This work is licensed under a Creative Commons Attribution 4.0 International License. License details: http://creativecommons.org/licenses/by/4.0/Entity linking (EL), mapping entity mentions in texts to a given knowledge base (KB), serves as a fundamental role in many fields, such as question answering BIBREF0 , semantic search BIBREF1 , and information extraction BIBREF2 , BIBREF3 . However, this task is non-trivial because entity mentions are usually ambiguous. As shown in Figure FIGREF1 , the mention England refers to three entities in KB, and an entity linking system should be capable of identifying the correct entity as England cricket team rather than England and England national football team.Entity linking is typically broken down into two main phases: (i) candidate generation obtains a set of referent entities in KB for each mention, and (ii) named entity disambiguation selects the possible candidate entity by solving a ranking problem. The key challenge lies in the ranking model that computes the relevance between candidates and the corresponding mentions based on the information both in texts and KBs BIBREF4 . In terms of the features used for ranking, we classify existing EL models into two groups: local models to resolve mentions independently relying on textual context information from the surrounding words BIBREF5 , BIBREF6 , BIBREF7 , BIBREF8 , and global (collective) models, which are the main focus of this paper, that encourage the target entities of all mentions in a document to be topically coherent BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12 , BIBREF13 , BIBREF14 .Global models usually build an entity graph based on KBs to capture coherent entities for all identified mentions in a document, where the nodes are entities, and edges denote their relations. The graph provides highly discriminative semantic signals (e.g., entity relatedness) that are unavailable to local model BIBREF15 . For example (Figure FIGREF1 ), an EL model seemly cannot find sufficient disambiguation clues for the mention England from its surrounding words, unless it utilizes the coherence information of consistent topic “cricket" among adjacent mentions England, Hussain, and Essex. Although the global model has achieved significant improvements, its limitation is threefold:To mitigate the first limitation, recent EL studies introduce neural network (NN) models due to its amazing feature abstraction and generalization ability. In such models, words/entities are represented by low dimensional vectors in a continuous space, and features for mention as well as candidate entities are automatically learned from data BIBREF4 . However, existing NN-based methods for EL are either local models BIBREF16 , BIBREF17 or merely use word/entity embeddings for feature extraction and rely on another modules for collective disambiguation, which thus cannot fully utilize the power of NN models for collective EL BIBREF18 , BIBREF19 , BIBREF20 .The second drawback of the global approach has been alleviated through approximate optimization techniques, such as PageRank/random walks BIBREF21 , graph pruning BIBREF22 , ranking SVMs BIBREF23 , or loopy belief propagation (LBP) BIBREF18 , BIBREF24 . However, these methods are not differentiable and thus difficult to be integrated into neural network models (the solution for the first limitation).To overcome the third issue of inadequate training data, BIBREF17 has explored a massive amount of hyperlinks in Wikipedia, but these potential annotations for EL contain much noise, which may distract a naive disambiguation model BIBREF6 .In this paper, we propose a novel Neural Collective Entity Linking model (NCEL), which performs global EL combining deep neural networks with Graph Convolutional Network (GCN) BIBREF25 , BIBREF26 that allows flexible encoding of entity graphs. It integrates both local contextual information and global interdependence of mentions in a document, and is efficiently trainable in an end-to-end fashion. Particularly, we introduce attention mechanism to robustly model local contextual information by selecting informative words and filtering out the noise. On the other hand, we apply GCNs to improve discriminative signals of candidate entities by exploiting the rich structure underlying the correct entities. To alleviate the global computations, we propose to convolute on the subgraph of adjacent mentions. Thus, the overall coherence shall be achieved in a chain-like way via a sliding window over the document. To the best of our knowledge, this is the first effort to develop a unified model for neural collective entity linking.In experiments, we first verify the efficiency of NCEL via theoretically comparing its time complexity with other collective alternatives. Afterwards, we train our neural model using collected Wikipedia hyperlinks instead of dataset-specific annotations, and perform evaluations on five public available benchmarks. The results show that NCEL consistently outperforms various baselines with a favorable generalization ability. Finally, we further present the performance on a challenging dataset WW BIBREF19 as well as qualitative results, investigating the effectiveness of each key module.We denote INLINEFORM0 as a set of entity mentions in a document INLINEFORM1 , where INLINEFORM2 is either a word INLINEFORM3 or a mention INLINEFORM4 . INLINEFORM5 is the entity graph for document INLINEFORM6 derived from the given knowledge base, where INLINEFORM7 is a set of entities, INLINEFORM8 denotes the relatedness between INLINEFORM9 and higher values indicate stronger relations. Based on INLINEFORM10 , we extract a subgraph INLINEFORM11 for INLINEFORM12 , where INLINEFORM13 denotes the set of candidate entities for INLINEFORM14 . Note that we don't include the relations among candidates of the same mention in INLINEFORM15 because these candidates are mutually exclusive in disambiguation.Formally, we define the entity linking problem as follows: Given a set of mentions INLINEFORM0 in a document INLINEFORM1 , and an entity graph INLINEFORM2 , the goal is to find an assignment INLINEFORM3 .To collectively find the best assignment, NCEL aims to improve the discriminability of candidates' local features by using entity relatedness within a document via GCN, which is capable of learning a function of features on the graph through shared parameters over all nodes. Figure FIGREF10 shows the framework of NCEL including three main components:Example As shown in Figure FIGREF10 , for the current mention England, we utilize its surrounding words as local contexts (e.g., surplus), and adjacent mentions (e.g., Hussian) as global information. Collectively, we utilize the candidates of England INLINEFORM0 as well as those entities of its adjacencies INLINEFORM1 to construct feature vectors for INLINEFORM2 and the subgraph of relatedness as inputs of our neural model. Let darker blue indicate higher probability of being predicted, the correct candidate INLINEFORM3 becomes bluer due to its bluer neighbor nodes of other mentions INLINEFORM4 . The dashed lines denote entity relations that have indirect impacts through the sliding adjacent window , and the overall structure shall be achieved via multiple sub-graphs by traversing all mentions.Before introducing our model, we first describe the component of candidate generation.Similar to previous work BIBREF24 , we use the prior probability INLINEFORM0 of entity INLINEFORM1 conditioned on mention INLINEFORM2 both as a local feature and to generate candidate entities: INLINEFORM3 . We compute INLINEFORM4 based on statistics of mention-entity pairs from: (i) Wikipedia page titles, redirect titles and hyperlinks, (ii) the dictionary derived from a large Web Corpus BIBREF27 , and (iii) the YAGO dictionary with a uniform distribution BIBREF22 . We pick up the maximal prior if a mention-entity pair occurs in different resources. In experiments, to optimize for memory and run time, we keep only top INLINEFORM5 entities based on INLINEFORM6 . In the following two sections, we will present the key components of NECL, namely feature extraction and neural network for collective entity linking.The main goal of NCEL is to find a solution for collective entity linking using an end-to-end neural model, rather than to improve the measurements of local textual similarity or global mention/entity relatedness. Therefore, we use joint embeddings of words and entities at sense level BIBREF28 to represent mentions and its contexts for feature extraction. In this section, we give a brief description of our embeddings followed by our features used in the neural model.Following BIBREF28 , we use Wikipedia articles, hyperlinks, and entity outlinks to jointly learn word/mention and entity embeddings in a unified vector space, so that similar words/mentions and entities have similar vectors. To address the ambiguity of words/mentions, BIBREF28 represents each word/mention with multiple vectors, and each vector denotes a sense referring to an entity in KB. The quality of the embeddings is verified on both textual similarity and entity relatedness tasks.Formally, each word/mention has a global embedding INLINEFORM0 , and multiple sense embeddings INLINEFORM1 . Each sense embedding INLINEFORM2 refers to an entity embedding INLINEFORM3 , while the difference between INLINEFORM4 and INLINEFORM5 is that INLINEFORM6 models the co-occurrence information of an entity in texts (via hyperlinks) and INLINEFORM7 encodes the structured entity relations in KBs. More details can be found in the original paper.Local features focus on how compatible the entity is mentioned in a piece of text (i.e., the mention and the context words). Except for the prior probability (Section SECREF9 ), we define two types of local features for each candidate entity INLINEFORM0 :String Similarity Similar to BIBREF16 , we define string based features as follows: the edit distance between mention's surface form and entity title, and boolean features indicating whether they are equivalent, whether the mention is inside, starts with or ends with entity title and vice versa.Compatibility We also measure the compatibility of INLINEFORM0 with the mention's context words INLINEFORM1 by computing their similarities based on joint embeddings: INLINEFORM2 and INLINEFORM3 , where INLINEFORM4 is the context embedding of INLINEFORM5 conditioned on candidate INLINEFORM6 and is defined as the average sum of word global vectors weighted by attentions: INLINEFORM7 where INLINEFORM0 is the INLINEFORM1 -th word's attention from INLINEFORM2 . In this way, we automatically select informative words by assigning higher attention weights, and filter out irrelevant noise through small weights. The attention INLINEFORM3 is computed as follows: INLINEFORM4 where INLINEFORM0 is the similarity measurement, and we use cosine similarity in the presented work. We concatenate the prior probability, string based similarities, compatibility similarities and the embeddings of contexts as well as the entity as the local feature vectors.The key idea of collective EL is to utilize the topical coherence throughout the entire document. The consistency assumption behind it is that: all mentions in a document shall be on the same topic. However, this leads to exhaustive computations if the number of mentions is large. Based on the observation that the consistency attenuates along with the distance between two mentions, we argue that the adjacent mentions might be sufficient for supporting the assumption efficiently.Formally, we define neighbor mentions as INLINEFORM0 adjacent mentions before and after current mention INLINEFORM1 : INLINEFORM2 , where INLINEFORM3 is the pre-defined window size. Thus, the topical coherence at document level shall be achieved in a chain-like way. As shown in Figure FIGREF10 ( INLINEFORM4 ), mentions Hussain and Essex, a cricket player and the cricket club, provide adequate disambiguation clues to induce the underlying topic “cricket" for the current mention England, which impacts positively on identifying the mention surrey as another cricket club via the common neighbor mention Essex.A degraded case happens if INLINEFORM0 is large enough to cover the entire document, and the mentions used for global features become the same as the previous work, such as BIBREF21 . In experiments, we heuristically found a suitable INLINEFORM1 which is much smaller than the total number of mentions. The benefits of efficiency are in two ways: (i) to decrease time complexity, and (ii) to trim the entity graph into a fixed size of subgraph that facilitates computation acceleration through GPUs and batch techniques, which will be discussed in Section SECREF24 .Given neighbor mentions INLINEFORM0 , we extract two types of vectorial global features and structured global features for each candidate INLINEFORM1 :Neighbor Mention Compatibility Suppose neighbor mentions are topical coherent, a candidate entity shall also be compatible with neighbor mentions if it has a high compatibility score with the current mention, otherwise not. That is, we extract the vectorial global features by computing the similarities between INLINEFORM0 and all neighbor mentions: INLINEFORM1 , where INLINEFORM2 is the mention embedding by averaging the global vectors of words in its surface form: INLINEFORM3 , where INLINEFORM4 are tokenized words of mention INLINEFORM5 .Subgraph Structure The above features reflect the consistent semantics in texts (i.e., mentions). We now extract structured global features using the relations in KB, which facilitates the inference among candidates to find the most topical coherent subset. For each document, we obtain the entity graph INLINEFORM0 by taking candidate entities of all mentions INLINEFORM1 as nodes, and using entity embeddings to compute their similarities as edges INLINEFORM2 . Then, we extract the subgraph structured features INLINEFORM3 for each entity INLINEFORM4 for efficiency.Formally, we define the subgraph as: INLINEFORM0 , where INLINEFORM1 . For example (Figure FIGREF1 ), for entity England cricket team, the subgraph contains the relation from it to all candidates of neighbor mentions: England cricket team, Nasser Hussain (rugby union), Nasser Hussain, Essex, Essex County Cricket Club and Essex, New York. To support batch-wise acceleration, we represent INLINEFORM2 in the form of adjacency table based vectors: INLINEFORM3 , where INLINEFORM4 is the number of candidates per mention.Finally, for each candidate INLINEFORM0 , we concatenate local features and neighbor mention compatibility scores as the feature vector INLINEFORM1 , and construct the subgraph structure representation INLINEFORM2 as the inputs of NCEL.NCEL incorporates GCN into a deep neural network to utilize structured graph information for collectively feature abstraction, while differs from conventional GCN in the way of applying the graph. Instead of the entire graph, only a subset of nodes is “visible" to each node in our proposed method, and then the overall structured information shall be reached in a chain-like way. Fixing the size of the subset, NCEL is further speeded up by batch techniques and GPUs, and is efficient to large-scale data.GCNs are a type of neural network model that deals with structured data. It takes a graph as an input and output labels for each node. As a simplification of spectral graph convolutions, the main idea of BIBREF26 is similar to a propagation model: to enhance the features of a node according to its neighbor nodes. The formulation is as follows: INLINEFORM0 where INLINEFORM0 is a normalized adjacent matrix of the input graph with self-connection, INLINEFORM1 and INLINEFORM2 are the hidden states and weights in the INLINEFORM3 -th layer, and INLINEFORM4 is a non-linear activation, such as ReLu.As shown in Figure FIGREF10 , NCEL identifies the correct candidate INLINEFORM0 for the mention INLINEFORM1 by using vectorial features as well as structured relatedness with candidates of neighbor mentions INLINEFORM2 . Given feature vector INLINEFORM3 and subgraph representation INLINEFORM4 of each candidate INLINEFORM5 , we stack them as inputs for mention INLINEFORM6 : INLINEFORM7 , and the adjacent matrix INLINEFORM8 , where INLINEFORM9 denotes the subgraph with self-connection. We normalize INLINEFORM10 such that all rows sum to one, denoted as INLINEFORM11 , avoiding the change in the scale of the feature vectors.Given INLINEFORM0 and INLINEFORM1 , the goal of NCEL is to find the best assignment: INLINEFORM2 where INLINEFORM0 is the output variable of candidates, and INLINEFORM1 is a probability function as follows: INLINEFORM2 where INLINEFORM0 is the score function parameters by INLINEFORM1 . NCEL learns the mapping INLINEFORM2 through a neural network including three main modules: encoder, sub-graph convolution network (sub-GCN) and decoder. Next, we introduce them in turn.Encoder The function of this module is to integrate different features by a multi-layer perceptron (MLP): INLINEFORM0 where INLINEFORM0 is the hidden states of the current mention, INLINEFORM1 and INLINEFORM2 are trainable parameters and bias. We use ReLu as the non-linear activation INLINEFORM3 .Sub-Graph Convolution Network Similar to GCN, this module learns to abstract features from the hidden state of the mention itself as well as its neighbors. Suppose INLINEFORM0 is the hidden states of the neighbor INLINEFORM1 , we stack them to expand the current hidden states of INLINEFORM2 as INLINEFORM3 , such that each row corresponds to that in the subgraph adjacent matrix INLINEFORM4 . We define sub-graph convolution as: INLINEFORM5 where INLINEFORM0 is a trainable parameter.Decoder After INLINEFORM0 iterations of sub-graph convolution, the hidden states integrate both features of INLINEFORM1 and its neighbors. A fully connected decoder maps INLINEFORM2 to the number of candidates as follows: INLINEFORM3 where INLINEFORM0 .The parameters of network are trained to minimize cross-entropy of the predicted and ground truth INLINEFORM0 : INLINEFORM1 Suppose there are INLINEFORM0 documents in training corpus, each document has a set of mentions INLINEFORM1 , leading to totally INLINEFORM2 mention sets. The overall objective function is as follows: INLINEFORM3 To avoid overfitting with some dataset, we train NCEL using collected Wikipedia hyperlinks instead of specific annotated data. We then evaluate the trained model on five different benchmarks to verify the linking precision as well as the generalization ability. Furthermore, we investigate the effectiveness of key modules in NCEL and give qualitative results for comprehensive analysis.We compare NCEL with the following state-of-the-art EL methods including three local models and three types of global models:Local models: He BIBREF29 and Chisholm BIBREF6 beat many global models by using auto-encoders and web links, respectively, and NTEE BIBREF16 achieves the best performance based on joint embeddings of words and entities.Iterative model: AIDA BIBREF22 links entities by iteratively finding a dense subgraph.Loopy Belief Propagation: Globerson BIBREF18 and PBoH BIBREF30 introduce LBP BIBREF31 techniques for collective inference, and Ganea BIBREF24 solves the global training problem via truncated fitting LBP.PageRank/Random Walk: Boosting BIBREF32 , AGDISTISG BIBREF33 , Babelfy BIBREF34 , WAT BIBREF35 , xLisa BIBREF36 and WNED BIBREF19 performs PageRank BIBREF37 or random walk BIBREF38 on the mention-entity graph and use the convergence score for disambiguation.For fairly comparison, we report the original scores of the baselines in the papers. Following these methods, we evaluate NCEL on the following five datasets: (1) CoNLL-YAGO BIBREF22 : the CoNLL 2003 shared task including testa of 4791 mentions in 216 documents, and testb of 4485 mentions in 213 documents. (2) TAC2010 BIBREF39 : constructed for the Text Analysis Conference that comprises 676 mentions in 352 documents for testing. (3) ACE2004 BIBREF23 : a subset of ACE2004 co-reference documents including 248 mentions in 35 documents, which is annotated by Amazon Mechanical Turk. (4) AQUAINT BIBREF40 : 50 news articles including 699 mentions from three different news agencies. (5) WW BIBREF19 : a new benchmark with balanced prior distributions of mentions, leading to a hard case of disambiguation. It has 6374 mentions in 310 documents automatically extracted from Wikipedia.Training We collect 50,000 Wikipedia articles according to the number of its hyperlinks as our training data. For efficiency, we trim the articles to the first three paragraphs leading to 1,035,665 mentions in total. Using CoNLL-Test A as the development set, we evaluate the trained NCEL on the above benchmarks. We set context window to 20, neighbor mention window to 6, and top INLINEFORM0 candidates for each mention. We use two layers with 2000 and 1 hidden units in MLP encoder, and 3 layers in sub-GCN. We use early stop and fine tune the embeddings. With a batch size of 16, nearly 3 epochs cost less than 15 minutes on the server with 20 core CPU and the GeForce GTX 1080Ti GPU with 12Gb memory. We use standard Precision, Recall and F1 at mention level (Micro) and at the document level (Macro) as measurements.Complexity Analysis Compared with local methods, the main disadvantage of collective methods is high complexity and expensive costs. Suppose there are INLINEFORM0 mentions in documents on average, among these global models, NCEL not surprisingly has the lowest time complexity INLINEFORM1 since it only considers adjacent mentions, where INLINEFORM2 is the number of sub-GCN layers indicating the iterations until convergence. AIDA has the highest time complexity INLINEFORM3 in worst case due to exhaustive iteratively finding and sorting the graph. The LBP and PageRank/random walk based methods achieve similar high time complexity of INLINEFORM4 mainly because of the inference on the entire graph.GERBIL BIBREF41 is a benchmark entity annotation framework that aims to provide a unified comparison among different EL methods across datasets including ACE2004, AQUAINT and CoNLL. We compare NCEL with the global models that report the performance on GERBIL.As shown in Table TABREF26 , NCEL achieves the best performance in most cases with an average gain of 2% on Micro F1 and 3% Macro F1. The baseline methods also achieve competitive results on some datasets but fail to adapt to the others. For example, AIDA and xLisa perform quite well on ACE2004 but poorly on other datasets, or WAT, PBoH, and WNED have a favorable performance on CoNLL but lower values on ACE2004 and AQUAINT. Our proposed method performs consistently well on all datasets that demonstrates the good generalization ability.In this section, we investigate the effectiveness of NCEL in the “easy" and “hard" datasets, respectively. Particularly, TAC2010, which has two mentions per document on average (Section SECREF19 ) and high prior probabilities of correct candidates (Figure FIGREF28 ), is regarded as the “easy" case for EL, and WW is the “hard" case since it has the most mentions with balanced prior probabilities BIBREF19 . Besides, we further compare the impact of key modules by removing the following part from NCEL: global features (NCEL-local), attention (NCEL-noatt), embedding features (NCEL-noemb), and the impact of the prior probability (prior).The results are shown in Table FIGREF28 and Table FIGREF28 . We can see the average linking precision (Micro) of WW is lower than that of TAC2010, and NCEL outperforms all baseline methods in both easy and hard cases. In the “easy" case, local models have similar performance with global models since only little global information is available (2 mentions per document). Besides, NN-based models, NTEE and NCEL-local, perform significantly better than others including most global models, demonstrating that the effectiveness of neural models deals with the first limitation in the introduction.Impact of NCEL Modules As shown in Figure FIGREF28 , the prior probability performs quite well in TAC2010 but poorly in WW. Compared with NCEL-local, the global module in NCEL brings more improvements in the “hard" case than that for “easy" dataset, because local features are discriminative enough in most cases of TAC2010, and global information becomes quite helpful when local features cannot handle. That is, our propose collective model is robust and shows a good generalization ability to difficult EL. The improvements by each main module are relatively small in TAC2010, while the modules of attention and embedding features show non-negligible impacts in WW (even worse than local model), mainly because WW contains much noise, and these two modules are effective in improving the robustness to noise and the ability of generalization by selecting informative words and providing more accurate semantics, respectively.The results of example in Figure FIGREF1 are shown in Table TABREF30 , which is from CoNLL testa dataset. For mention Essex, although both NCEL and NCEL-local correctly identify entity Essex County Cricket Club, NCEL outputs higher probability due to the enhancement of neighbor mentions. Moreover, for mention England, NCEL-local cannot find enough disambiguation clues from its context words, such as surplus and requirements, and thus assigns a higher probability of 0.42 to the country England according to the prior probability. Collectively, NCEL correctly identifies England cricket team with a probability of 0.72 as compared with 0.20 in NCEL-local with the help of its neighbor mention Essex.In this paper, we propose a neural model for collective entity linking that is end-to-end trainable. It applies GCN on subgraphs instead of the entire entity graph to efficiently learn features from both local and global information. We design an attention mechanism that endows NCEL robust to noisy data. Trained on collected Wikipedia hyperlinks, NCEL outperforms the state-of-the-art collective methods across five different datasets. Besides, further analysis of the impacts of main modules as well as qualitative results demonstrates its effectiveness.In the future, we will extend our method into cross-lingual settings to help link entities in low-resourced languages by exploiting rich knowledge from high-resourced languages, and deal with NIL entities to facilitate specific applications.The work is supported by National Key Research and Development Program of China (2017YFB1002101), NSFC key project (U1736204, 61661146007), and THUNUS NExT Co-Lab.

Q: Which datasets do they use?

Q: How effective is their NCEL approach overall?

Q: How do they verify generalization ability?
A: By calculating Macro F1 metric at the document level.
by evaluating their model on five different benchmarks

Q: Do they only use adjacent entity mentions or use more than that in some cases (next to adjacent)?
A: NCEL considers only adjacent mentions.
More than that in some cases (next to adjacent)