{K\}\)^\{2\}\), which is notably smaller compared to other methods requiringO⁡\(N×𝒦×N\)O\(N\\times\\mathcal\{K\}\\times N\)complexity for triple prediction\. In addition, it also has an efficient decoding efficiency\. Although OD\-RTE\([Ning et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib5)\)enhances the tagging scheme based on OneRel\([Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15)\)and introduces the Bi\-DW decoding algorithm, its prediction space remains atO⁡\(N×𝒦×N\)O\(N\\times\\mathcal\{K\}\\times N\)\.

The*Interaction Map*fuses Entity\-Entity \(E\-E\) table, Head\-Relation \(H\-R\) table, Relation\-Tail \(R\-T\) table in the same table for labeling\. Consider the example “Biden lives in the USA\.”, which is visualized in Figure[4](https://arxiv.org/html/2610.26952#S3.F4)\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/IM.png)Figure 4:An Example of entity\-pair tagging\.The triple \(Biden, live\_in, USA\) can be determined if \(Biden, USA\) is tagged in the Entity\-Entity section, \(Biden, live\_in\) is tagged in the Head\-Relation section, and \(live\_in, USA\) is tagged in the Relation\-Tail section\. Thus, the*Interaction Map*is of size\(N\+𝒦\)×\(N\+𝒦\)\(N\+\\mathcal\{K\}\)\\times\(N\+\\mathcal\{K\}\)\(see[Tang et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib16)for details\)\.

In decoding, we first obtain all valid head/tail entities per relation from the Head\-Relation and Relation\-Tail regions\. Then, for each relation, we examine candidate entity pairs after pruning by the Entity\-Entity region\.

The loss function for our framework is formulated as:

ℒ=−1\(N\+𝒦\)2∑iN\+𝒦∑jN\+𝒦\(ℐi​j∗logℐi​jOPEN\+\(1−ℐi​j∗\)​log⁡\(1−ℐi​j\)\)\\begin\{array\}\[\]\{r\}\\mathcal\{L\}=\-\\frac\{1\}\{\(N\+\\mathcal\{K\}\)^\{2\}\}\\sum\_\{i\}^\{N\+\\mathcal\{K\}\}\\sum\_\{j\}^\{N\+\\mathcal\{K\}\}\\left\(\\mathcal\{I\}\_\{ij\}^\{\*\}\\log\\mathcal\{I\}\_\{ij\}\\right\.\\\\ \\left\.\+\\left\(1\-\\mathcal\{I\}\_\{ij\}^\{\*\}\\right\)\\log\\left\(1\-\\mathcal\{I\}\_\{ij\}\\right\)\\right\)\\end\{array\}\(15\)
whereℐ∗\\mathcal\{I\}^\{\*\}denotes the ground\-truth Interaction Map matrix\.

## 4Experiment

### 4\.1Experimental Settings

Table 3:Statistics of the datasets\.CategoryDetails of the datasetType of tripleTrainValidTestRelationEntirePartialUnseenOthersNYT\-R5619650005000243483307886459WebNLG\-R5019500703216155178174196NYT561955000500024429247388147WebNLG5019500703171580421764Table 4:Overlapping patterns in datasets\.NNdenotes the total count of relational triples\.DatasetOverlapping PatternNormalSEOEPOSOON=1N=1N=2N=2N=3N=3N=4N=4N≥5N\\geq 5NYT\-R396570940811039587331925048WebNLG\-R389293984411143815810NYT32661297978453,2441,045312291108WebNLG24545726842661711319045Datasets: we assess our method using two benchmark datasets introduced by\([Lee et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib33)\): NYT\-R and WebNLG\-R\. These datasets, derived from the NYT dataset\([Riedel et al\., 2010](https://arxiv.org/html/2610.26952#bib.bib23)\)and the WebNLG dataset\([Gardent et al\., 2017](https://arxiv.org/html/2610.26952#bib.bib24)\), are primarily designed to assess relational triple extraction performance on “unseen” entities\. The NYT\-R dataset was constructed colle by aligning relations in Freebase articles in the New York Times corpus\. It contains 24 predefined relations\. On the other hand, the WebNLG\-R dataset is initially devised for the Natural Language Generation Challenge\. It is annotated with 171 predefined relations types\.

Table[3](https://arxiv.org/html/2610.26952#S4.T3)provides the statistical breakdown of these datasets, which are categorized into four groups: Entire, Partial, Unseen, and Others\. The Entire, Partial and Unseen indicate that all relation triples in the sentence are of the corresponding relational triple type\. The Others suggest that relational triples may contain Entire, Partial or Unseen types of relational triples\. According to\([Zheng et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib27)\), SEO stands for Single Entity Overlapping, EPO refers to Entity Pair Overlapping, and SOO denotes Subject Object Overlapping\. To maintain consistency with prior research\([Zhan et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib8);[Sui et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib4);[Ning et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib5)\), we adopt the conventional micro Precision \(Prec\.\), Recall \(Rec\.\), and F1\-score metrics for gauge model performance\.

Baseline: For comparison, we used the following model as a baseline: \(1\)CasRel\\mathrm\{CasRel\}\([Wei et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib26)\)first identifies all possible head\-entities within a sentence\. Subsequently, for each head\-entity, it determines all potential relations and their corresponding tail\-entities\. \(2\)TPlinker\\mathrm\{TPlinker\}\([Wang et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib14)\)can identify overlapping relations that share either one or two entities, and it remains unaffected by exposure bias\. \(3\)PRGC\\mathrm\{PRGC\}\([Zheng et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib27)\)approaches the task from a new angle by breaking it down into three subtasks: Relation Judgement, Entity Extraction, and Subject\-object Alignment\. Subsequently, it introduces a joint extraction framework based on Potential Relation and Global Correspondence\. \(4\)BiRTE\\mathrm\{BiRTE\}\([Ren et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib35)\)operates as a bidirectional extraction framework\. It generates triples by leveraging entity pairs obtained from two complementary directions\. \(5\)OneRel\\mathrm\{OneRel\}\([Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15)\)reinterprets joint extraction as a fine\-grained triple classification task\. Its architecture comprises a scoring\-based classifier along with a relation\-specific horns tagging strategy\. \(6\)SPN\\mathrm\{SPN\}\([Sui et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib4)\)frames joint entity and relation extraction as a direct set prediction task\. This allows the extraction model to avoid the difficulty of determining the order of multiple triples\. \(7\)UniRel\\mathrm\{UniRel\}\([Tang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib16)\)unifies the representations of entities and relations and unify the modeling of interactions with a Interaction Map\. \(8\)RTF\\mathrm\{RTF\}\([An et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib30)\)introduces a novel region\-based tagging scheme along with a bi\-directional decoding strategy\. This approach treats every relational triple as a region within a relation\-specific table, and extracts triples by locating the two endpoints of each region\. \(9\)SOIRP\\mathrm\{SOIRP\}\([Dai et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib36)\)comprises a Subject\-Object Interaction module, which is built from multiple distinct interactions, along with a Reasoning Path Extraction module inspired by the Transformer decoder architecture\.

Implementation Details: for fair comparison purposes, the Bert\-base\-cased language model111Available at https://huggingface\.co/bert\-base\-casedis used\. It features 12 Transformer blocks and a hidden size ofd=768d=768\. All parameters are optimized via the Adam optimizer\([Kingma and Ba, 2014](https://arxiv.org/html/2610.26952#bib.bib25)\)on two rearranged datasets, employing a learning rate of3e\-5and batch sizes of 6/4\. In equation[6](https://arxiv.org/html/2610.26952#S3.E6), the hidden size ofdr=512d\_\{r\}=512and the vector space based on tensor operations ism=5m=5\. In Section[3\.2\.3](https://arxiv.org/html/2610.26952#S3.SS2.SSS3), CCA unrolled into 1/2 loops onNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}/WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}rearrange datasets\. In Section[3\.2\.4](https://arxiv.org/html/2610.26952#S3.SS2.SSS4), Self Interaction employed MHA/MLP and Multi\-Object Interaction adopt CA/MLP onNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}/WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}rearrange datasets\. Additionally, the interaction network is iterated only once, and sentences are truncated to a maximum length of 100, in accordance with previous work\. \(Note that this limit excludes the number of relations\.\)\. All experiments ran on a single NVIDIA RTX A6000 GPU\.

### 4\.2Main Results

Table 5:Main results\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}Prec\.Rec\.F1EntirePartialUnseenPrec\.Rec\.F1EntirePartialUnseenCasRel†\\mathrm\{CasRel\}^\{\\dagger\}\([Wei et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib26)\)65\.960\.162\.985\.865\.042\.373\.664\.268\.689\.652\.341\.5TPlinker†\\mathrm\{TPlinker\}^\{\\dagger\}\([Wang et al\., 2020](https://arxiv.org/html/2610.26952#bib.bib14)\)69\.060\.864\.783\.366\.746\.875\.163\.969\.188\.552\.742\.9PRGC†\\mathrm\{PRGC\}^\{\\dagger\}\([Zheng et al\., 2021](https://arxiv.org/html/2610.26952#bib.bib27)\)63\.561\.662\.681\.664\.245\.161\.662\.061\.879\.247\.228\.3BiRTE§\\mathrm\{BiRTE\}^\{\\lx@sectionsign\}\([Ren et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib35)\)64\.565\.464\.986\.167\.045\.271\.064\.667\.689\.253\.936\.7OneRel§\\mathrm\{OneRel\}^\{\\lx@sectionsign\}\([Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15)\)70\.8¯\\underline\{70\.8\}58\.263\.982\.566\.544\.275\.966\.570\.990\.8¯\\underline\{90\.8\}57\.2¯\\underline\{57\.2\}39\.2SPN§\\mathrm\{SPN\}^\{\\lx@sectionsign\}\([Sui et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib4)\)68\.461\.264\.684\.868\.248\.564\.160\.262\.181\.353\.344\.4UniRel§\\mathrm\{UniRel\}^\{\\lx@sectionsign\}\([Tang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib16)\)74\.257\.164\.681\.266\.844\.872\.964\.068\.285\.751\.343\.3RTF\\mathrm\{RTF\}\([An et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib30)\)68\.862\.365\.4\-\-\-76\.566\.5¯\\underline\{66\.5\}71\.2\-\-\-SOIRP§\\mathrm\{SOIRP\}^\{\\lx@sectionsign\}\([Dai et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib36)\)68\.566\.567\.586\.969\.849\.575\.262\.968\.590\.553\.938\.2O​u​r​sOurs70\.267\.1\\mathbf\{67\.1\}68\.6\\mathbf\{68\.6\}89\.1\\mathbf\{89\.1\}70\.8\\mathbf\{70\.8\}52\.6\\mathbf\{52\.6\}78\.1\\mathbf\{78\.1\}67\.8\\mathbf\{67\.8\}72\.6\\mathbf\{72\.6\}90\.8\\mathbf\{90\.8\}57\.2\\mathbf\{57\.2\}58\.7\\mathbf\{58\.7\}

We evaluate our model against nine competitive baselines\. Table[5](https://arxiv.org/html/2610.26952#S4.T5)presents the experimental outcomes on two rearranged datasets, where the top performance is highlighted in bold and the runner\-up is underlined\. The performance of Entire, Partial and Unseen metrics is given in F1 scores\. § means that the results are not reported in the paper, while†\\daggerdenotes that the results are reported in[Lee et al\. \(2022\)](https://arxiv.org/html/2610.26952#bib.bib33)\. They are obtained through re\-implemented its source code with the same evaluated datasets\. The experimental findings reveal that:

\(1\) Some models have higher F1 scores, but it does not balance the performance between seen and unseen relational triples\. For instance, theOneRel\\mathrm\{OneRel\}model achieves an F1 score 1\.8% points higher than theTPlinker\\mathrm\{TPlinker\}model on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset, but it is 3\.7% points lower in the Unseen entity triples\. OneRel’s effectiveness is largely tied to the availability of annotated entities in the training data\. Its performance easily overfitting to the seen relational triples\. Therefore, the final performance is strongly influenced by the types of relational triples encountered during training\.

\(2\) Our model surpasses all compared baseline methods and achieves the highest F1 results on the two rearranged datasets\. This underscores our approach’s efficacy in handling entirely seen, partially seen and unseen relational triples, a capability attributed to its effective interaction network\. This network not only utilizes word\-word, entity\-relation and head\-tail interactions in the relational triples, but also integrates the information on these effective interactions\. As a result, the interaction network encodes rich entity and relation semantic features\. They are effective to improve the performance\.

\(3\) The experimental results show that our model surpasses all compared baseline models, achieving the best performance across the Entire, Partial, and Unseen metrics on the rearranged dataset\. In the Entire metric, the model may encounter relational triples during training, demonstrating its capacity for memorization\. In the Partial and Unseen metrics, the model encountered relational triples that were partially seen or unseen during training, highlighting its strong generalization capabilities\. This performance is attributed to the integration of word\-word, entity\-relation and head\-tail interaction information, which gives it the ability to memorize and generalize\.

### 4\.3Ablation Study

Table 6:Ablation study\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}Prec\.Rec\.F1EntirePartialUnseenPrec\.Rec\.F1EntirePartialUnseenFully Model70\.267\.1\\mathbf\{67\.1\}68\.6\\mathbf\{68\.6\}89\.170\.8\\mathbf\{70\.8\}52\.6\\mathbf\{52\.6\}78\.1\\mathbf\{78\.1\}67\.8\\mathbf\{67\.8\}72\.6\\mathbf\{72\.6\}90\.8\\mathbf\{90\.8\}57\.2\\mathbf\{57\.2\}58\.7\\mathbf\{58\.7\}w/o​WWI\{w/o\\ \\mathrm\{WWI\}\}70\.365\.067\.688\.469\.550\.777\.163\.569\.787\.055\.950\.0w/o​ERI\{w/o\\ \\mathrm\{ERI\}\}69\.465\.067\.189\.3\\mathbf\{89\.3\}69\.251\.7¯\\underline\{51\.7\}76\.867\.071\.690\.054\.755\.8w/o​HTI\{w/o\\ \\mathrm\{HTI\}\}70\.664\.067\.287\.969\.450\.475\.867\.8\\mathbf\{67\.8\}71\.690\.555\.956\.4w/o​ALL\{w/o\\ \\mathrm\{ALL\}\}74\.2¯\\underline\{74\.2\}57\.164\.681\.266\.844\.868\.152\.859\.575\.743\.543\.5w/o​SEP\{w/o\\ \\mathrm\{SEP\}\}74\.8\\mathbf\{74\.8\}54\.262\.876\.065\.945\.277\.7¯\\underline\{77\.7\}66\.571\.790\.453\.452\.1In this section, we conducted ablation experiments to assess the impact of each component of the model\. The highest scores are in bold and second scores are in underline\. The performance of Entire, Partial and Unseen metrics is given in F1 scores\.

\(1\)*w/o WWI*denotes the model where word\-word interaction is removed from the interaction network\. In this setting, the model cannot make full use of relation and entity information\. Experimental results reveal a slight performance degeneration on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, with a reduction of 1\.0% in the F1\-score\. The degeneration suggests that word\-word interactions are vital for capturing contextual relationships between words, thereby enhancing the discriminability of the model\. The performance on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset shows a more significant decline, with a 2\.9% decrease in F1 score\. This highlights the critical role of word\-word interactions in reinforcing the semantic features of relational triples\.

By comparison, the performance of*w/o WWI*on the Unseen metric is notably lower than the full model, especially in theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset, where the performance is decreased about 8\.7% in F1 score\. The result indicates that word\-word interactions significantly bolster the ability of model generalization\. Comparing the performance betweenNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}, the word\-word interaction is more influential in the latter\. The marked difference across the two datasets stems from the greater number of relation types inWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\(171 relations\) relative toNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}\(24 relations\)\. This difference highlights the critical role of word\-to\-word interactions in a dataset with a greater number of relations\.

\(2\)*w/o ERI*denotes the model where entity\-relation interaction is removed from interaction network\. Experimental findings indicate that our model’s F1 score lags 0\.5% behind that of w/o WWI on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset\. It suggests the entity\-relation interaction strengthens the long\-distance semantic dependencies between relations and entities, effectively filtering out the semantic features related to redundant relational triples\. It is worth noting that the highest F1 score is achieved on the Entire indicator, which may be due to the reason that many parameters can impact the model’s ability to effectively retain information\.

In contrast, the degradation on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset is relatively minor\. In the Partial metric, the model’s F1 score is 1\.2% lower than w/o WWI, highlighting the importance of entity\-relation interactions in effectively handling partially seen relational triples\. The performance differences between the two datasets may stem from greater relational overlapping patterns \(e\.g\., SEO, EPO and SOO\)\. Hence, theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset exhibits more pronounced entity\-relation interactions\.

\(3\)*w/o HTI*denotes the model where head\-tail interaction is removed from the interaction network\. It disables the model to encode the global semantic features of relational triples\. Experimental results show a significant performance decline on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, particularly in the Entire and Unseen metrics\. The result highlights the importance of head\-tail interaction information\. This interaction enhances global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps\.

In contrast, the performance degradation on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset is smaller\. Compared to theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset, theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset contains more complex sentences and general features longer sentences\. These characteristics can contribute to the performance differences observed between the two datasets\. Global semantic information proves to be more effective for handling complex and lengthy sentences\.

\(4\)*w/o ALL*is the model in which word\-word, entity\-relation, and head\-tail interactions are excluded from the interaction network\. Experimental results show a significant performance decline in the two datasets\. This validates the capability of our method to handle entirely seen, partially seen, and unseen relational triples\. This effectiveness stems from the efficiency of our interaction network\. Furthermore, it can be concluded that leveraging any two types of semantic interaction information substantially enhances the discriminability of the model\. The semantic interactions among multiple objects empower the model to recognize unseen relationship triples, offering a theoretical framework for applying natural language processing to tackle various other tasks\.

\(5\) In the Encoder module \(Section[3\.2\.1](https://arxiv.org/html/2610.26952#S3.SS2.SSS1)\), sentences and relations are combined for encoding\. While increasing the interaction between relations and sentences, this also introduces additional complexity to the model\. To explore its impact, we isolate the relation sequence from the input sentence to model the two types of interactions separately, as represented in Table[6](https://arxiv.org/html/2610.26952#S4.T6)under the label “*w/o SEP*”\. Specifically, the same BERT encoder is used to separately derive the sequence embeddings for the input sentence and the natural language descriptions of each relation\. Then, after embedding both sentences, we concatenate them together and input them into a multi\-granularity interaction network\.

Given that “*w/o SEP*” considers entities and relations as separate input representations, the deep Transformer network is only able to model correlations within entity pairs and relation pairs independently\. As shown in Table[6](https://arxiv.org/html/2610.26952#S4.T6), the performance of “*w/o SEP*” significantly decreases on both datasets compared to the Fully Model, highlighting the importance of combining sentences and relations for effective encoding\. We further analyze the performance of “*w/o SEP*” and other models across different interaction types\. On theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, Unseen outperforms “*w/o ALL*”, while Entire shows the opposite result\. This further proves that the interaction network can effectively enhance the ability to identify triples consisting of “unseen” entities\. Moreover, since the encoder module forms the foundation for subsequent modules, the lack of interactive semantic information negatively affects the performance of later stages\.

## 5Analytical Experiments

### 5\.1Performance on Different Overlapping Patterns

Table 7:F1\-score \(%\) on sentences with different overlapping patterns and different numbers of triples for the NYT and WebNLG datasets\.NNrepresents the number of triples within a sentence\.DatasetModelNormal\\mathrm\{Normal\}EPO\\mathrm\{EPO\}SEO\\mathrm\{SEO\}SOO\\mathrm\{SOO\}N=1\\mathrm\{N\}=1N=2\\mathrm\{~N\}=2N=3\\mathrm\{~N\}=3N=4\\mathrm\{~N\}=4N≥5\\mathrm\{~N\}\\geq 5NYT\\mathrm\{NYT\}CasRel\\mathrm\{CasRel\}87\.392\.091\.477\.088\.290\.391\.994\.283\.7TPLinker\\mathrm\{TPLinker\}90\.194\.093\.490\.190\.092\.893\.196\.190\.0SPN\\mathrm\{SPN\}90\.894\.194\.081\.890\.993\.494\.295\.590\.6PRGC\\mathrm\{PRGC\}91\.091\.094\.594\.090\.891\.193\.093\.595\.593\.0DirectRel\\mathrm\{DirectRel\}91\.7\\mathbf\{91\.7\}94\.890\.090\.091\.7\\mathbf\{91\.7\}94\.1\\mathbf\{94\.1\}93\.596\.392\.7BiRTE\\mathrm\{BiRTE\}91\.494\.294\.7\-91\.593\.793\.995\.892\.1Ours\\mathrm\{Ours\}91\.195\.3\\mathbf\{95\.3\}95\.2\\mathbf\{95\.2\}91\.6\\mathbf\{91\.6\}91\.193\.795\.1\\mathbf\{95\.1\}97\.0\\mathbf\{97\.0\}94\.3\\mathbf\{94\.3\}WebNLG\\mathrm\{WebNLG\}CasRel\\mathrm\{CasRel\}89\.494\.792\.290\.489\.390\.894\.292\.490\.9TPLinker\\mathrm\{TPLinker\}87\.995\.392\.586\.088\.090\.194\.693\.391\.6SPN\\mathrm\{SPN\}89\.590\.894\.194\.689\.591\.396\.494\.793\.8PRGC\\mathrm\{PRGC\}90\.495\.993\.694\.989\.991\.695\.094\.892\.8DirectRel\\mathrm\{DirectRel\}92\.097\.194\.594\.691\.692\.296\.095\.094\.9BiRTE\\mathrm\{BiRTE\}90\.194\.395\.9\\mathbf\{95\.9\}\-90\.292\.995\.794\.692\.0Ours\\mathrm\{Ours\}92\.5\\mathbf\{92\.5\}97\.7\\mathbf\{97\.7\}94\.996\.3\\mathbf\{96\.3\}92\.1\\mathbf\{92\.1\}94\.3\\mathbf\{94\.3\}96\.5\\mathbf\{96\.5\}95\.3\\mathbf\{95\.3\}95\.4\\mathbf\{95\.4\}Two relational triples may share none, one or two named entities, which leads to the overlapping problem\. Table[4](https://arxiv.org/html/2610.26952#S4.T4)also gives statistical information about overlapping patterns about theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets\. Compared to the originalNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}datasets, there are fewer triples and EPO patterns in theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets\. Therefore, in this section, we conducted experiments specifically on theNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}datasets to evaluate our model’s capability in handling diverse overlapping patterns\. We chose six recent top\-performing models to serve as our benchmarks\. The experimental result is listed in Table[7](https://arxiv.org/html/2610.26952#S5.T7)\.

As shown from the experimental results, our proposed model achieves the best performance in 14 of the 18 subsets of the two test sets, particularly excelling in scenarios involving numerous relational triples \(N ¿ 3\) and overlapping patterns\. The integration of multiple semantic information interactions proves especially advantageous in complex, lengthy sentences\. However, the indicators Normal, N=1, and N=2 did not achieve the best results on the NYT dataset\. Our model is specifically designed to leverage multiple semantic interactions and handle complex dependencies, which are less prevalent in simpler sentences\. Our approach may not provide advantages over baseline models optimized for straightforward cases\. Simpler sentences often require less sophisticated semantic modeling, which limits the full utilization of our model’s capabilities in these subsets\.

Another advantage of our model is that it does not depend prior exposure to all relational triples encountered during training\. It effectively interacts with word\-to\-word interactions through extracted semantic information about entities, relations, as well as head and tail representations\. Therefore, our model learns richer interaction semantic information in the above complex scenarios, so as to achieve competitive performance\.

### 5\.2Influence of the Word\-Word Interaction

In our model, Word\-Word Interaction is adopted to reinforce semantic features of the elements in the two\-dimensional table, making them rich in relation and entity information\. This experiment aims to demonstrate how the tensor\-based operation affects overall performance\. We evaluate our model on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets\. Table[5](https://arxiv.org/html/2610.26952#S5.F5)shows the effectiveness of tensor\-based operations with vector space dimensions \{3, 4, 5, 6, 8, 10, 12\}\. For a fair comparison, we trained on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets with 20 and 50 epochs, respectively\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/wwi.png)Figure 5:The performance of tensor\-based operations with different vector spaces \{3, 4, 5, 6, 8, 10, 12\}\.As shown in Table[5](https://arxiv.org/html/2610.26952#S5.F5), performance declines when the number of tensor\-based operations increases across different vector spaces, particularly at vector space dimension 12\. This decline may stem from an excess of introducing vector space, which could introduce noise and potentially interfere with the model’s extraction capabilities\. In addition, the performance of both datasets improves when tensor\-based operations across vector space 5 is introduced using the default settings of our model\. This experiment underscores the value of tensor\-based operations in enriching semantic information within two\-dimensional tables\. By leveraging interactive information between words, these operations enhance the model’s memory and generalization capabilities in extracting relational triples\.

### 5\.3Influence of the Entity\-Relation Interaction

Table 8:The performance of CCA with different configurations onNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}Prec\.Rec\.F1Prec\.Rec\.F1CCAO​u​r\(×1\)CCA\_\{Our\}\(\\times 1\)70\.267\.168\.678\.167\.872\.6CCAO​u​r\(×2\)CCA\_\{Our\}\(\\times 2\)69\.761\.365\.279\.766\.072\.2CCAO​r​i\(×1\)CCA\_\{Ori\}\(\\times 1\)73\.258\.465\.077\.765\.371\.0CCAO​r​i\(×2\)CCA\_\{Ori\}\(\\times 2\)75\.157\.765\.378\.965\.871\.8In our model, the entity\-relation interaction captures long\-distance semantic dependencies between relations and entities, effectively filtering out the semantic features related to redundant relational triples\. To assess how our optimized CCA affects ERI, we ran a set of experiments and contrasted our model’s performance against the original CCA\. The experiments were conducted on bothNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}datasets\. Table[8](https://arxiv.org/html/2610.26952#S5.T8)summarizes these experimental results, highlighting the performance across various configurations\. The notation “Ori” refers to the use of the convolution operation from the original CCA, while “×1/2\\times 1/2” indicates that the CCA was unrolled into 1 or 2 loops\.

From the experimental results presented for “CCAO​u​r\(×1\)CCA\_\{Our\}\(\\times 1\)” and “CCAO​r​i\(×1\)CCA\_\{Ori\}\(\\times 1\)”, it is clear that the fully connected layer in “CCAO​u​r\(×1\)CCA\_\{Our\}\(\\times 1\)” exhibits a robust nonlinear fitting ability, which allows the model to learn task\-relevant semantic features more effectively\. This results in stronger performance, especially on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, where “CCAO​u​r\(×1\)CCA\_\{Our\}\(\\times 1\)” outperforms “CCAO​r​i\(×1\)CCA\_\{Ori\}\(\\times 1\)” in both precision and recall\.

Interestingly, for “C​C​AO​r​iCCA\_\{Ori\}”, unrolling the CCA into 2 loops \(×2\\times 2\) improves the model’s performance\. The reason lies in the convolutional operations, which, although effective in capturing local dependencies, may struggle to model long\-range semantic relationships between entities and relations\. By unrolling the model into multiple loops, the convolution operation can leverage a wider context, thus better capturing these long\-distance dependencies, which is in line with the findings of[Huang et al\. \(2019\)](https://arxiv.org/html/2610.26952#bib.bib22)\.

However, for “C​C​AO​u​rCCA\_\{Our\}”, we observe a performance drop on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset when unrolled into two loops \(×2\\times 2\)\. This could be due to the fact that, in this configuration, the fully connected layer already captures most of the useful semantic information when the training set is sufficiently large\. When additional loops are added, the model may overfit or fail to extract additional meaningful information, leading to a reduction in performance\. In contrast, when considering theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset, unrolling into two loops \(×2\\times 2\) results in a slight improvement in performance\. This likely stems from the training set’s limited size and the higher quantity of relation types, where extra loops help the model capture diverse semantic relationships more effectively\. In such cases, the increased capacity for modeling long\-range dependencies, facilitated by the unrolling of loops, can help the model navigate the complexities of the dataset more effectively\. In summary, our experiments demonstrate that the entity\-relation interaction mechanism plays a significant role in improving model performance, with the fully connected layer in “C​C​AO​u​rCCA\_\{Our\}” showing notable advantages in capturing semantic features\. The comparison between configurations also highlights the importance of adjusting the architecture depending on the dataset size and complexity to achieve the best results\.

### 5\.4Influence of the Head\-Tail Interaction

Table 9:The performance of Self Interaction and Multi\-Object Interaction with different configurations onNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}Prec\.Rec\.F1Prec\.Rec\.F1\[MLP,CA\]\[\\mathrm\{MLP\},\\mathrm\{CA\}\]71\.559\.765\.178\.564\.070\.6\[MHA,MLP\]\[\\mathrm\{MHA\},\\mathrm\{MLP\}\]73\.857\.464\.679\.566\.472\.4\[MLP,MLP\]\[\\mathrm\{MLP\},\\mathrm\{MLP\}\]73\.957\.064\.378\.167\.872\.6\[MHA,CA\]\[\\mathrm\{MHA\},\\mathrm\{CA\}\]70\.267\.168\.679\.766\.072\.2In our model, the head\-tail interaction plays a crucial role in enhancing the global semantic features associated with relational triples\. This interaction helps to identify and remediate triples that may have been overlooked or omitted in earlier stages of processing, ensuring a more comprehensive understanding of the relational triples\. To evaluate the impact of Self Interaction and Multi\-Object Interaction on HTI, we ran a set of experiments on a pair of rearranged datasets, namelyNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\.

The experimental results are presented in Table[9](https://arxiv.org/html/2610.26952#S5.T9), which compares the performance of different configurations of Self Interaction and Multi\-Object Interaction within the context of HTI\. Specifically, the table showcases the precision \(Prec\.\), recall \(Rec\.\), and F1\-score for each model configuration on both datasets\. The model structure ”\[ε,δ\]\[\\varepsilon,\\delta\]” indicates that the specified module \(Self Interaction or Multi\-Object Interaction\) are in different configurations\. For example, when we denote “\[MLP,MLP\\mathrm\{MLP\},\\mathrm\{MLP\}\]”, it implies that bothε\\varepsilonandδ\\deltaare adopted with a Multilayer Perceptron structure\.

As observed from the table, the performance of different configurations varies across datasets\. On theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, the model’s performance experiences degradation to varying degrees when configured with MLP\. This decline in performance highlights the indispensable role that CA and MHA play in the HTI mechanism\. These attention mechanisms are far more effective than MLPs in capturing and processing the relational semantics of the entities involved in the triples\. The experimental results for the configurations “\[MLP,CA\]\[\\mathrm\{MLP\},\\mathrm\{CA\}\]” and “\[MHA,MLP\]\[\\mathrm\{MHA\},\\mathrm\{MLP\}\]” indicate a notable drop in performance, especially in recall and F1\-score\. This suggests that CA’s capability for capturing head\-tail entity interactions is essential to the HTI module’s effectiveness\. By attending to the semantic features of both the entities \(head and tail\) and the relations between them, CA enables the model to capture more nuanced, contextualized information that is crucial for accurate relational triple extraction\.

Conversely, on theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset, the performance of the model with “\[MLP,MLP\]\[\\mathrm\{MLP\},\\mathrm\{MLP\}\]” improves\. This improvement may be attributed to the specific characteristics of the dataset, which contains 171 relational types and a relatively small training set\. In such cases, the attention mechanisms \(CA and MHA\) may struggle to effectively capture the complex relations, leading to diminished performance\. As a result, simplifying the model with MLP helps to enhance performance, particularly when attention mechanisms fail to generalize well in this context\.

### 5\.5Influence of the Number of Iterations on the Interaction Network

Table 10:The performance of interaction network with different number of iterations of onNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}WebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}Prec\.Rec\.F1Prec\.Rec\.F1I=1I=170\.267\.168\.678\.167\.872\.6I=2I=269\.261\.965\.470\.537\.348\.8I=3I=364\.664\.164\.469\.436\.647\.9In our model, the multi\-granularity interaction network has been shown to effectively refine the feature vectors for head and tail entities\. To assess the number of iterations that influence model performance, we ran multiple experiments across two standard datasets, namelyNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}andWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\. The performance metrics, including Precision \(Prec\.\), Recall \(Rec\.\), and F1\-score, were evaluated across different iteration settings, specifically with 1, 2, and 3 iterations of the interaction network\.

Table[10](https://arxiv.org/html/2610.26952#S5.T10)illustrates how different iteration counts affect performance\. For each dataset, we trained the models for a fixed number of epochs—10 epochs for theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset and 20 epochs for theWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}dataset—to ensure a fair comparison across different iteration configurations\.

From the table, we observe that: \(1\) ForNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}, the optimal performance occurs at 1 iteration, yielding an F1 score of 68\.6\. At 2 iterations, both Precision and Recall drop, resulting in a reduced F1 score of 65\.4\. Further increasing the iterations to 3 results in a notable drop, with the F1 score falling to 64\.4\. \(2\) ForWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}, the pattern is somewhat similar, with the first iteration yielding the highest F1 score of 72\.1\. However, as the iterations increase, the performance degrades sharply, especially in the case of Recall, which drops significantly from 68\.0 at 1 iteration to just 37\.3 at 2 iterations\. This suggests diminishing returns and potential overfitting with additional iterations\.

These results indicate that while increasing the number of iterations can refine entity representations, there is a point beyond which additional iterations may lead to diminishing performance or even overfitting, particularly with more complex datasets likeWebNLG\\mathrm\{WebNLG\}\-R\\mathrm\{R\}\. Thus, the number of iterations should be chosen carefully, balancing the benefits of interaction refinement with the potential for performance decline\. In other words, when the individual models are sufficiently strong, it is possible to accurately extract the corresponding relational triples in just one iteration\.

### 5\.6Performance on Widely\-Used Datasets

Table 11:Performance onNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}\.ModelNYT\\mathrm\{NYT\}WebNLG\\mathrm\{WebNLG\}Prec\.Rec\.F1Prec\.Rec\.F1BiRTE92\.293\.8¯\\underline\{93\.8\}93\.093\.294\.093\.6OneRel92\.892\.992\.894\.194\.494\.3BitCoin92\.992\.893\.194\.4¯\\underline\{94\.4\}94\.5¯\\underline\{94\.5\}94\.4SOIRP93\.3¯\\underline\{93\.3\}92\.993\.194\.394\.194\.2RTF93\.293\.493\.394\.095\.3\\mathbf\{95\.3\}94\.6\\mathbf\{94\.6\}BiSDRTE92\.894\.2\\mathbf\{94\.2\}93\.5¯\\underline\{93\.5\}94\.194\.694\.4Ours93\.5\\mathbf\{93\.5\}93\.793\.6\\mathbf\{93\.6\}95\.0\\mathbf\{95\.0\}94\.094\.5¯\\underline\{94\.5\}In this experiment, for a fair benchmark against additional baselines, we performed evaluations on the popularNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}datasets\. These datasets contain primarily Entire type relational triples, along with a smaller proportion of Unseen type triples\. This composition allows the evaluation to better reflect the model’s memory capabilities\. Table[11](https://arxiv.org/html/2610.26952#S5.T11)presents the outcomes\.

In Table[11](https://arxiv.org/html/2610.26952#S5.T11), our model is compared with six strong baselines: BiRTE\([Ren et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib35)\), OneRel\([Shang et al\., 2022](https://arxiv.org/html/2610.26952#bib.bib15)\), BitCoin\([He et al\., 2023](https://arxiv.org/html/2610.26952#bib.bib7)\), SOIRP\([Dai et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib36)\), RTF\([An et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib30)\)and BiSDRTE\([Chen et al\., 2024](https://arxiv.org/html/2610.26952#bib.bib43)\)\. Our model exhibits strong performance, as evidenced by the experimental results\. It achieves similar performance across theNYT\\mathrm\{NYT\}andWebNLG\\mathrm\{WebNLG\}datasets, outperforming almost all of compared baselines\. These findings suggest that the interaction network positively impacts the model’s memory capacity, driven by the integration of word\-word, entity\-relation, and head\-tail semantic interactions\.

### 5\.7Computational Efficiency

Table 12:Comparison of model efficiency\.ModelNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}Training TimeGPU MemoryF1SOIRP\\mathrm\{SOIRP\}6738 seconds4278 MB67\.5O​u​r​s\{Ours\}7113 seconds5180 MB68\.6O​u​r​sw/o​WWI\{Ours\}\_\{w/o\\mathrm\{WWI\}\}6474 seconds4612 MB67\.6O​u​r​sw/o​ERI\{Ours\}\_\{w/o\\mathrm\{ERI\}\}5724 seconds4338 MB67\.1O​u​r​sw/o​HTI\{Ours\}\_\{w/o\\mathrm\{HTI\}\}6418 seconds5042 MB67\.2O​u​r​sw/o​ALL\{Ours\}\_\{w/o\\mathrm\{ALL\}\}4779 seconds3144 MB64\.6O​u​r​sw/o​SEP\{Ours\}\_\{w/o\\mathrm\{SEP\}\}9363 seconds5170 MB62\.8In this section, we present an analysis of model efficiency measured by training time and GPU memory usage\. We tested on theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset with a batch size of 1\. A single NVIDIA RTX A6000 GPU, with default configuration, was used for all experiments\. The outcomes are reported in Table[12](https://arxiv.org/html/2610.26952#S5.T12), which includes the Training Time \(in seconds\), GPU Memory usage \(in MB\), and F1\-score for each model\.

As shown in the table, our model achieves a significant F1\-score gain over the previous method \(SOIRP\), albeit with increased memory usage and somewhat extended training time\. Specifically, Ours takes 7113 seconds per epoch to train, occupying 5180 MB of GPU memory, and achieves an F1\-score of 68\.6\. This performance surpasses that of SOIRP, which has an F1\-score of 67\.5, although it requires less memory \(4278 MB\) and takes slightly less time \(6738 seconds\)\.

Furthermore, we report the outcomes of ablation experiments in which various modules of our framework were removed to examine their effects on efficiency and performance\. Notably, “O​u​r​sw/o​SEP\{Ours\}\_\{w/o\\mathrm\{SEP\}\}” results in a 30% increase in training time compared to our approach\. This indicates that separately encoding relations and sentences not only reduces performance but also significantly increases training time\. While WWI, ERI, and HTI increase both training time and GPU memory usage, they contribute to improved performance\.

Overall, the results highlight the trade\-offs between memory usage, training time, and performance\. While the inclusion of each component of our model increases memory consumption and training time, it leads to improved model performance\. Lower memory usage would likely boost our approach’s performance\.

### 5\.8Case Study

![Refer to caption](https://arxiv.org/html/2610.26952v1/case_study.png)Figure 6:Examples of sentences of the Entire, Partial, and Unseen three triple types from OneRel and our models and the corresponding predictions\. The orange mark indicates an error in the extracted relational triples\. The blue mark indicates that the extracted relational triple is missing\.Figure[6](https://arxiv.org/html/2610.26952#S5.F6)presents a comparison between OneRel and our model across five examples sourced from the WebNLG\-R dataset\. These examples can be divided into three triple types: Entire, Partial, and Unseen\. For the Entire, we selected five sentences containing relational triples \(includingS​O​OSOOandS​E​OSEOpatterns\) to evaluate memory capability\. For the Partial, we chose a long and complex sentence containing one relational triple\. For the Unseen, three short sentences were selected, each containing one relational triple that was unseen during training\.

In the entirely seen examples, our model outperforms OneRel, which fails to predict the relational triple \(Sri Lanka, currency, Sri\) of theS​O​OSOOpattern\. In partially seen examples, OneRel often predicts redundant relational triples prone to inaccuracies due to noise\. In unseen examples, where relational triples are entirely new, OneRel exhibits errors such as insensitivity to unseen entity spans and misjudgment of relation types between entity pairs\.

Our model leverages comprehensive semantic interaction information among multiple objects, whereas OneRel only captures partial semantic information, resulting in inferior predictions\. These observations underscore the effectiveness of integrating multiple semantic interactions for relational triple extraction, enhancing both memory and generalization capabilities\.

### 5\.9Visualization Of Different Model Components

In this visualization, we focus on depicting Word\-Word and Entity\-Relation Interactions, excluding Head\-Tail Interactions\. The Head\-Tail Interaction component transforms the two\-dimensional sentence representation into a one\-dimensional sequential form, integrating the global semantic aspects of the sentence\. One\-dimensional sequence formats are often difficult to visualize\. We gather two sentences from theNYT\\mathrm\{NYT\}\-R\\mathrm\{R\}dataset, which encompass various types of relational triples\. Below is an introduction to these collected sentences:

1\) 1\-th sentence: the sentence states, “Passed away surrounded by her family on Friday, July 22, 2005, in Regina, Saskatchewan, Canada, at age 82”\. It contains five relational triples as: \(Canada, contains, Saskatchewan\), \(Canada, contains, Regina\), \(Canada, administrative, Saskatchewan\), \(Sa\-skatchewan, country, Canada\) and \(Saskatchewan, contains, Regina\)\. Partially seen relational triples include: \(Canada, contains,⋅\\cdot\), \(⋅\\cdot, country, Canada\) and \(Canada, administrative,⋅\\cdot\)\. Entirely seen relational triples are: \(Saskatchewan, contains, Regina\) and \(Canada, contains, Regina\)\. In addition, it incorporates EPO, SEO and SOO overlapping patterns\.

2\) 2\-th sentence: the sentence states, “Albert Scott Crossfield was born in Berkeley, Calif\., on Oct\. 2, 1921”\. It contains one Unseen relational triples as: \(Albert Scott Crossfield, birthplace, Berkeley\), and it does not have any overlapping patterns\.

For visual analysis, each 2D representation\(Me​r,M^e​r∈ℝN×N×drM^\{er\},\\hat\{M\}^\{er\}\\in\\mathbb\{R\}^\{N\\times N\\times d\_\{r\}\}\) is converted into an image\(Me​r,M^e​r∈ℝN×NM^\{er\},\\hat\{M\}^\{er\}\\in\\mathbb\{R\}^\{N\\times N\}\) using a global average pooling operation\. The resulting image functions as a heat map that reveals the semantic plane\. Visualizations of these semantic maps for the two example sentences are provided in Figure[7](https://arxiv.org/html/2610.26952#S5.F7), where color intensity reflects the semantic strength of each element within the plane\.

![Refer to caption](https://arxiv.org/html/2610.26952v1/vis.png)Figure 7:Visualization of different model components for two sentences\.It is noteworthy that following the utilization of Word\-Word Interaction, certain important semantic information exhibits distinct contour features, although there are instances of noise between entities and relations\. For instance, in 1\-th sentence, entities like \(Canada, Canada\), \(Regina, Regina\), and \(Saskatchewan, Saskatchewan\) demonstrate stronger semantic strength\. The semantic relations within entity, Head\-Relation, and Relation\-Tail pairs have also been moderately enhanced\. Consequently, redundant semantic features in Head\-Relation and Relation\-Tail pairs, such as ’nationality,’ ’lived,’ and ’birthplace’ relations, may emerge\. This could be attributed to the insensitivity of word\-to\-word interactions towards specific entity pairs and relations\.

Subsequently, after applying Entity\-Relation interaction, these redundant relational semantic features are attenuated while preserving all pertinent semantic information within the sentence\. For example, in 1\-th sentence, redundant relational semantic features like ’nationality,’ ’lived,’ and ’birthplace,’ which were generated in the previous stage, diminish and disappear\. Meanwhile, the correct entity pairs, head\-relation, and relation\-tail pairs are retained\. This observation is further validated in the case of “Unseen”\. This effectiveness comes from the way semantic information flows between entities and relations, which helps identify and retain useful semantic patterns while cutting down on relation redundancy\.

## 6Conclusion

This paper introduces a multi\-granularity interaction network designed for jointly extracting*entirely seen*,*partially seen*, and*unseen*relational triples\. Our model leverages the semantic interactions of word\-word interaction, entity\-relation interaction and head\-tail interaction\. The word\-word interaction reinforces the semantic features of elements in a 2D sentence encoding, which makes the use of relation and entity information\. The entity\-relation interaction captures long\-distance semantic dependencies between relations and entities, effectively filtering out the semantic features related to redundant relational triples\. The head\-tail interaction enhances the global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps\. By incorporating multiple iterations, the multi\-granularity interaction network is effective to progressively refine the representations of head and tail entities\. After evaluation on two rearranged datasets, the experimental results show clear and consistent improvements over the compared baselines, and establish the capability of our approach in relational triple extraction\. We perform detailed analyses to understand how each model component affects performance and to confirm its importance\. Future research efforts may develop this model into a framework capable of supporting a spectrum of related multi\-objective natural language processing tasks\.

## Limitations

The table\-filling method involves creating a two\-dimensional representation of sentences\. This approach not only effectively captures the semantic structure of the sentence but also allows for visualizing the model’s components, thereby enhancing interpretability\. However, it comes with a computational complexity ofO⁡\(N2\)O\(N^\{2\}\), which is notably larger compared to theO⁡\(N\)O\(N\)complexity of sequence representation\. Consequently, the table\-filling method requires more memory than other approaches, posing a challenge for our specific method\.

## Acknowledgements

The authors thank the anonymous reviewers for their valuable suggestions\. This work is supported by National Key R&D Program of China under Grant No\. 2023YFC3304500 and the Major Science and Technology Projects of Guizhou Province under Grant \[2024\]003\.

## References

- Achiamet al\.\(2023\)J\. Achiam, S\. Adler, S\. Agarwal, L\. Ahmad, I\. Akkaya, F\. L\. Aleman, D\. Almeida, J\. Altenschmidt, S\. Altman, S\. Anadkat,et al\.Gpt\-4 technical report\.arXiv preprint arXiv:2303\.08774\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Agarap \(2018\)A\. AgarapDeep learning using rectified linear units \(relu\)\.arXiv preprint arXiv:1803\.08375\.Cited by:[§3\.2\.2](https://arxiv.org/html/2610.26952#S3.SS2.SSS2.p3.1)\.
- Anet al\.\(2024\)N\. An, L\. Hei, Y\. Jiang, W\. Meng, J\. Hu, B\. Huang, and F\. RenRTF: region\-based table filling method for relational triple extraction\.arXiv preprint arXiv:2404\.19154\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.10.1),[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Baet al\.\(2016\)J\. L\. Ba, J\. R\. Kiros, and G\. E\. HintonLayer normalization\.arXiv preprint arXiv:1607\.06450\.Cited by:[§3\.2\.4](https://arxiv.org/html/2610.26952#S3.SS2.SSS4.p10.1)\.
- Chan and Roth \(2011\)Y\. S\. Chan and D\. RothExploiting syntactico\-semantic structures for relation extraction\.InACL,pp\. 551–560\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1),[§2](https://arxiv.org/html/2610.26952#S2.p1.1)\.
- Chenet al\.\(2024\)Y\. Chen, Y\. Li, and M\. WenA comprehensive but effective sharedependent bidirectional framework for relational triple extraction\.IEEE Access\.Cited by:[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Daiet al\.\(2024\)Q\. Dai, W\. Yang, L\. Wang, F\. Wei, and M\. TuoSOIRP: subject\-object interaction and reasoning path based joint relational triple extraction by table filling\.Neurocomputing580,pp\. 127492\.Cited by:[§3\.2](https://arxiv.org/html/2610.26952#S3.SS2.p4.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.11.1),[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Dinget al\.\(2024\)Z\. Ding, W\. Huang, J\. Liang, D\. Yang, and Y\. XiaoImproving recall of large language models: a model collaboration approach for relational triple extraction\.arXiv preprint arXiv:2404\.09593\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Donget al\.\(2014\)X\. Dong, E\. Gabrilovich, G\. Heitz, W\. Horn, N\. Lao, K\. Murphy, T\. Strohmann, S\. Sun, and W\. ZhangKnowledge vault: a web\-scale approach to probabilistic knowledge fusion\.InKDD,pp\. 601–610\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p1.1)\.
- Dubeyet al\.\(2024\)A\. Dubey, A\. Jauhri, A\. Pandey, A\. Kadian, A\. Al\-Dahle, A\. Letman, A\. Mathur, A\. Schelten, A\. Yang, A\. Fan,et al\.The llama 3 herd of models\.arXiv preprint arXiv:2407\.21783\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Eberts and Ulges \(2020\)M\. Eberts and A\. UlgesSpan\-based joint entity and relation extraction with transformer pre\-training\.InPAIS\-ECAI,pp\. 2006–2013\.Cited by:[§3\.2\.1](https://arxiv.org/html/2610.26952#S3.SS2.SSS1.p1.1)\.
- Gardentet al\.\(2017\)C\. Gardent, A\. Shimorina, S\. Narayan, and L\. Perez\-BeltrachiniCreating training corpora for nlg micro\-planning\.InACL,Cited by:[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p1.1)\.
- Heet al\.\(2023\)L\. He, Z\. Zhang, S\. Su, and Y\. ChenBitCoin: bidirectional tagging and supervised contrastive learning based joint relational triple extraction framework\.arXiv preprint arXiv:2309\.11853\.Cited by:[§2\.1](https://arxiv.org/html/2610.26952#S2.SS1.p1.1),[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Hendrycks and Gimpel \(2016\)D\. Hendrycks and K\. GimpelGaussian error linear units \(gelus\)\.arXiv preprint arXiv:1606\.08415\.Cited by:[§3\.2\.2](https://arxiv.org/html/2610.26952#S3.SS2.SSS2.p10.1)\.
- Huaet al\.\(2015\)W\. Hua, Z\. Wang, H\. Wang, K\. Zheng, and X\. ZhouShort text understanding through lexical\-semantic analysis\.InICDE,pp\. 495–506\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p1.1)\.
- Huanget al\.\(2019\)Z\. Huang, X\. Wang, L\. Huang, C\. Huang, Y\. Wei, and W\. LiuCCNet: criss\-cross attention for semantic segmentation\.InICCV,pp\. 603–612\.Cited by:[§3\.2\.3](https://arxiv.org/html/2610.26952#S3.SS2.SSS3.p2.1),[§3\.2\.3](https://arxiv.org/html/2610.26952#S3.SS2.SSS3.p3.1),[§3\.2\.3](https://arxiv.org/html/2610.26952#S3.SS2.SSS3.p8.1),[§5\.3](https://arxiv.org/html/2610.26952#S5.SS3.p3.1)\.
- Kingma and Ba \(2014\)D\. P\. Kingma and J\. BaAdam: a method for stochastic optimization\.arXiv preprint arXiv:1412\.6980\.Cited by:[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p4.1)\.
- Leeet al\.\(2022\)J\. Lee, M\. Lee, J\. Y\. Yang, and E\. YangDoes it really generalize well on unseen data? systematic evaluation of relational triple extraction methods\.InACL,pp\. 3849–3858\.Cited by:[Table 2](https://arxiv.org/html/2610.26952#S1.T2),[§1](https://arxiv.org/html/2610.26952#S1.p4.1),[§1](https://arxiv.org/html/2610.26952#S1.p5.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p1.1),[§4\.2](https://arxiv.org/html/2610.26952#S4.SS2.p1.1)\.
- Liet al\.\(2021\)X\. Li, X\. Luo, C\. Dong, D\. Yang, B\. Luan, and Z\. HeTDEER: an efficient translating decoding schema for joint extraction of entities and relations\.InEMNLP,pp\. 8055–8064\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1)\.
- Liet al\.\(2022\)Y\. Li, D\. Choi, J\. Chung, N\. Kushman, J\. Schrittwieser, R\. Leblond, T\. Eccles, J\. Keeling, F\. Gimeno, A\. Dal Lago,et al\.Competition\-level code generation with alphacode\.Science378\(6624\),pp\. 1092–1097\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Nayak and Ng \(2020\)T\. Nayak and H\. T\. NgEffective modeling of encoder\-decoder architecture for joint entity and relation extraction\.InAAAI,Vol\.34,pp\. 8528–8535\.Cited by:[§2\.2](https://arxiv.org/html/2610.26952#S2.SS2.p1.1)\.
- Ninget al\.\(2023\)J\. Ning, Z\. Yang, Y\. Sun, Z\. Wang, and H\. LinOD\-rte: a one\-stage object detection framework for relational triple extraction\.InACL,pp\. 11120–11135\.Cited by:[§2](https://arxiv.org/html/2610.26952#S2.p2.1),[§3\.2\.2](https://arxiv.org/html/2610.26952#S3.SS2.SSS2.p2.1),[§3\.2\.5](https://arxiv.org/html/2610.26952#S3.SS2.SSS5.p3.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p2.1)\.
- Renet al\.\(2021\)F\. Ren, L\. Zhang, S\. Yin, X\. Zhao, S\. Liu, B\. Li, and Y\. LiuA novel global feature\-oriented relational triple extraction model based on table filling\.InEMNLP,pp\. 2646–2656\.Cited by:[§3\.2](https://arxiv.org/html/2610.26952#S3.SS2.p4.1)\.
- Renet al\.\(2022\)F\. Ren, L\. Zhang, X\. Zhao, S\. Yin, S\. Liu, and B\. LiA simple but effective bidirectional framework for relational triple extraction\.InWSDM,pp\. 824–832\.Cited by:[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.6.1),[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Riedelet al\.\(2010\)S\. Riedel, L\. Yao, and A\. McCallumModeling relations and their mentions without labeled text\.InECML\-PKDD,pp\. 148–163\.Cited by:[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p1.1)\.
- Shanget al\.\(2022\)Y\. Shang, H\. Huang, and X\. MaoOneRel: joint entity and relation extraction with one module in one step\.InAAAI,Vol\.36,pp\. 11285–11293\.Cited by:[§2\.3](https://arxiv.org/html/2610.26952#S2.SS3.p1.1),[§3\.2\.2](https://arxiv.org/html/2610.26952#S3.SS2.SSS2.p2.1),[§3\.2\.5](https://arxiv.org/html/2610.26952#S3.SS2.SSS5.p3.1),[§3\.2](https://arxiv.org/html/2610.26952#S3.SS2.p4.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.7.1),[§5\.6](https://arxiv.org/html/2610.26952#S5.SS6.p2.1)\.
- Sinhaet al\.\(2015\)A\. Sinha, Z\. Shen, Y\. Song, H\. Ma, D\. Eide, B\. Hsu, and K\. WangAn overview of microsoft academic service \(mas\) and applications\.InWWW,pp\. 243–246\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p1.1)\.
- Suiet al\.\(2023\)D\. Sui, X\. Zeng, Y\. Chen, K\. Liu, and J\. ZhaoJoint entity and relation extraction with set prediction networks\.TNNLS\.Cited by:[§2](https://arxiv.org/html/2610.26952#S2.p2.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p2.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.8.1)\.
- Tanget al\.\(2022\)W\. Tang, B\. Xu, Y\. Zhao, Z\. Mao, Y\. Liu, Y\. Liao, and H\. XieUniRel: unified representation and interaction for joint relational triple extraction\.InEMNLP,pp\. 7087–7099\.Cited by:[§2\.3](https://arxiv.org/html/2610.26952#S2.SS3.p1.1),[§3\.2\.5](https://arxiv.org/html/2610.26952#S3.SS2.SSS5.p3.1),[§3\.2\.5](https://arxiv.org/html/2610.26952#S3.SS2.SSS5.p5.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.9.1)\.
- Team \(2024\)Q\. TeamQwen2\. 5: a party of foundation models\.September\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Wanget al\.\(2020\)Y\. Wang, B\. Yu, Y\. Zhang, T\. Liu, H\. Zhu, and L\. SunTPLinker: single\-stage joint extraction of entities and relations through token pair linking\.InCOLING,pp\. 1572–1582\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p6.1),[§2\.3](https://arxiv.org/html/2610.26952#S2.SS3.p1.1),[§3\.2\.2](https://arxiv.org/html/2610.26952#S3.SS2.SSS2.p2.1),[§3\.2](https://arxiv.org/html/2610.26952#S3.SS2.p4.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.4.1)\.
- Wanget al\.\(2023\)Z\. Wang, C\. Wei, J\. Li, L\. Zhang, and C\. LvCLFM: contrastive learning and filter\-attention mechanism for joint relation extraction\.IJACSA\.Cited by:[§2\.1](https://arxiv.org/html/2610.26952#S2.SS1.p1.1)\.
- Weiet al\.\(2020\)Z\. Wei, J\. Su, Y\. Wang, Y\. Tian, and Y\. ChangA novel cascade binary tagging framework for relational triple extraction\.InACL,pp\. 1476–1488\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1),[§1](https://arxiv.org/html/2610.26952#S1.p6.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.3.1)\.
- Yonaet al\.\(2024\)G\. Yona, R\. Aharoni, and M\. GevaNarrowing the knowledge evaluation gap: open\-domain question answering with multi\-granularity answers\.arXiv preprint arXiv:2401\.04695\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p2.1)\.
- Yuet al\.\(2020\)J\. Yu, B\. Bohnet, and M\. PoesioNamed entity recognition as dependency parsing\.InACL,pp\. 6470–6476\.Cited by:[§3\.2\.5](https://arxiv.org/html/2610.26952#S3.SS2.SSS5.p1.1)\.
- Zelenkoet al\.\(2003\)D\. Zelenko, C\. Aone, and A\. RichardellaKernel methods for relation extraction\.JMLR3\(Feb\),pp\. 1083–1106\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1),[§2](https://arxiv.org/html/2610.26952#S2.p1.1)\.
- Zenget al\.\(2020\)D\. Zeng, H\. Zhang, and Q\. LiuCopyMTL: copy mechanism for joint extraction of entities and relations with multi\-task learning\.InAAAI,Vol\.34,pp\. 9507–9514\.Cited by:[§2\.2](https://arxiv.org/html/2610.26952#S2.SS2.p1.1)\.
- Zenget al\.\(2019\)X\. Zeng, S\. He, D\. Zeng, K\. Liu, S\. Liu, and J\. ZhaoLearning the extraction order of multiple relational facts in a sentence with reinforcement learning\.InEMNLP\-IJCNLP,pp\. 367–377\.Cited by:[§2\.2](https://arxiv.org/html/2610.26952#S2.SS2.p1.1)\.
- Zenget al\.\(2018\)X\. Zeng, D\. Zeng, S\. He, K\. Liu, and J\. ZhaoExtracting relational facts by an end\-to\-end neural model with copy mechanism\.InACL,pp\. 506–514\.Cited by:[§2\.2](https://arxiv.org/html/2610.26952#S2.SS2.p1.1)\.
- Zhanet al\.\(2022\)Y\. Zhan, Z\. Li, X\. Zhao, C\. Zhang, and T\. ChenA simple overlapping relation extraction method based on dropout\.InIJCNN,pp\. 01–08\.Cited by:[§2\.1](https://arxiv.org/html/2610.26952#S2.SS1.p1.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p2.1)\.
- Zhanget al\.\(2023\)J\. Zhang, X\. Jiang, Y\. Sun, and H\. LuoRS\-tts: a novel joint entity and relation extraction model\.InCSCWD,pp\. 71–76\.Cited by:[§2](https://arxiv.org/html/2610.26952#S2.p2.1)\.
- Zhenget al\.\(2021\)H\. Zheng, R\. Wen, X\. Chen, Y\. Yang, Y\. Zhang, Z\. Zhang, N\. Zhang, B\. Qin, M\. Xu, and Y\. ZhengPRGC: potential relation and global correspondence based joint relational triple extraction\.InACL\-IJCNN,pp\. 6225–6235\.Cited by:[§1](https://arxiv.org/html/2610.26952#S1.p3.1),[§1](https://arxiv.org/html/2610.26952#S1.p6.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p2.1),[§4\.1](https://arxiv.org/html/2610.26952#S4.SS1.p3.1),[Table 5](https://arxiv.org/html/2610.26952#S4.T5.4.1.5.1)\.
- Zhouet al\.\(2005\)G\. Zhou, J\. Su, J\. Zhang, and M\. ZhangExploring various knowledge in relation extraction\.InACL,pp\. 427–434\.Cited by:[§2](https://arxiv.org/html/2610.26952#S2.p1.1)\.