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A Survey on Knowledge Graphs:Representation, Acquisition and Applications

Shaoxiong Ji, Shirui Pan, Erik Cambria, Senior Member, IEEE,Pekka Marttinen, Philip S. Yu, Fellow, IEEE,

Abstract—Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relationsbetween entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey,we provide a comprehensive review on knowledge graph covering overall research topics about 1) knowledge graph representationlearning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarizerecent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomieson these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding modelsand auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference andlogical rule reasoning are reviewed. We further explore several emerging topics including meta relational learning, commonsensereasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection ofdatasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.

Index Terms—Knowledge graph, representation learning, knowledge graph completion, relation extraction, reasoning.

F

1 INTRODUCTION

INCORPORATING human knowledge is one of the researchdirections of artificial intelligence (AI). Knowledge rep-

resentation and reasoning, inspired by human’s problemsolving, is to represent knowledge for intelligent systems togain the ability to solve complex tasks. Recently, knowledgegraphs as a form of structured human knowledge havedrawn great research attention from both the academia andthe industry. A knowledge graph is a structured representa-tion of facts, consisting of entities, relationships and semanticdescriptions. Entities can be real-world objects and abstractconcepts, relationships represent the relation between entities,and semantic descriptions of entities and their relationshipscontain types and properties with a well-defined meaning.Property graphs or attributed graphs are widely used, inwhich nodes and relations have properties or attributes.

The term of knowledge graph is synonymous withknowledge base with a minor difference. A knowledgegraph can be viewed as a graph when considering itsgraph structure. When it involves formal semantics, itcan be taken as a knowledge base for interpretationand inference over facts. Examples of knowledge baseand knowledge graph are illustrated in Fig. 1. Knowl-edge can be expressed in a factual triple in the form of(head, relation, tail) or (subject, predicate, object) under

• S. Ji is with Aalto University, Finland and The University of Queensland,Australia. E-mail: shaoxiong.ji@aalto.fi

• S. Pan is with Monash University, Australia. E-mail: shirui.pan@monash.edu

• E. Cambria is with Nanyang Technological University, Singapore. E-mail: cambria@ntu.edu.sg

• P. Marttinen is with Aalto University, Finland. E-mail: pekka.marttinen@aalto.fi

• P. S. Yu is with University of Illinois at Chicago, USA. E-mail: psyu@uic.edu

• S. Pan is the corresponding author.

the resource description framework (RDF), for example,(Albert Einstein, WinnerOf, Nobel Prize). It can also be repre-sented as a directed graph with nodes as entities and edges asrelations. For simplicity and following the trend of researchcommunity, this paper uses the terms knowledge graph andknowledge base interchangeably.

(Albert Einstein, BornIn, German Empire)(Albert Einstein, SonOf, Hermann Einstein)

(Albert Einstein, GraduateFrom, University of Zurich)(Albert Einstein, WinnerOf, Nobel Prize in Physics)

(Albert Einstein, ExpertIn, Physics) (Nobel Prize in Physics, AwardIn, Physics)

(The theory of relativity, TheoryOf, Physics)(Albert Einstein, SupervisedBy, Alfred Kleiner)

(Alfred Kleiner, ProfessorOf, University of Zurich)(The theory of relativity, ProposedBy, Albert Einstein)

(Hans Albert Einstein, SonOf, Albert Einstein)

(a) Factual triples in knowl-edge base

Albert Einstein

Nobel Prize in Physics

German Empire

The theory of relativity

Hans Albert Einstein

Physics

Alfred Kleiner

Hermann Einstein

University of Zurich

AwardIn

SonOf

SonOf ProposedBy

TheoryOf

ExpertIn

WinnerOf

SupervisedBy

ProfessorOf

GraduateFromBornIn

(b) Entities and relations inknowledge graph

Fig. 1: An example of knowledge base and knowledge graph

Recent advances in knowledge-graph-based researchfocus on knowledge representation learning (KRL) or knowl-edge graph embedding (KGE) by mapping entities andrelations into low-dimensional vectors while capturing theirsemantic meanings. Specific knowledge acquisition tasksinclude knowledge graph completion (KGC), triple classifica-tion, entity recognition, and relation extraction. Knowledge-aware models benefit from the integration of heterogeneousinformation, rich ontologies and semantics for knowledgerepresentation, and multi-lingual knowledge. Thus, manyreal-world applications such as recommendation systems andquestion answering have been brought about prosperity withthe ability of commonsense understanding and reasoning.Some real-world products, for example, Microsoft’s Satoriand Google’s Knowledge Graph, have shown a strongcapacity to provide more efficient services.

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To have a comprehensive survey of current literatures,this paper focuses on knowledge representation whichenriches graphs with more context, intelligence and se-mantics for knowledge acquisition and knowledge-awareapplications. Our main contributions are summarized asfollows.

• Comprehensive review. We conduct a comprehen-sive review on the origin of knowledge graph andmodern techniques for relational learning on knowl-edge graphs. Major neural architectures of knowledgegraph representation learning and reasoning areintroduced and compared. Moreover, we provide acomplete overview of many applications on differentdomains.

• Full-view categorization and new taxonomies. Afull-view categorization of research on knowledgegraph, together with fine-grained new taxonomies arepresented. Specifically, in the high-level we reviewknowledge graph in three aspects: KRL, knowledgeacquisition, and knowledge-aware application. ForKRL approaches, we further propose fine-grainedtaxonomies into four views including representa-tion space, scoring function, encoding models, andauxiliary information. For knowledge acquisition,KGC is reviewed under embedding-based ranking,relational path reasoning, logical rule reasoning andmeta relational learning; entity-relation acquisitiontasks are divided into entity recognition, typing, dis-ambiguation, and alignment; and relation extractionis discussed according to the neural paradigms.

• Wide coverage on emerging advances. Knowledgegraph has experienced rapid development. This sur-vey provides a wide coverage on emerging topicsincluding transformer-based knowledge encoding,graph neural network (GNN) based knowledge prop-agation, reinforcement learning based path reasoning,and meta relational learning.

• Summary and outlook on future directions. Thissurvey provides a summary on each category andhighlights promising future research directions.

The remainder of this survey is organized as follows:first, an overview of knowledge graphs including history,notations, definitions and categorization is given in Section 2;then, we discuss KRL in Section 3 from four scopes; next, ourreview goes to tasks of knowledge acquisition and temporalknowledge graphs in Section 4 and Section 5; downstreamapplications are introduced in Section 6; finally, we discussfuture research directions, together with a conclusion in theend. Other information, including KRL model training anda collection of knowledge graph datasets and open-sourceimplementations can be found in the appendices.

2 OVERVIEW

2.1 A Brief History of Knowledge BasesKnowledge representation has experienced a long-periodhistory of development in the fields of logic and AI. Theidea of graphical knowledge representation firstly datedback to 1956 as the concept of semantic net proposed byRichens [1], while the symbolic logic knowledge can go

back to the General Problem Solver [2] in 1959. The knowl-edge base is firstly used with knowledge-based systemsfor reasoning and problem solving. MYCIN [3] is one ofthe most famous rule-based expert systems for medicaldiagnosis with a knowledge base of about 600 rules. Later,the community of human knowledge representation sawthe development of frame-based language, rule-based, andhybrid representations. Approximately at the end of thisperiod, the Cyc project1 began, aiming at assembling humanknowledge. Resource description framework (RDF)2 andWeb Ontology Language (OWL)3 were released in turn, andbecame important standards of the Semantic Web4. Then,many open knowledge bases or ontologies were publishedsuch as WordNet, DBpedia, YAGO, and Freebase. Stokmanand Vries [4] proposed a modern idea of structure knowledgein a graph in 1988. However, it was in 2012 that the conceptof knowledge graph gained great popularity since its firstlaunch by Google’s search engine5, where the knowledgefusion framework called Knowledge Vault [5] was proposedto build large-scale knowledge graphs. A brief road map ofknowledge base history is illustrated in Appendix A

2.2 Definitions and NotationsMost efforts have been made to give a definition by de-scribing general semantic representation or essential char-acteristics. However, there is no such wide-accepted formaldefinition. Paulheim [6] defined four criteria for knowledgegraphs. Ehrlinger and Woß [7] analyzed several existingdefinitions and proposed Definition 1 which emphasizes thereasoning engine of knowledge graphs. Wang et al. [8] pro-posed a definition as a multi-relational graph in Definition 2.Following previous literature, we define a knowledge graphas G = {E ,R,F}, where E , R and F are sets of entities,relations and facts, respectively. A fact is denoted as a triple(h, r, t) ∈ F .

Definition 1 (Ehrlinger and Woß [7]). A knowledge graphacquires and integrates information into an ontology andapplies a reasoner to derive new knowledge.

Definition 2 (Wang et al. [8]). A knowledge graph is a multi-relational graph composed of entities and relations which areregarded as nodes and different types of edges, respectively.

Specific notations and their descriptions are listed inTable 1. Details of several mathematical operations areexplained in Appendix B.

2.3 Categorization of Research on Knowledge GraphThis survey provides a comprehensive literature review onthe research of knowledge graphs, namely KRL, knowledgeacquisition, and a wide range of downstream knowledge-aware applications, where many recent advanced deeplearning techniques are integrated. The overall categorizationof the research is illustrated in Fig. 2.

1. http://cyc.com2. Released as W3C recommendation in 1999 available at http://w3.

org/TR/1999/REC-rdf-syntax-19990222.3. http://w3.org/TR/owl-guide4. http://w3.org/standards/semanticweb5. http://blog.google/products/search/

introducing-knowledge-graph-things-not

3

TABLE 1: Notations and descriptions

Notation Description

G A knowledge graphF A set of facts(h, r, t) A triple of head, relation and tail(h, r, t) Embedding of head, relation and tailr ∈ R, e ∈ E Relation set and entity setv ∈ V Vertex in vertice seteG ∈ EG Edge in edge setes, eq, et Source/query/current entityrq Query relation< w1, . . . , wn > Text corpusfr(h, t) Scoring functionσ(·), g(·) Non-linear activation functionMr Mapping matrixM TensorL Loss functionRd d dimensional real-valued spaceCd d dimensional complex spaceHd d dimensional hypercomplex spaceTd d dimensional torus spaceN (u, σ2I) Gaussian distribution〈h, t〉 Hermitian dot productt⊗ r Hamilton producth ◦ t, h� t Hadmard (element-wise) producth ? t Circular correlationconcat(), [h, r] Vectors/matrices concatenationω Convolutional filters∗ Convolution operator

Knowledge Representation Learning is a critical re-search issue of knowledge graph which paves a way for manyknowledge acquisition tasks and downstream applications.We categorize KRL into four aspects of representation space,scoring function, encoding models and auxiliary information,providing a clear workflow for developing a KRL model.Specific ingredients include:

1) representation space in which the relations and entitiesare represented;

2) scoring function for measuring the plausibility offactual triples;

3) encoding models for representing and learning rela-tional interactions;

4) auxiliary information to be incorporated into theembedding methods.

Representation learning includes point-wise space, man-ifold, complex vector space, Gaussian distribution, anddiscrete space. Scoring metrics are generally divided intodistance-based and similarity matching based scoring func-tions. Current research focuses on encoding models includinglinear/bilinear models, factorization, and neural networks.Auxiliary information considers textual, visual and typeinformation.

Knowledge Acquisition tasks are divided into threecategories, i.e., KGC, relation extraction and entity discovery.The first one is for expanding existing knowledge graphs,while the other two discover new knowledge (aka relationsand entities) from text. KGC falls into the following cate-gories: embedding-based ranking, relation path reasoning,rule-based reasoning and meta relational learning. Entitydiscovery includes recognition, disambiguation, typing andalignment. Relation extraction models utilize attention mech-anism, graph convolutional networks (GCNs), adversarial

training, reinforcement learning, deep residual learning, andtransfer learning.

Temporal Knowledge Graphs incorporate temporal in-formation for representation learning. This survey catego-rizes four research fields including temporal embedding,entity dynamics, temporal relational dependency, and tem-poral logical reasoning.

Knowledge-aware Applications include natural lan-guage understanding (NLU), question answering, recommen-dation systems, and miscellaneous real-world tasks, whichinject knowledge to improve representation learning.

Knowledge Graph

Knowledge Representation

Learning

Knowledge-Aware

Applications

Temporal Knowledge

Graph

Knowledge Acquisition

Scoring Function

Encoding Models

Representation Space Question Answering

Dialogue Systems

Natural Language Understanding

Relation Extraction

Entity Discovery

Knowledge Graph Completion

Auxiliary Information

Recommender Systems

Others Applications

- Embedding-based Ranking- Path-based Reasoning- Rule-based Reasoning- Meta Relational Learning- Triple Classification

- Recognition- Typing- Disambiguation- Alignment - Neural Nets

- Attention- GCN- GAN- RL- Others

- Single-fact QA- Multi-hop Reasoning

- Question Generation- Search Engine- Medical Applications- Mental Healthcare- Zero-shot Image Classification- Text Generation- Sentiment Analysis

- Point-wise - Manifold- Complex - Gaussian- Discrete

- Distance- Semantic Matching- Others

- Linear/Bilinear- Factorization- Neural Nets- CNN- RNN- Transformers- GCN

Temporal Embedding

Entity Dynamics

Temporal Relational Dependency

Temporal Logical Reasoning

- Textual - Type - Visual

Fig. 2: Categorization of research on knowledge graphs

2.4 Related SurveysPrevious survey papers on knowledge graphs mainly focuson statistical relational learning [9], knowledge graph re-finement [6], Chinese knowledge graph construction [10],KGE [8] or KRL [11]. The latter two surveys are morerelated to our work. Lin et al. [11] presented KRL in a linearmanner, with a concentration on quantitative analysis. Wanget al. [8] categorized KRL according to scoring functions, andspecifically focused on the type of information utilized inKRL. It provides a general view of current research only fromthe perspective of scoring metric. Our survey goes deeperto the flow of KRL, and provides a full-scaled view fromfour folds including representation space, scoring function,encoding models, and auxiliary information. Besides, ourpaper provides a comprehensive review on knowledgeacquisition and knowledge-aware applications with severalemerging topics such as knowledge-graph-based reasoningand few-shot learning discussed.

3 KNOWLEDGE REPRESENTATION LEARNING

KRL is also known as KGE, multi-relation learning, and statis-tical relational learning in the literature. This section reviewsrecent advances on distributed representation learning withrich semantic information of entities and relations form fourscopes including representation space (representing entitiesand relations, Section 3.1), scoring function (measuring theplausibility of facts, Section 3.2), encoding models (modelingthe semantic interaction of facts, Section 3.3), and auxiliaryinformation (utilizing external information, Section 3.4). Wefurther provide a summary in Section 3.5. The trainingstrategies for KRL models are reviewed in Appendix D.

4

3.1 Representation SpaceThe key issue of representation learning is to learn low-dimensional distributed embedding of entities and relations.Current literature mainly uses real-valued point-wise space(Fig. 3a) including vector, matrix and tensor space, whileother kinds of space such as complex vector space (Fig. 3b),Gaussian space (Fig. 3c), and manifold (Fig. 3d) are utilizedas well.

3.1.1 Point-Wise SpacePoint-wise Euclidean space is widely applied for representingentities and relations, projecting relation embedding invector or matrix space, or capturing relational interactions.TransE [12] represents entities and relations in d-dimensionvector space, i.e., h, t, r ∈ Rd, and makes embeddingsfollow the translational principle h + r ≈ t. To tacklethis problem of insufficiency of a single space for bothentities and relations, TransR [13] then further introducesseparated spaces for entities and relations. The authorsprojected entities (h, t ∈ Rk) into relation (r ∈ Rd) spaceby a projection matrix Mr ∈ Rk×d. NTN [14] models entitiesacross multiple dimensions by a bilinear tensor neural layer.The relational interaction between head and tail hTMt iscaptured as a tensor denoted as M ∈ Rd×d×k.

Many other translational models such as TransH [15] alsouse similar representation space, while semantic matchingmodels use plain vector space (e.g., HolE [16]) and relationalprojection matrix (e.g., ANALOGY [17]). Principles of thesetranslational and semantic matching models are introducedin Section 3.2.1 and 3.2.2, respectively.

3.1.2 Complex Vector SpaceInstead of using a real-valued space, entities and relationsare represented in a complex space, where h, t, r ∈ Cd. Takehead entity as an example, h has a real part Re(h) andan imaginary part Im(h), i.e., h = Re(h) + i Im(h). Com-plEx [18] firstly introduces complex vector space shown inFig. 3b which can capture both symmetric and antisymmetricrelations. Hermitian dot product is used to do compositionfor relation, head and the conjugate of tail. Inspired byEuler’s identity eiθ = cos θ + i sin θ, RotatE [19] proposes arotational model taking relation as a rotation from head entityto tail entity in complex space as t = h ◦ r where ◦ denotesthe element-wise Hadmard product. QuatE [20] extends thecomplex-valued space into hypercomplex h, t, r ∈ Hd bya quaternion Q = a + bi + cj + dk with three imaginarycomponents, where the quaternion inner product, i.e., theHamilton product h⊗ r, is used as compositional operatorfor head entity and relation.

3.1.3 Gaussian DistributionInspired by Gaussian word embedding, the density-basedembedding model KG2E [21] introduces Gaussian distri-bution to deal with the (un)certainties of entities and re-lations. The authors embedded entities and relations intomulti-dimensional Gaussian distribution H ∼ N (µh,Σh)and T ∼ N (µt,Σt). The mean vector u indicates enti-ties and relations’ position, and the covariance matrix Σmodels their (un)certainties. Following the translationalprinciple, the probability distribution of entity transformation

H− T is denoted as Pe ∼ N (µh − µt,Σh + Σt). Similarly,TransG [22] represents entities with Gaussian distributions,while it draws a mixture of Gaussian distribution forrelation embedding, where the m-th component transla-tion vector of relation r is denoted as ur,m = t − h ∼N(ut − uh,

(σ2h + σ2

t

)E).

3.1.4 Manifold and GroupThis section reviews knowledge representation in manifoldspace, Lie group and dihedral group. A manifold is atopological space which could be defined as a set of pointswith neighborhoods by the set theory, while the group isalgebraic structures defined in abstract algebra. Previouspoint-wise modeling is an ill-posed algebraic system wherethe number of scoring equations is far more than the numberof entities and relations. And embeddings are restricted inan overstrict geometric form even in some methods withsubspace projection. To tackle these issues, ManifoldE [23]extends point-wise embedding into manifold-based embed-ding. The authors introduced two settings of manifold-based embedding, i.e., Sphere and Hyperplane. An exampleof a sphere is shown in Fig. 3d. For the sphere setting,Reproducing Kernel Hilbert Space is used to represent themanifold function, i.e.,

M(h, r, t) = ‖ϕ(h) + ϕ(r)− ϕ(t)‖2

= K(h, h) + K(t, t) + K(r, r)

− 2K(h, t)− 2K(r, t) + 2K(r, h),

(1)

where ϕ maps the original space to the Hilbert space, and Kis the kernel function. Another “hyperplane” setting is intro-duced to enhance the model with intersected embeddings,i.e.,

M(h, r, t) = (h + r head )> (t + r tail ) . (2)

TorusE [24] solves the regularization problem of TransEvia embedding in an n-dimensional torus space which is acompact Lie group. With the projection from vector spaceinto torus space defined as π : Rn → Tn, x 7→ [x], entitiesand relations are denoted as [h], [r], [t] ∈ Tn. Similar toTransE, it also learns embeddings following the relationaltranslation in torus space, i.e., [h] + [r] ≈ [t]. Recently,DihEdral [25] proposes dihedral symmetry group preservinga 2-dimensional polygon.

3.2 Scoring FunctionThe scoring function is used to measure the plausibility offacts, which is also referred to the energy function in theenergy-based learning framework. Energy-based learningaims to learn the energy function Eθ(x) parameterized byθ taking x as input, and to make sure positive sampleshave higher scores than negative samples. In this paper, theterm of scoring function is adopted for unification. Thereare two typical types of scoring functions, i.e., distance-based (Fig. 4a) and similarity-based (Fig. 4b) functions, tomeasure the plausibility of a fact. Distance-based scoringfunction measures the plausibility of facts by calculating thedistance between entities, where addictive translation withrelations as h + r ≈ t is widely used. Semantic similaritybased scoring measures the plausibility of facts by semanticmatching, which usually adopts multiplicative formulation,i.e., h>Mr ≈ t>, to transform head entity near the tail in therepresentation space.

5

r 2 Rd

Mr 2 Rd⇥d

cMr 2 Rd⇥d⇥k

(a) Point-wise space

Im(u)

u = a + bi

b 2 Rda 2 Rdu 2 Cd

Re(u)

(b) Complex vector space

−2−1.5

−1−0.5

00.5

11.5

2−2−1.5−1−0.5

00.5

11.5

20

0.2

0.4

P (x1) P (x2)

x1 x2

P

0

0.1

0.2

0.3

P (x1, x2)

(c) Gaussian distribution

0

(Face, HasInstance, *)

0(Clock, HasPart, *)

0

Clock Dial

(d) Manifold space

Fig. 3: An illustration of knowledge representation in different spaces

ht

r distance

(a) Translational distance-based scoring of TransE

h t

r

fr(h, r)

(b) Semantic similarity-based scoring of DistMult

Fig. 4: Illustrations of distance-based and similarity matchingbased scoring functions taking TransE [12] and DistMult [26]as examples.

3.2.1 Distance-based Scoring FunctionAn intuitional distance-based approach is to calculate theEuclidean distance between the relational projection ofentities. Structural Embedding (SE) [27] uses two projectionmatrices and L1 distance to learn structural embedding as

fr(h, t) = ‖Mr,1h−Mr,2t‖L1 . (3)

A more intensively used principle is the translation-basedscoring function that aims to learn embeddings by repre-senting relations as translations from head to tail entities.Bordes et al. [12] proposed TransE by assuming that theadded embedding of h + r should be close to the embeddingof t with the scoring function is defined under L1 or L2

constraints as

fr(h, t) = ‖h + r− t‖L1/L2. (4)

Since that, many variants and extensions of TransE havebeen proposed. For example, TransH [15] projects entitiesand relations into a hyperplane as

fr(h, t) = −∥∥∥(h−w>r hwr

)+ r−

(t−w>r twr

)∥∥∥2

2, (5)

TransR [13] introduces separate projection spaces for entitiesand relations as

fr(h, t) = −‖Mrh + r−Mrt‖22 , (6)

and TransD [28] constructs dynamic mapping matricesMrh = rph

>p + I and Mrt = rpt

>p + I by the projection

vectors hp, tp, rp ∈ Rn, with the scoring function as

fr(h, t) = −∥∥∥(rph

>p + I

)h + r−

(rpt>p + I

)t∥∥∥2

2. (7)

By replacing Euclidean distance, TransA [29] uses Maha-lanobis distance to enable more adaptive metric learning,with the scoring function defined as

fr(h, t) = (|h + r− t|)>Wr(|h + r− t|). (8)

Previous methods used additive score functions, TransF [30]relaxes the strict translation and uses dot product asfr(h, t) = (h + r)>t. To balance the constraints on headand tail, a flexible translation scoring function is furtherdefined as

fr(h, t) = (h + r)>t + h>(t− r). (9)

Recently, ITransF [31] enables hidden concepts discoveryand statistical strength transferring by learning associationsbetween relations and concepts via sparse attention vectors.TransAt [32] integrates relation attention mechanism withtranslational embedding, and TransMS [33] transmits multi-directional semantics with nonlinear functions and linearbias vectors, with the scoring function as

fr(h, t) = ‖− tanh(t◦r)◦h+r− tanh(h◦r)◦t+α · (h◦t)‖`1/2 .(10)

KG2E [21] in Gaussian space and ManifoldE [23] withmanifold also use the translational distance-based scoringfunction. KG2E uses two scoring methods, i.e, asymmetricKL-divergence as

fr(h, t) =

∫x∈Rke

N (x;µr,Σr) logN (x;µe,Σe)

N (x;µr,Σr)dx, (11)

and symmetric expected likelihood as

fr(h, t) = log

∫x∈Rke

N (x;µe,Σe)N (x;µr,Σr) dx. (12)

While the scoring function of ManifoldE is defined as

fr(h, t) =∥∥M(h, r, t)−D2

r

∥∥2, (13)

where M is the manifold function, and Dr is a relation-specific manifold parameter.

3.2.2 Semantic MatchingAnother direction is to calculate the semantic similarity.SME [34] proposes to semantically match separate combina-tions of entity-relation pairs of (h, r) and (r, t). Its scoringfunction is defined with two versions of matching blocks -linear and bilinear block, i.e.,

fr(h, t) = gleft(h, r)>gright(r, t). (14)

6

The linear matching block is defined as gleft(h, t) = Ml,1h>+

Ml,2r>+b>l , and the bilinear form is gleft(h, r) = (Ml,1h) ◦

(Ml,2r)+b>l . By restricting relation matrixMr to be diagonalfor multi-relational representation learning, DistMult [26]proposes a simplified bilinear formulation defined as

fr(h, t) = h> diag(Mr)t. (15)

To capture rich interactions in relational data and com-pute efficiently, HolE [16] introduces circular correlationof embedding, which can be interpreted as compressedtensor product, to learn compositional representations. Bysemantically matching circular correlation with the relationembedding, the scoring function of HolE is defined as

fr(h, t) = r>(h ? t). (16)

By defining a perturbed holographic compositional operatoras p(a, b; c) = (c ◦ a) ? b, where c is a fixed vector,the expanded holographic embedding model HolEx [35]interpolates the HolE and full tensor product method. Givenl vectors c0, · · · , cl−1, the rank-l semantic matching metricof HolEx is defined as

fr(h, t) =

l∑j=0

p (h, r; cj) · t. (17)

It can be viewed as linear concatenation of perturbed HolE.Focusing on multi-relational inference, ANALOGY [17]models analogical structures of relational data. It’s scoringfunction is defined as

fr(h, t) = h>Mrt, (18)

with relation matrix constrained to be normal matrices in lin-ear mapping, i.e., M>

r Mr = MrM>r for analogical inference.

Crossover interactions are introduced by CrossE [36] with aninteraction matrix C ∈ Rnr×d to simulate the bi-directionalinteraction between entity and relation. The relation specificinteraction is obtained by looking up interaction matrix ascr = x>r C. By combining the interactive representationsand matching with tail embedding, the scoring function isdefined as

f(h, r, t) = σ(tanh (cr ◦ h + cr ◦ h ◦ r + b) t>

). (19)

The semantic matching principle can be encoded by neuralnetworks further discussed in Sec. 3.3.

Aforementioned two methods in Sec. 3.1.4 with grouprepresentation also follow the semantic matching principle.The scoring function of TorusE [24] is defined as:

min(x,y)∈([h]+[r])×[t]

‖x− y‖i. (20)

By modeling 2L relations as group elements, the scoringfunction of DihEdral [25] is defined as the summation ofcomponents:

fr(h, t) = h>Rt =

L∑l=1

h(l)>R(l)t(l), (21)

where the relation matrix R is defined in block diagonal formfor R(l) ∈ DK , and entities are embedded in real-valuedspace for h(l) and t(l) ∈ R2.

3.3 Encoding ModelsThis section introduces models that encode the interactionsof entities and relations through specific model architectures,including linear/bilinear models, factorization models, andneural networks. Linear models formulate relations as alinear/bilinear mapping by projecting head entities into arepresentation space close to tail entities. Factorization aimsto decompose relational data into low-rank matrices forrepresentation learning. Neural networks encode relationaldata with non-linear neural activation and more complexnetwork structures. Several neural models are illustrated inFig. 5.

3.3.1 Linear/Bilinear ModelsLinear/bilinear models encode interactions of entities andrelations by applying linear operation as:

gr (h, t) = MTr

(ht

), (22)

or bilinear transformation operations as Eq. 18. Canonicalmethods with linear/bilinear encoding include SE [27],SME [34], DistMult [26], ComplEx [18], and ANALOGY [17].For TransE [12] with L2 regularization, the scoring functioncan be expanded to the form with only linear transformationwith one-dimensional vectors, i.e.,

‖h + r− t‖22 = 2rT (h− t)− 2hT t+ ‖r‖22 + ‖h‖22 + ‖t‖

22 . (23)

Wang et al. [40] studied various bilinear models and evalu-ated their expressiveness and connections by introducing theconcepts of universality and consistency. The authors furthershowed that the ensembles of multiple linear models canimprove the prediction performance through experiments.Recently, to solve the independence embedding issue of en-tity vectors in canonical Polyadia decomposition, SimplE [41]introduces the inverse of relations and calculates the averagecanonical Polyadia score of (h, r, t) and (t, r−1, h) as

fr(h, t) =1

2

(h ◦ rt + t ◦ r′t

), (24)

where r′ is the embedding of inversion relation. Morebilinear models are proposed from a factorization perspectivediscussed in the next section.

3.3.2 Factorization ModelsFactorization methods formulated KRL models as three-way tensor X decomposition. A general principle of tensorfactorization can be denoted as Xhrt ≈ h>Mrt, withthe composition function following the semantic matchingpattern. Nickel et al. [42] proposed the three-way rank-rfactorization RESCAL over each relational slice of knowledgegraph tensor. For k-th relation of m relations, the k-th sliceof X is factorized as

Xk ≈ ARkAT . (25)

The authors further extended it to handle attributes of entitiesefficiently [43]. Jenatton et al. [44] then proposed a bilinearstructured latent factor model (LFM), which extends RESCALby decomposing Rk =

∑di=1α

ki uiv

>i . By introducing three-

way Tucker tensor decomposition, TuckER [45] learns em-bedding by outputting a core tensor and embedding vectorsof entities and relations. Its scoring function is defined as

fr (h, t) =W ×1 h×2 r×3 t, (26)

7

h r t

W W W

tanh

w

(a) MLP

Convolution Features maps

*

hrt

Score

Filters

(b) CNN

···

GCN

Activation

Entity/Relation Embedding

KG

(c) GCN

combine combineRNN unit

e1 e2 e3r1 r2

(d) RSN

Fig. 5: Illustrations of neural encoding models. (a) MLP [5] and (b) CNN [37] input triples into dense layer and convolutionoperation to learn semantic representation, (c) GCN [38] acts as encoder of knowledge graphs to produce entity and relationembeddings. (d) RSN [39] encodes entity-relation sequences and skips relations discriminatively.

where W ∈ Rde×dr×de is the core tensor of Tucker decom-position and ×n denotes the tensor product along the n-thmode.

3.3.3 Neural Networks

Neural networks for encoding semantic matching haveyielded remarkable predictive performance in recent studies.Encoding models with linear/bilinear blocks can also bemodeled using neural networks, for example, SME [34].Representative neural models include multi-layer perceptron(MLP) [5], neural tensor network (NTN) [14], and neuralassociation model (NAM) [46]. Generally, they take entitiesand/or relations into deep neural networks and compute asemantic matching score. MLP [5] (Fig. 5a) encodes entitiesand relations together into a fully-connected layer, and usesa second layer with sigmoid activation for scoring a triple as

fr(h, t) = σ(w> σ(W[h, r, t])), (27)

where W ∈ Rn×3d is the weight matrix and [h, r, t] isa concatenation of three vectors. NTN [14] takes entityembeddings as input associated with a relational tensor andoutputs predictive score in as

fr(h, t) = r>σ(hTMt + Mr,1h + Mr,2t + br), (28)

where br ∈ Rk is bias for relation r, Mr,1 and Mr,2 arerelation-specific weight matrices. It can be regarded asa combination of MLPs and bilinear models. NAM [46]associates the hidden encoding with the embedding of tailentity, and proposes the relational-modulated neural network(RMNN).

3.3.4 Convolutional Neural Networks

CNNs are utilized for learning deep expressive features.ConvE [47] uses 2D convolution over embeddings andmultiple layers of nonlinear features to model the inter-actions between entities and relations by reshaping headentity and relation into 2D matrix, i.e., Mh ∈ Rdw×dh andMr ∈ Rdw×dh for d = dw×dh. Its scoring function is definedas

fr (h, t) = σ (vec (σ ([Mh;Mr] ∗ ω))W) t, (29)

where ω is the convolutional filters and vec is the vectoriza-tion operation reshaping a tensor into a vector. ConvE canexpress semantic information by non-linear feature learningthrough multiple layers. ConvKB [37] adopts CNNs for

encoding the concatenation of entities and relations withoutreshaping (Fig. 5b). Its scoring function is defined as

fr(h, t) = concat (σ ([h, r, t] ∗ ω)) ·w. (30)

The concatenation of a set for feature maps generated byconvolution increases the learning ability of latent features.Compared with ConvE which captures the local relationships,ConvKB keeps the transitional characteristic and showsbetter experimental performance. HypER [48] utilizes hy-pernetwork H for 1D relation-specific convolutional filtergeneration to achieve multi-task knowledge sharing, andmeanwhile simplifies 2D ConvE. It can also be interpreted asa tensor factorization model when taking hypernetwork andweight matrix as tensors.

3.3.5 Recurrent Neural NetworksAforementioned MLP- and CNN-based models learn triple-level representation. To capture long-term relational depen-dency in knowledge graphs, recurrent networks are utilized.Gardner et al. [49] and Neelakantan et al. [50] propose RNN-based model over relation path to learn vector representationwithout and with entity information, respectively. RSN [39](Fig. 5d) designs a recurrent skip mechanism to enhancesemantic representation learning by distinguishing relationsand entities. The relational path as (x1, x2, . . . , xT ) withentities and relations in an alternating order is generated byrandom walk, and it is further used to calculate recurrent hid-den state ht = tanh (Whht−1 + Wxxt + b). The skippingoperation is conducted as

h′t =

{ht xt ∈ ES1ht + S2xt−1 xt ∈ R , (31)

where S1 and S2 are weight matrices.

3.3.6 TransformersTransformer-based models have boosted contextualized textrepresentation learning. To utilize contextual informationin knowledge graphs, CoKE [51] employs transformers toencode edges and path sequences. Similarly, KG-BERT [52]borrows the idea form language model pre-training and takesBidirectional Encoder Representations from Transformer(BERT) as encoder for entities and relations.

3.3.7 Graph Neural NetworksGNNs are introduced for learning connectivity structureunder an encoder-decoder framework. R-GCN [53] proposes

8

relation-specific transformation to model the directed natureof knowledge graphs. Its forward propagation is defined as

x(l+1)i = σ

∑r∈R

∑j∈Nri

1

ci,rW (l)r x

(l)j +W

(l)0 x

(l)i

, (32)

where x(l)i ∈ Rd

(l)

is the hidden state of the i-th entity inl-th layer, Nr

i is a neighbor set of i-th entity within relationr ∈ R, W (l)

r and W (l)0 are the learnable parameter matrices,

and ci,r is normalization such as ci,r = |Nri |. Here, the

GCN [54] acts as a graph encoder. To enable specific tasks,an encoder model still needs to be developed and integratedinto the R-GCN framework. R-GCN takes the neighborhoodof each entity equally. SACN [38] introduces weighted GCN(Fig. 5c), defining the strength of two adjacent nodes with thesame relation type, to capture the structural informationin knowledge graphs by utilizing node structure, nodeattributes, and relation types. The decoder module calledConv-TransE adopts ConvE model as semantic matchingmetric and preserves the translational property. By aligningthe convolutional outputs of entity and relation embeddingswith C kernels to be M (h, r) ∈ RC×d, its scoring functionis defined as

fr(h, t) = g (vec (M (h, r))W ) t. (33)

Nathani et al. [55] introduced graph attention networkswith multi-head attention as encoder to capture multi-hopneighborhood features by inputing the concatenation ofentity and relation embeddings.

3.4 Embedding with Auxiliary Information

To facilitate more effective knowledge representation, multi-modal embedding incorporates external information suchas text descriptions, type constraints, relational paths, andvisual information, with a knowledge graph itself.

3.4.1 Textual Description

Entities in knowledge graphs have textual descriptions de-noted as D =< w1, w2, . . . , wn >, providing supplementarysemantic information. The challenge of KRL with textualdescription is to embed both structured knowledge andunstructured textual information in the same space. Wanget al. [56] proposed two alignment models for aligningentity space and word space by introducing entity namesand Wikipedia anchors. DKRL [57] extends TransE [12]to learn representation directly from entity descriptionsby a convolutional encoder. SSP [58] models the strongcorrelations between triples and textual descriptions byprojecting them in a semantic subspace. Joint loss functionis widely applied when incorporating KGE with textualdescription. Wang et al. [56] used a three-component lossL = LK +LT +LA of knowledge model LK , text model LTand alignment model LA. SSP [58] uses a two-componentobjective function L = Lembed + µLtopic of embedding-specific loss Lembed and topic-specific loss Ltopic withintextual description, traded off by a parameter µ.

3.4.2 Type InformationEntities are represented with hierarchical classes or types,and consequently, relations with semantic types. SSE [59]incorporates semantic categories of entities to embed entitiesbelonging to the same category smoothly in semantic space.TKRL [60] proposes type encoder model for projectionmatrix of entities to capture type hierarchy. Noticing thatsome relations indicate attributes of entities, KR-EAR [61]categorizes relation types into attributes and relations andmodeled the correlations between entity descriptions. Zhanget al. [62] extended existing embedding methods withhierarchical relation structure of relation clusters, relationsand sub-relations.

3.4.3 Visual InformationVisual information (e.g., entity images) can be utilized toenrich KRL. Image-embodied IKRL [63], containing cross-modal structure-based and image-based representation, en-codes images to entity space, and follows the translationprinciple. The cross-modal representations make sure thatstructure-based and image-based representations are in thesame representation space.

There still remains many kinds of auxiliary informationfor KRL such as attributes, relation path and logical rules.Wang et al. [8] gave a detailed review on these information.This paper discusses relation path and logical rules underthe umbrella of KGC in Sec. 4.1.2 and 4.1.4, respectively.

3.5 SummaryKnowledge representation learning is important in theresearch community of knowledge graph . This sectionreviews four folds of KRL with several recent methodssummarized in Table 2 and more in Appendix C. Overall,developing a novel KRL model is to answer the followingfour questions: 1) which representation space to choose; 2)how to measure the plausibility of triples in specific space; 3)what encoding model to modeling relational interaction; 4)whether to utilize auxiliary information.

The most popularly used representation space is Eu-clidean point-based space by embedding entities in vectorspace and modeling interactions via vector, matrix or tensor.Other representation spaces including complex vector space,Gaussian distribution, and manifold space and group arealso studied. Manifold space has an advantage over point-wise Euclidean space by relaxing the point-wise embedding.Gaussian embeddings are able to express the uncertaintiesof entities and relations, and multiple relation semantics.Embedding in complex vector space can model differentrelational connectivity patterns effectively, especially thesymmetry/antisymmetry pattern. The representation spaceplays an important role in encoding the semantic informationof entities and capturing the relational properties. Whendeveloping a representation learning model, appropriate rep-resentation space should be selected and designed carefullyto match the nature of encoding methods and balance theexpressiveness and computational complexity. The scoringfunction with distance-based metric utilizes the translationprinciple, while the semantic matching scoring function em-ploys compositional operators. Encoding models, especiallyneural networks, play a critical role in modeling interactions

9

of entities and relations. The bilinear models also have drawnmuch attention, and some tensor factorization can also beregarded as this family. Other methods incorporate auxiliaryinformation of textual description, relation/entity types, andentity images.

TABLE 2: A summary of recent KRL models. See more inAppendix C.

Model Ent. & Rel. embed. Scoring Function fr(h, t)

RotatE [19] h, t ∈ Cd , r ∈ Cd ‖h ◦ r− t‖TorusE [24] [h], [t] ∈ Tn , [r] ∈ Tn min(x,y)∈([h]+[r])×[t] ‖x− y‖iSimplE [41] h, t ∈ Rd , r, r′ ∈ Rd 1

2

(h ◦ rt + t ◦ r′t

)TuckER [45] h, t ∈ Rde , r ∈ Rdr W ×1 h×2 r×3 t

ITransF [31] h, t ∈ Rd , r ∈ Rd∥∥∥αHr ·D · h + r− αTr ·D · t

∥∥∥`

HolEx [35] h, t ∈ Rd , r ∈ Rd∑lj=0 p (h, r; cj) · t

CrossE [36] h, t ∈ Rd , r ∈ Rd σ(σ (cr ◦ h + cr ◦ h ◦ r + b) t>

)QuatE [20] h, t ∈ Hd , r ∈ Hd h⊗ r

|r| · tSACN [38] h, t ∈ Rd , r ∈ Rd g (vec (M (h, r))W ) t

ConvKB [37] h, t ∈ Rd , r ∈ Rd concat (g ([h, r, t] ∗ ω)) w

ConvE [47] Mh ∈ Rdw×dh , t ∈ Rdσ (vec (σ ([Mh; Mr] ∗ ω)) W) t

Mr ∈ Rdw×dh

DihEdral [25] h(l), t(l) ∈ R2 ∑Ll=1 h(l)>R(l)t(l)

R(l) ∈ DK

4 KNOWLEDGE ACQUISITION

Knowledge acquisition aims to construct knowledge graphsfrom unstructured text, complete an existing knowledgegraph, and discover and recognize entities and relations.Well-constructed and large-scale knowledge graphs can beuseful for many downstream applications and empowerknowledge-aware models with the ability of commonsensereasoning, thereby paving the way for AI. The main tasks ofknowledge acquisition include relation extraction, KGC, andother entity-oriented acquisition tasks such entity recognitionand entity alignment. Most methods formulate KGC andrelation extraction separately. These two tasks, however, canalso be integrated into a unified framework. Han et al. [64]proposed a joint learning framework with mutual attentionfor data fusion between knowledge graphs and text, whichsolves KGC and relation extraction from text. There arealso other tasks related to knowledge acquisition such astriple classification and relation classification. In this section,three-fold knowledge acquisition techniques on KGC, entitydiscovery and relation extraction are reviewed thoroughly.

4.1 Knowledge Graph Completion

Because of the nature of incompleteness of knowledgegraphs, KGC is developed to add new triples to a knowledgegraph. Typical subtasks include link prediction, entity pre-diction and relation prediction. Here gives a task-orienteddefinition as Def. 3.

Definition 3. Given an incomplete knowledge graphG = (E ,R,F), KGC is to infer missing triples T ={(h, r, t)|(h, r, t) /∈ F}.

Preliminary research on KGC focused on learning low-dimensional embedding for triple prediction. In this survey,we term those methods as embedding-based methods. Most of

them, however, failed to capture multi-step relationships.Thus, recent work turns to explore multi-step relation pathsand incorporate logical rules, termed as relation path inferenceand rule-based reasoning, respectively. Triple classification asan associated task of KGC, which evaluates the correctnessof a factual triple, is additionally reviewed in this section.

4.1.1 Embedding-based Models

Taking entity prediction as an example, embedding-basedranking methods as shown in Fig. 6a firstly learn embeddingvectors based on existing triples, and then replace tail entityor head entity with each entity e ∈ E to calculate scoresof all the candidate entities and rank the top k entities.Aforementioned KRL methods (e.g., TransE [12], TransH [15],TransR [13], HolE [16], and R-GCN [53]) and joint learningmethods like DKRL [57] with textual information can beenused for KGC.

Unlike representing inputs and candidates in the unifiedembedding space, ProjE [65] proposes a combined embed-ding by space projection of the known parts of input triples,i.e., (h, r, ?) or (?, r, t), and the candidate entities with thecandidate-entity matrix Wc ∈ Rs×d, where s is the numberof candidate entities. The embedding projection functionincluding a neural combination layer and a output projectionlayer is defined as h(e, r) = g (Wcσ(e⊕ r) + bp), wheree ⊕ r = Dee + Drr + bc is the combination operator ofinput entity-relation pair. Previous embedding methodsdo not differentiate entities and relation prediction, andProjE does not support relation prediction. Based on theseobservations, SENN [66] distinguishes three KGC subtasksexplicitly by introducing a unified neural shared embeddingwith adaptively weighted general loss function to learndifferent latent features. Existing methods rely heavily onexisting connections in knowledge graphs and fail to capturethe evolution of factual knowledge or entities with a fewconnections. ConMask [67] proposes relationship-dependentcontent masking over the entity description to select relevantsnippets of given relations, and CNN-based target fusion tocomplete the knowledge graph with unseen entities. It canonly make prediction when query relations and entities areexplicitly expressed in the text description. Previous methodsare discriminative models which rely on preprepared entitypairs or text corpus. Focusing on medical domain, REM-EDY [68] proposes a generative model called conditionalrelationship variational autoencoder for entity pair discoveryfrom latent space.

composition

score

candidate

queries

(a) Embedding-based Ranking

composition

composition

e1 e2 e3 e4r1 r2 r3

r

(b) Relation paths [50]

Fig. 6: Illustrations of embedding-based ranking and relationpath reasoning.

10

4.1.2 Relation Path ReasoningEmbedding learning of entities and relations has gainedremarkable performance in some benchmarks, but it failsto model complex relation paths. Relation path reasoningturns to leverage path information over the graph structure.Random walk inference has been widely investigated, forexample, the Path-Ranking Algorithm (PRA) [69] choosesrelational path under a combination of path constraints, andconducts maximum-likelihood classification. To improvepath search, Gardner et al. [49] introduced vector spacesimilarity heuristics in random work by incorporating textualcontent, which also relieves the feature sparsity issue in PRA.Neural multi-hop relational path modeling is also studied.Neelakantan et al. [50] developed a RNN model to composethe implications of relational paths by applying composi-tionality recursively (in Fig. 6b). Chain-of-Reasoning [70],a neural attention mechanism to enable multiple reasons,represents logical composition across all relations, entitiesand text. Recently, DIVA [71] proposes a unified variationalinference framework that takes multi-hop reasoning as twosub-steps of path-finding (a prior distribution for underlyingpath inference) and path-reasoning (a likelihood for linkclassification).

4.1.3 RL-based Path FindingDeep reinforcement learning (RL) is introduced for multi-hop reasoning by formulating path-finding between entitypairs as sequential decision making, specifically a Markovdecision process (MDP). The policy-based RL agent learnsto find a step of relation to extend the reasoning paths viathe interaction between the knowledge graph environment,where the policy gradient is utilized for training RL agents.

DeepPath [72] firstly applies RL into relational pathlearning and develops a novel reward function to improveaccuracy, path diversity, and path efficiency. It encodesstates in the continuous space via a translational embeddingmethod, and takes the relation space as its action space.Similarly, MINERVA [73] takes path walking to the correctanswer entity as a sequential optimization problem bymaximizing the expected reward. It excludes the targetanswer entity and provides more capable inference. Insteadof using a binary reward function, Multi-Hop [74] proposesa soft reward mechanism. To enable more effective pathexploration, action dropout is also adopted to mask someoutgoing edges during training. M-Walk [75] applies an RNNcontroller to capture the historical trajectory and uses theMonte Carlo Tree Search (MCTS) for effective path generation.By leveraging text corpus with the sentence bag of currententity denoted as bet , CPL [76] proposes collaborative policylearning for path finding and fact extraction from text.

With source, query and current entity denoted as es,eq and et, and query relation denoted as rq , the MDPenvironment and policy networks of these methods aresummarized in Table 3, where MINERVA, M-Walk and CPLuse binary reward. For the policy networks, DeepPath usesfully-connected network, the extractor of CPL employs CNN,while the rest uses recurrent networks.

4.1.4 Rule-based ReasoningTo better make use of the symbolic nature of knowledge,another research direction of KGC is logical rule learning.

A rule is defined by the head and body in the form ofhead← body. The head is an atom, i.e., a fact with variablesubjects and/or objects, while the body can be a set of atoms.For example, given relations sonOf, hasChild and gender,and entities X and Y , there is a rule in the reverse form oflogic programming as:

(Y,sonOf,X)← (X,hasChild,Y) ∧ (Y,gender,Male) (34)

Logical rules can been extracted by rule mining tools likeAMIE [77]. The recent RLvLR [78] proposes a scalable rulemining approach with efficient rule searching and pruning,and uses the extracted rules for link prediction.

More research attention focuses on injecting logical rulesinto embeddings to improve reasoning, with joint learningor iterative training applied to incorporate first-order logicrules. For example, KALE [79] proposes a unified joint modelwith t-norm fuzzy logical connectives defined for compatibletriples and logical rules embedding. Specifically, three com-positions of logical conjunction, disjunction and negationare defined to compose the truth value of complex formula.Fig. 7a illustrates a simple first-order Horn clause inference.RUGE [80] proposes an iterative model, where soft rulesare utilized for soft label prediction from unlabeled triplesand labeled triples for embedding rectification. IterE [81]proposes an iterative training strategy with three componentsof embedding learning, axiom induction and axiom injection.

The combination of neural and symbolic models has alsoattracted increasing attention to do rule-based reasoning inan end-to-end manner. Neural Theorem Provers (NTP) [82]learns logical rules for multi-hop reasoning which utilizesradial basis function kernel for differentiable computation onvector space. NeuralLP [83] enables gradient-based optimiza-tion to be applicable in the inductive logic programming,where a neural controller system is proposed by integratingattention mechanism and auxiliary memory. pLogicNet [84]proposes probabilistic logic neural networks (Fig. 7b) toleverage first-order logic and learn effective embedding bycombining the advantages of Markov logic networks andKRL methods, while handling the uncertainty of logic rules.ExpressGNN [85] generalizes pLogicNet by tuning graphnetworks and embedding, and achieves more efficient logicalreasoning.

+ +

Logic Connectives

Truth Vaules

(Paris, CaptialOf, France) (Paris, LocatedIn, France)

Logic

Knowledge

(a) KALE [79]

(London,

CityOf, UK)

(Alan Turing,

BornIn,

London)

BornIn ^ CityOf) Nationality

(Alan Turing,

Nationality, UK)

(Alan Turing,

PoliticianOf,

UK)

(Alan Turing,

LiveIn,

UK)

Nation

ality

( LiveIn

Nationality

(PoliticianOf

⇥

p p

p

?

p

⇥?

1.5

ObservedHidden

TrueFalse

To predictWeight

0.2

2.6

1.5

(b) pLogicNet [84]

Fig. 7: Illustrations of logical rule learning.

4.1.5 Meta Relational LearningThe long-tail phenomena exist in the relations of knowledgegraphs. Meanwhile, the real-world scenario of knowledge isdynamic, where unseen triples are usually acquired. The new

11

TABLE 3: Comparison of RL-based path finding for knowledge graph reasoning

Method State st Action at Reward γ Policy Network

DeepPath [72]Global 1 et = eq or −1 et 6= eq

(et, eq − et) {r} Efficiency 1length(p)

Fully-connected network (FCN)

Diversity − 1|F |∑|F |i=1 cos (p,pi)

MINERVA [73] (et, es, rq, eq) {(et, r, v)} I {et = eq} ht = LSTM (ht−1, [at−1; ot])Multi-Hop [74] (et, (es, rq))

{(r′, e′

)|(et, r

′, e′)∈ G

}γ + (1− γ) frq (es, eT ) ht = LSTM (ht−1, at−1)

M-Walk [75] st−1 ∪{at−1, vt, EGvt ,Vvt

} ⋃t EGvt ∪ {STOP} I {et = eq} GRU-RNN + FCN

CPL [76] Reasoner (es, rq, ht) {eG} I {et = eq} ht = LSTM (ht−1, [rt, et])CPL [76] Extractor

(bet , et

) {(r′, e′

)}(et,r′,e′)

∈ bet step-wise delayed from reasoner PCNN-ATT

scenario, called as meta relational learning or few-shot relationallearning, requires models to predict new relational facts withonly a very few samples.

Targeting at the previous two observations, GMatch-ing [86] develops a metric based few-shot learning methodwith entity embeddings and local graph structures. It encodesone-hop neighbors to capture the structural information withR-GCN, and then takes the structural entity embedding formulti-step matching guided by long short-term memory(LSTM) networks to calculate the similarity scores. Meta-KGR [87], an optimization-based meta learning approach,adopts model agnostic meta learning for fast adaptionand reinforcement learning for entity searching and pathreasoning. Inspired by model-based and optimization-basedmeta learning, MetaR [88] transfers relation-specific metainformation from support set to query set, and archivesfast adaption via loss gradient of high-order relationalrepresentation.

4.1.6 Triple Classification

Triple classification is to determine whether facts are correctin testing data, which is typically regarded as a binaryclassification problem. The decision rule is based on thescoring function with a specific threshold. Aforementionedembedding methods could be applied for triple classifica-tion, including translational distance-based methods likeTransH [15] and TransR [13] and semantic matching-basedmethods such as NTN [14], HolE [16] and ANALOGY [17].

Vanilla vector-based embedding methods failed to dealwith 1-to-n relations. Recently, Dong et al. [89] extendedthe embedding space into region-based n-dimensional ballswhere tail region is in head region for 1-to-n relationusing fine-grained type chains, i.e., tree-structure conceptualclusterings. This relaxation of embedding to n-balls turnstriple classification into a geometric containment problem,and improves the performance for entities with long typechains. However, it relies on the type chains of entities, andsuffers from the scalability problem.

4.2 Entity Discovery

This section distinguishes entity-based knowledge acquisi-tion into several fractionized tasks, i.e., entity recognition,entity disambiguation, entity typing, and entity alignment.We term them as entity discovery as they all explore entity-related knowledge under different settings.

4.2.1 Entity Recognition

Entity recognition or named entity recognition (NER), whenit focuses on specifically named entities, is a task that tagsentities in text. Hand-crafted features such as capitalizationpatterns and language-specific resources like gazetteers areapplied in many literatures. Recent work applies sequence-to-sequence neural architectures, for example, LSTM-CNN [90]for learning character-level and word-level features andencoding partial lexicon matches. Lample et al. [91] proposedstacked neural architectures by stacking LSTM layers andCRF layers, i.e., LSTM-CRF (in Fig. 8a) and Stack-LSTM.Recently, MGNER [92] proposes an integrated frameworkwith entity position detection in various granularities andattention-based entity classification for both nested and non-overlapping named entities.

4.2.2 Entity Typing

Entity typing includes coarse and fine-grained types, whilethe latter one uses a tree-structured type category and istypically regarded as multi-class and multi-label classifi-cation. To reduce label noise, PLE [93] focuses on correcttype identification and proposes a partial-label embeddingmodel with a heterogenous graph for the representationof entity mentions, text features and entity types and theirrelationships. To tackle the increasing growth of type setand noisy labels, Ma et al. [94] proposed prototype-drivenlabel embedding with hierarchical information for zero-shotfine-grained named entity typing.

4.2.3 Entity Disambiguation

Entity disambiguation or entity linking is a unified taskwhich links entity mentions to the corresponding entitiesin a knowledge graph. For example, Einstein won NoblePrize in Physics in 1921. The entity mention of “Einstein”should be linked to the entity of Albert Einstein. Thetrendy end-to-end learning approaches have made effortsthrough representation learning of entities and mentions, forexample, DSRM [95] for modeling entity semantic relatednessand EDKate [96] for the joint embedding of entity andtext. Ganea and Hofmann [97] proposed an attentive neuralmodel over local context windows for entity embeddinglearning and differentiable message passing for inferringambiguous entities. By regarding relations between entitiesas latent variables, Le and Titov [98] developed an end-to-end neural architecture with relation-wise and mention-wisenormalization.

12

4.2.4 Entity Alignment

Aforementioned tasks involve with entity discovery fromtext or a single knowledge graph, while entity alignment (EA)aims to fuse knowledge among heterogeneous knowledgegraphs. Given E1 and E2 as two different entity sets of twodifferent knowledge graphs, EA is to find an alignment setA = {(e1, e2) ∈ E1 × E2|e1 ≡ e2}, where entity e1 and entitye2 hold an equivalence relation ≡. In practice, a small set ofalignment seeds (i.e., synonymous entities appear in differentknowledge graphs) is given to start the alignment process asshown in the left box of Fig. 8b.

Embedding-based alignment calculates the similaritybetween embeddings of a pair of entities. IPTransE [99]maps entities into a unified representation space undera joint embedding framework (Fig. 8b) through alignedtranslation as

∥∥∥e1 + r(E1→E2) − e2

∥∥∥, linear transformation as∥∥∥M(E1→E2)e1 − e2

∥∥∥, and parameter sharing as e1 ≡ e2. Tosolve error accumulation in iterative alignment, BootEA [100]proposes a bootstrapping approach in an incremental train-ing manner, together with an editing technique for checkingnewly-labeled alignment.

Additional information of entities is also incorporatedfor refinement, for example, JAPE [101] capturing thecorrelation between cross-lingual attributes, KDCoE [102]embedding multi-lingual entity descriptions via co-training,MultiKE [103] learning multiple views of entity name, rela-tion and attributes, and alignment with character attributeembedding [104].

W1

LSTM

W2

LSTM

W3

LSTM

W4

LSTM

B-PER E-PER S-LOCCRF

(a) Entity recognition withLSTM-CRF [91]

⌘

+

+

'

'

AlignmentSeeds

Newly Aligned

Entity Pairs

KG1

KG2

e1

e2 e3r2

e1

e2

e1

e2

e3

r2

e1

e2

r2

e3

R=1

R( , )

(b) Entity alignment with IP-TransE [99]

Fig. 8: Illustrations of several entity discovery tasks

4.3 Relation Extraction

Relation extraction is a key task to build large-scale knowl-edge graphs automatically by extracting unknown relationalfacts from plain text and adding them into knowledgegraphs. Due to the lack of labeled relational data, distantsupervision [105], also referred as weak supervision or selfsupervision, uses heuristic matching to create training databy assuming that sentences containing the same entity men-tions may express the same relation under the supervisionof a relational database. Mintz et al. [106] adopted thedistant supervision for relation classification with textualfeatures including lexical and syntactic features, namedentity tags, and conjunctive features. Traditional methods relyhighly on feature engineering [106], with a recent approachexploring the inner correlation between features [107]. Deepneural networks is changing the representation learning of

knowledge graphs and texts. This section reviews recentadvances of neural relation extraction (NRE) methods, withan overview illustrated in Fig. 9.

Neural Relation Extraction

(Eg. CNNs/RNNs)

Attentive RE

+ Attention

Deep Residual

RE

Adversarial RE

RL-based RE

+ ResNet

+ GAN+ RL

Other Tasks

+ Transfer learning

Auxiliary Information

KGs

+ GCN

Few-ShotRE

+FSL

Fig. 9: An overview of neural relation extraction

4.3.1 Neural Relation ExtractionTrendy neural networks are widely applied to NRE. CNNswith position features of relative distances to entities [108] arefirstly explored for relation classification, and then extendedto relation extraction by multi-window CNN [109] withmultiple sized convolutional filters. Multi-instance learningtakes a bag of sentences as input to predict the relation ofentity pair. PCNN [110] applies the piecewise max poolingover the segments of convolutional representation dividedby entity position. Compared with vanilla CNN [108], PCNNcan more efficiently capture the structural information withinentity pair. MIMLCNN [111] further extends it to multi-label learning with cross-sentence max pooling for featureselection. Side information such as class ties [112] and relationpath [113] is also utilized.

RNNs are also introduced, for example, SDP-LSTM [114]adopts multi-channel LSTM while utilizing the shortestdependency path between entity pair, and Miwa et al. [115]stacks sequential and tree-structure LSTMs based on de-pendency tree. BRCNN [116] combines RNN for capturingsequential dependency with CNN for representing localsemantics using two-channel bidirectional LSTM and CNN.

4.3.2 Attention MechanismMany variants of attention mechanisms are combined withCNNs, for example, word-level attention to capture se-mantic information of words [117] and selective attentionover multiple instances to alleviate the impact of noisyinstances [118]. Other side information is also introduced forenriching semantic representation. APCNN [119] introducesentity description by PCNN and sentence-level attention,while HATT [120] proposes hierarchical selective attentionto capture the relation hierarchy by concatenating attentiverepresentation of each hierarchical layer. Rather than CNN-based sentence encoders, Att-BLSTM [121] proposes word-level attention with BiLSTM.

4.3.3 Graph Convolutional NetworksGCNs are utilized for encoding dependency tree over sen-tences or learning KGEs to leverage relational knowledgefor sentence encoding. C-GCN [122] is a contextualizedGCN model over pruned dependency tree of sentences afterpath-centric pruning. AGGCN [123] also applies GCN overdependency tree, but utilizes multi-head attention for edge

13

selection in a soft weighting manner. Unlike previous twoGCN-based models, Zhang et al., [124] applied GCN forrelation embedding in knowledge graph for sentence-basedrelation extraction. The authors further proposed a coarse-to-fine knowledge-aware attention mechanism for the selectionof informative instance.

4.3.4 Adversarial TrainingAdversarial Training (AT) is applied to add adversarial noiseto word embeddings for CNN- and RNN-based relation ex-traction under the MIML learning setting [125]. DSGAN [126]denoises distantly supervised relation extraction by learninga generator of sentence-level true positive samples and adiscriminator that minimizes the probability of being truepositive of the generator.

4.3.5 Reinforcement LearningRL has been integrated into neural relation extraction recentlyby training instance selector with policy network. Qin etal. [127] proposed to train policy-based RL agent of sententialrelation classifier to redistribute false positive instances intonegative samples to mitigate the effect of noisy data. Theauthors took F1 score as evaluation metric and used F1 scorebased performance change as the reward for policy networks.Similarly, Zeng et al. [128] and Feng et al. [129] proposeddifferent reward strategies. The advantage of RL-based NREis that the relation extractor is model-agnostic. Thus, itcould be easily adapted to any neural architectures foreffective relation extraction. Recently, HRL [130] proposed ahierarchical policy learning framework of high-level relationdetection and low-level entity extraction.

4.3.6 Other AdvancesOther advances of deep learning are also applied for neuralrelation extraction. Noticing that current NRE methodsdo not use very deep networks, Huang and Wang [131]applied deep residual learning to noisy relation extractionand found that 9-layer CNNs have improved performance.Liu et al. [132] proposed to initialize the neural modelby transfer learning from entity classification. The coop-erative CORD [133] ensembles text corpus and knowledgegraph with external logical rules by bidirectional knowledgedistillation and adaptive imitation. TK-MF [134] enrichessentence representation learning by matching sentences andtopic words. The existence of low-frequency relations inknowledge graphs requires few-shot relation classificationwith unseen classes or only a few instances. Gao et al. [135]proposed hybrid attention-based prototypical networks tocompute prototypical relation embedding and compare itsdistance between the query embedding.

4.4 SummaryThis section reviews knowledge completion for incompleteknowledge graph and acquisition from plain text.

Knowledge graph completion completes missing links be-tween existing entities or infers entities given entity andrelation queries. Embedding-based KGC methods generallyrely on triple representation learning to capture semantics,and do candidate ranking for completion. Embedding-basedreasoning remains in individual relation level, and is poor at

complex reasoning because it ignores the symbolical natureof knowledge graph, and lack of interpretability. Hybridmethods with symbolics and embedding incorporate rule-based reasoning, overcome the sparsity of knowledge graphto improve the quality of embedding, facilitate efficientrule injection, and induce interpretable rules. With theobservation of graphical nature of knowledge graphs, pathsearch and neural path representation learning are studied,but they suffer from connectivity deficiency when traversesover large-scale graphs. The emerging direction of metarelational learning aims to learn fast adaptation over unseenrelations in low-resource settings.

Entity discovery acquires entity-oriented knowledge fromtext and fuses knowledge between knowledge graphs. Thereare several categories according to specific settings. Entityrecognition is explored in a sequence-to-sequence manner,entity typing discusses noisy type labels and zero-shot typing,and entity disambiguation and alignment learn unified em-beddings with iterative alignment model proposed to tacklethe issue of limited number of alignment seed. But it may facethe error accumulation problems if newly-aligned entitiessuffer from poor performance. Language-specific knowledgehas increased recent years, and consequentially motivatesthe research on cross-lingual knowledge alignment.

Relation extraction suffers from noisy patterns underthe assumption of distant supervision, especially in textcorpus of different domains. Thus, it is important for weaklysupervised relation extraction to mitigate the impact of noisylabeling, for example, multi-instance learning taking bags ofsentences as inputs, attention mechanism [118] for soft selec-tion over instances to reduce noisy patterns, and RL-basedmethods formulating instance selection as hard decision.Another principle is to learn richer representation as possible.As deep neural networks can solve error propagation intraditional feature extraction methods, this field is dominatedby DNN-based models as summarized in Table 4.

5 TEMPORAL KNOWLEDGE GRAPH

Current knowledge graph research mostly focuses on staticknowledge graphs where facts are not changed with time,while the temporal dynamics of a knowledge graph is lessexplored. However, the temporal information is of greatimportance because the structured knowledge only holdswithin a specific period, and the evolution of facts followsa time sequence. Recent research begins to take temporalinformation into KRL and KGC, which is termed as temporalknowledge graph in contrast to the previous static knowledgegraph. Research efforts have been made for learning temporaland relational embedding simultaneously.

5.1 Temporal Information EmbeddingTemporal information is considered in temporal awareembedding by extending triples into temporal quadrupleas (h, r, t, τ), where τ provides additional temporal infor-mation about when the fact held. Leblay and Chekol [136]investigated temporal scope prediction over time-annotatedtriple, and simply extended existing embedding methods,for example, TransE with the vector-based TTransE definedas

fτ (h, r, t) = −‖h + r + τ − t‖L1/2. (35)

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TABLE 4: A summary of neural relation extraction and recent advances

Category Method Mechanism Auxiliary Information

CNNs

O-CNN [108] CNN + max pooling position embeddingMulti CNN [109] Multi-window convolution + max pooling position embeddingPCNN [110] CNN + piecewise max pooling position embeddingMIMLCNN [111] CNN + piecewise and cross-sentence max pooling position embeddingYe et al. [112] CNN/PCNN + pairwise ranking position embedding, class tiesZeng et al. [113] CNN + max pooling position embedding, relation path

RNNsSDP-LSTM [114] Multichannel LSTM + dropout dependency tree, POS, GR, hypernymsLSTM-RNN [115] Bi-LSTM + Bi-TreeLSTM POS, dependency treeBRCNN [116] Two-channel LSTM + CNN + max pooling dependency tree, POS, NER

Attention

Attention-CNN [117] CNN + word-level attention + max pooling POS, position embeddingLin et al. [118] CNN/PCNN + selective attention + max pooling position embeddingAtt-BLSTM [121] Bi-LSTM + word-level attention position indicatorAPCNN [119] PCNN + sentence-level attention entity descriptionsHATT [120] CNN/PCNN + hierarchical attention position embedding, relation hierarchy

GCNsC-GCN [122] LSTM + GCN + path-centric pruning dependency treeKATT [124] Pre-training + GCN + CNN + attention position embedding, relation hierarchyAGGCN [123] GCN + multi-head attention + dense layers dependency tree

Adversarial Wu et al. [125] AT + PCNN/RNN + selective attention indicator encodingDSGAN [126] GAN + PCNN/CNN + attention position embedding

RL

Qin et al. [127] Policy gradient + CNN + performance change reward position embeddingZeng et al. [128] Policy gradient + CNN + +1/-1 bag-result reward position embeddingFeng et al. [129] Policy gradient + CNN + predictive probability reward position embeddingHRL [130] Hierarchical policy learning + Bi-LSTM + MLP relation indicator

Others

ResCNN-x [131] Residual convolution block + max pooling position embeddingLiu et al. [132] Transfer learning + sub-tree parse + attention position embeddingCORD [133] BiGRU + hierarchical attention + cooperative module position embedding, logic rulesTK-MF [134] Topic modeling + multi-head self attention position embedding, topic wordsHATT-Proto [135] Prototypical networks + CNN + hybrid attention position embedding

Temporally scoped quadruple extends triples by adding atime scope [τs, τe], where τs and τe stand for the beginningand ending of the valid period of a triple, and then a staticsubgraph Gτ can be derived from the dynamic knowledgegraph when given a specific timestamp τ . HyTE [137] takesa time stamp as a hyperplane wτ and projects entity andrelation representation as Pτ (h) = h−

(w>τ h

)wτ , Pτ (t) =

t−(w>τ t

)wτ , and Pτ (r) = r−

(w>τ r

)wτ . The temporally

projected scoring function is calculated as

fτ (h, r, t) = ‖Pτ (h) + Pτ (r)− Pτ (t)‖L1/L2(36)

within the projected translation of Pτ (h) + Pτ (r) ≈ Pτ (t).Garcıa-Duran et al. [138] concatenated predicate tokensequence and temporal token sequence, and used LSTMto encode the concatenated time-aware predicate sequences.The last hidden state of LSTM is taken as temporal-awarerelational embedding rtemp. The scoring function of extendedTransE and DistMult are calculated as ‖h + rtemp − t‖2 and(h ◦ t) rTtemp, respectively. By defining the context of an entitye as an aggregate set of facts containing e, Liu et al. [139]proposed context selection to capture useful contexts, andmeasured temporal consistency with selected context.

5.2 Entity DynamicsReal-world events change entities’ state, and consequently,affect the corresponding relations. To improve temporalscope inference, the contextual temporal profile model [140]formulates the temporal scoping problem as state changedetection, and utilizes the context to learn state and statechange vectors. Know-evolve [141], a deep evolutionaryknowledge network, investigates the knowledge evolutionphenomenon of entities and their evolved relations. Amultivariate temporal point process is used to model theoccurrence of facts, and a novel recurrent network is de-veloped to learn the representation of non-linear temporal

evolution. To capture the interaction between nodes, RE-NET [142] models event sequences via RNN-based eventencoder and neighborhood aggregator. Specifically, RNNis used to capture the temporal entity interaction, and theconcurrent interactions are aggregated by the neighborhoodaggregator.

5.3 Temporal Relational DependencyThere exists temporal dependencies in relational chainsfollowing the timeline, for example, wasBornIn →graduateFrom → workAt → diedIn. Jiang et al. [143],[144] proposed time-aware embedding, a joint learningframework with temporal regularization, to incorporatetemporal order and consistency information. The authorsdefined a temporal scoring function as

f (〈rk, rl〉) = ‖rkT− rl‖L1/2, (37)

where T ∈ Rd×d is an asymmetric matrix that encodesthe temporal order of relation, for a temporal orderingrelation pair 〈rk, rl〉. Three temporal consistency constraintsof disjointness, ordering, and spans are further applied byinteger linear programming formulation.

5.4 Temporal Logical ReasoningLogical rules are also studied for temporal reasoning. Chekolet al. [145] explored Markov logic network and probabilisticsoft logic for reasoning over uncertain temporal knowledgegraphs. RLvLR-Stream [78] considers temporal close-pathrules and learns the structure of rules from knowledge graphstream for reasoning.

6 KNOWLEDGE-AWARE APPLICATIONS

Rich structured knowledge can be useful for AI applications.But how to integrate such symbolic knowledge into the

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computational framework of real-world applications remainsa challenge. This section introduces several recent DNN-based knowledge-driven approaches with the applicationson NLU, recommendation, and question answering. Moremiscellaneous applications such as digital health and searchengine are introduced in Appendix E.

6.1 Natural Language UnderstandingKnowledge-aware NLU enhances language representationwith structured knowledge injected into a unified semanticspace. Recent knowledge-driven advances utilize explicitfactual knowledge and implicit language representation, withmany NLU tasks explored. Chen et al. [146] proposed double-graph random walks over two knowledge graphs, i.e., a slot-based semantic knowledge graph and a word-based lexicalknowledge graph, to consider inter-slot relations in spo-ken language understanding. Wang et al. [147] augmentedshort text representation learning with knowledge-basedconceptualization by a weighted word-concept embedding.Peng et al. [148] integrated external knowledge base to buildheterogeneous information graph for event categorization inshort social text.

Language modeling as a fundamental NLP task predictsthe next word given preceding words in the given sequence.Traditional language modeling does not exploit factualknowledge with entities frequently observed in the textcorpus. How to integrate knowledge into language repre-sentation has drawn increasing attention. Knowledge graphlanguage model (KGLM) [149] learns to render knowledge byselecting and copying entities. ERNIE-Tsinghua [150] fusesinformative entities via aggregated pre-training and randommasking. BERT-MK [151] encodes graph contextualizedknowledge and focuses on the medical corpus. ERNIE-Baidu [152] introduces named entity masking and phrasemasking to integrate knowledge into language model, and isfurther improved by ERNIE 2.0 [153] via continual multi-tasklearning. Rethinking about large-scale training on languagemodel and querying over knowledge graphs, Petroni etal. [154] conducted an analysis on language model andknowledge base, and found that certain factual knowledgecan be acquired via pre-training language model.

6.2 Question Answeringknowledge-graph-based question answering (KG-QA) an-swers natural language questions with facts from knowledgegraphs. Neural network based approaches represent ques-tions and answers in distributed semantic space, and somealso conduct symbolic knowledge injection for commonsensereasoning.

6.2.1 Single-fact QATaking knowledge graph as an external intellectual source,simple factoid QA or single-fact QA is to answer simplequestion involving with a single knowledge graph fact.Bordes et al. [155] adapted memory network for simplequestion answering, taking knowledge base as externalmemory. Dai et al. [156] proposed a conditional focusedneural network equipped with focused pruning to reduce thesearch space. To generate natural answers in a user-friendlyway, COREAQ [157] introduces copying and retrieving

mechanisms to generate smooth and natural responsesin a seq2seq manner, where an answer is predicted fromthe corpus vocabulary, copied from the given question orretrieved from the knowledge graph. BAMnet [158] modelsthe two-way interaction between questions and knowledgegraph with a bidirectional attention mechanism.

Although deep learning techniques are intensively ap-plied in KG-QA, they inevitably increase the model com-plexity. Through evaluation on simple KG-QA with andwithout neural networks, Mohammed et al. [159] found thatsophisticated deep models such as LSTM and gated recurrentunit (GRU) with heuristics achieve the state of the art, andnon-neural models also gain reasonably well performance.

6.2.2 Multi-hop ReasoningThose neural network based methods gain improvementswith the combination of neural encoder-decoder models, butto deal with complex multi-hop relation requires a morededicated design to be capable of multi-hop commonsensereasoning. Structured knowledge provides informative com-monsense observations and acts as relational inductive biases,which boosts recent studies on commonsense knowledgefusion between symbolic and semantic space for multi-hopreasoning. Bauer et al. [160] proposed multi-hop bidirectionalattention and pointer-generator decoder for effective multi-hop reasoning and coherent answer generation, where exter-nal commonsense knowledge is utilized by relational pathselection from ConceptNet and injection with selectively-gated attention. Variational Reasoning Network (VRN) [161]conducts multi-hop logic reasoning with reasoning-graphembedding, while handles the uncertainty in topic entityrecognition. KagNet [162] performs concept recognitionto build a schema graph from ConceptNet and learnspath-based relational representation via GCN, LSTM andhierarchical path-based attention. CogQA [163] combinesimplicit extraction and explicit reasoning, and proposes acognitive graph model based on BERT and GNN for multi-hop QA.

6.3 Recommender Systems

Recommender systems have been widely explored by col-laborative filtering which makes use of users’ historicalinformation. However, it often fails to solve the sparsity issueand the cold start problem. Integrating knowledge graphsas external information enables recommendation systems tohave the ability of commonsense reasoning.

By injecting knowledge-graph-based side informationsuch as entities, relations, and attributes, many efforts workon embedding-based regularization to improve recommen-dation. The collaborative CKE [164] jointly trains KGEs,item’s textual information and visual content via transla-tional KGE model and stacked auto-encoders. Noticing thattime-sensitive and topic-sensitive news articles consist ofcondensed entities and common knowledge, DKN [165]incorporates knowledge graph by a knowledge-aware CNNmodel with multi-channel word-entity-aligned textual inputs.However, DKN cannot be trained in an end-to-end manneras entity embedding need to be learned in advance. Toenable end-to-end training, MKR [166] associates multi-taskknowledge graph representation and recommendation by

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sharing latent features and modeling high-order item-entityinteraction. While other works consider the relational pathand structure of knowledge graphs, KPRN [167] regardsthe interaction between users and items as entity-relationpath in knowledge graph and conducts preference infer-ence over the path with LSTM to capture the sequentialdependency. PGPR [168] performs reinforcement policy-guided path reasoning over knowledge-graph-based user-item interaction. KGAT [169] applies graph attention networkover the collaborative knowledge graph of entity-relationand user-item graphs to encode high-order connectivities viaembedding propagation and attention-based aggregation.

7 FUTURE DIRECTIONS

Many efforts have been conducted to tackle the challenges ofknowledge representation and its related applications. Butthere still remains several formidable open problems andpromising future directions.

7.1 Complex Reasoning

Numerical computing for knowledge representation andreasoning requires a continuous vector space to capture thesemantic of entities and relations. While embedding-basedmethods have a limitation on complex logical reasoning, twodirections on the relational path and symbolic logic are wor-thy of being further explored. Some promising methods suchas recurrent relational path encoding, GNN-based messagepassing over knowledge graph, and reinforcement learning-based path finding and reasoning are very promising forhandling complex reasoning. For the combination of logicrules and embeddings, recent works [84], [85] combinesMarkov logic networks with KGE, aiming to leveraginglogic rules and handling their uncertainty. Enabling proba-bilistic inference for capturing the uncertainty and domainknowledge with efficiently embedding will be a noteworthyresearch direction.

7.2 Unified Framework

Several knowledge graph representation learning modelshave been verified as equivalence, for example, Hayshiand Shimbo [170] proved that HolE and ComplEx aremathematically equivalent for link prediction with a certainconstraint. ANALOGY [17] provides a unified view ofseveral representative models including DistMult, ComplEx,and HolE. Wang et al. [40] explored connections amongseveral bilinear models. Chandrahas et al. [171] explored thegeometric understanding of additive and multiplicative KRLmodels. Most work formulated knowledge acquisition KGCand relation extraction separately with different models. Hanet al. [64] put them under the same roof and proposed a jointlearning framework with mutual attention for informationsharing between knowledge graph and text. A unifiedunderstanding of knowledge representation and reasoning isless explored. An investigation towards unification in a waysimilar to the unified framework of graph networks [172],however, will be worthy to bridge the research gap.

7.3 InterpretabilityInterpretability of knowledge representation and injection isa key issue for knowledge acquisition and real-world applica-tions. Preliminary efforts have been done for interpretability.ITransF [31] uses sparse vectors for knowledge transferringand interprets with attention visualization. CrossE [36] ex-plores the explanation scheme of knowledge graphs by usingembedding-based path searching to generate explanationsfor link prediction. Recent neural models, however, havelimitations on transparency and interpretability, althoughthey have gained impressive performance. Some methodscombine black-box neural models and symbolic reasoningby incorporating logical rules to increase the interoperability.Interpretability can convince people to trust predictions.Thus, further work should go into interpretability andimprove the reliability of predicted knowledge.

7.4 ScalabilityScalability is crucial in large-scale knowledge graphs. Thereis a trade-off between computational efficiency and modelexpressiveness, with a limited number of works applied tomore than 1 million entities. Several embedding methods usesimplification to reduce the computation cost, for example,simplifying tensor product with circular correlation opera-tion [16]. However, these methods still struggle with scalingto millions of entities and relations.

Probabilistic logic inference such as using Markov logicnetworks is computationally intensive, making it hard to bescalable to large-scale knowledge graphs. Rules in a recentneural logical model [84] are generated by simple brute-force search, making it insufficient on large-scale knowledgegraphs. ExpressGNN [85] attempts to use NeuralLP [83]for efficient rule induction. But there still has a long wayto go to deal with cumbersome deep architectures and theincreasingly growing knowledge graphs.

7.5 Knowledge AggregationThe aggregation of global knowledge is the core ofknowledge-aware applications. For example, recommen-dation systems use knowledge graph to model user-iteminteraction and text classification jointly to encode text andknowledge graph into a semantic space. Most of currentknowledge aggregation methods design neural architecturessuch as attention mechanism and GNNs. The natural lan-guage processing community has been boosted from large-scale pre-training via transformers and variants like BERTmodels, while a recent finding [154] reveals that pre-traininglanguage model on unstructured text can actually acquirecertain factual knowledge. Large-scale pre-training can bea straightforward way for injecting knowledge. However,rethinking the way of knowledge aggregation in an efficientand interpretable manner is also of significance.

7.6 Automatic Construction and DynamicsCurrent knowledge graphs rely highly on manual construc-tion, which is labor-intensive and expensive. The widespreadapplications of knowledge graphs on different cognitiveintelligence fields require automatic knowledge graph con-struction from large-scale unstructured content. Recent re-search mainly works on semi-automatic construction under

17

the supervision of existing knowledge graphs. Facing themultimodality, heterogeneity and large-scale application,automatic construction is still of great challenge.

The mainstream research focuses on static knowledgegraphs, with several work on predicting temporal scopevalidity and learning temporal information and entity dy-namics. Many facts only hold within a specific time period.Considering the temporal nature, dynamic knowledge graphcan address the limitation of traditional knowledge represen-tation and reasoning.

8 CONCLUSION

Knowledge graphs as the ensemble of human knowledgehave attracted increasing research attention, with the recentemergence of knowledge representation learning, knowledgeacquisition methods, and a wide variety of knowledge-awareapplications. The paper conducts a comprehensive surveyon the following four scopes: 1) knowledge graph embed-ding, with a full scale systematic review from embeddingspace, scoring metrics, encoding models, embedding withexternal information, and training strategies; 2) knowledgeacquisition of entity discovery, relation extraction, andgraph completion from three perspectives of embeddinglearning, relational path inference and logical rule reasoning;3) temporal knowledge graph representation learning andcompletion; 4) real-world knowledge-aware applications onnatural language understanding, recommendation systems,question answering and other miscellaneous applications.In addition, some useful resources of datasets and open-source libraries, and future research directions are introducedand discussed. Knowledge graph hosts a large researchcommunity and has a wide range of methodologies andapplications. We conduct this survey to have a summary ofcurrent representative research efforts and trends, and expectit can facilitate future research.

APPENDIX AA BRIEF HISTORY OF KNOWLEDGE BASES

Knowledge bases experienced a development timeline asillustrated in Fig. 10.

APPENDIX BMATHEMATICAL OPERATIONS

Hermitian dot product (Eq. 38) and Hamilton product (Eq. 39)are used in complex vector space (Sec. 3.1.2). Given h and trepresented in complex space Cd, the Hermitian dot product〈, 〉 : Cd × Cd −→ C is calculated as the sesquilinear form of

〈h, t〉 = hTt, (38)

where h = Re(h)− i Im(h) is the conjugate operation overh ∈ Cd. The quaternion extends complex numbers into four-dimensional hypercomplex space. With two d-dimensionalquaternions defined as Q1 = a1 + b1i + c1j + d1k andQ2 = a2 + b2i + c2j + d2k, the Hamilton product ⊗ :Hd ×Hd → Hd is defined as

Q1 ⊗Q2 = (a1 ◦ a2 − b1 ◦ b2 − c1 ◦ c2 − d1 ◦ d2)

+ (a1 ◦ b2 + b1 ◦ a2 + c1 ◦ d2 − d1 ◦ c2) i

+ (a1 ◦ c2 − b1 ◦ d2 + c1 ◦ a2 + d1b2) j

+ (a1 ◦ d2 + b1 ◦ c2 − c1 ◦ b2 + d1 ◦ a2)k.

(39)

The Hadmard product (Eq. 40) and circular correlation(Eq. 41) are utilized in semantic matching based methods(Sec. 3.2.2). Hadmard product, denoted as ◦ or� : Rd×Rd →Rd, is also known as element-wise product or Schur product.

(h ◦ t)i = (h� t)i = (h)i(t)i (40)

Circular correlation ? : Rd × Rd → Rd is an efficientcomputation calcuated as:

[a ? b]k =

d−1∑i=0

aib(k+i) mod d. (41)

APPENDIX CA SUMMARY OF KRL MODELS

We conduct a comprehensive summary on KRL modelsin Table 5. The representation space has an impact on theexpressiveness of KRL methods to some extent. By expand-ing point-wise Euclidean space [12], [14], [16], manifoldspace [23], complex space [18], [19], [20] and Gaussian distri-bution [21], [22] are introduced. ManifoldE [23] relaxes thereal-valued point-wise space into manifold space with moreexpressive representation from the geometric perspective.When M(h, r, t) = ‖h + r − t‖22 and Dr is set to be zero,the manifold collapses into a point. With the introductionof rotational Hadmard product, RotatE [19] can also captureinversion and composition patterns as well as symmetry andantisymmetry. QuatE [20] uses Hamilton product to capturelatent inter-dependency within four-dimensional space ofentities and relations, and gains more expressive rotationalcapability than RotatE. Group theory remains less exploredto capture rich information of relations. The very recentDihEdral [25] firstly introduces the finite non-Abelian groupto preserve the relational properties of symmetry/skew-symmetry, inversion and composition effectively with therotation and reflection properties in the dihedral group. Ebisuand Ichise [24] summarized that the embedding space shouldfollow three conditions, i.e., differentiability, calculationpossibility, and definability of a scoring function.

Distance-based and semantic matching scoring functionsconsist of the foundation stones of plausibility measure inKRL. Translational distance-based methods, especially thegroundbreaking TransE [12], borrowed the idea of distributedword representation learning and inspired many followingapproaches such as TransH [15] and TransR [13] whichspecify complex relations (1-to-N, N-to-1, and N-to-N) andthe recent TransMS [33] which models multi-directionalsemantics. As for the semantic matching side, many methodsutilizes mathematical operations or compositional operatorsincluding linear matching in SME [34], bilinear mapping inDistMult [26], tensor product in NTN [14], circular correlationin HolE [16] and ANALOGY [17], Hadamard product inCrossE [36], and quaternion inner product in QuatE [20].

Recent encoding models for knowledge representationhave developed rapidly, and generally fall into two familiesof bilinear and neural networks. Linear and bilinear modelsuse product-based functions over entities and relations, whilefactorization models regard knowledge graphs as three-waytensors. With the multiplicative operations, RESCAL [42],ComplEx [18], and SimplE [41] also belong to the bilinearmodels. DistMult [26] can only model symmetric relations,

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Fig. 10: A brief history of knowledge bases

General Problem Solver

1959

Expert Systems

1970s

Knowledge Engineering Environment (KEE)

1983

KL-ONEFrame Language

mid 1980s

Semantic Web

2001

Frame-based Languages

mid 1980s

Resource Description Framework (RDF)

1999

Google’s Knowledge Graph

2012

OWL 2 Web Ontology Language

2009

Knowledge Representation Hypothesis

1985

Cyc Project

1984

OWL Web Ontology Language

2004

Semantic Net

1956

while its extension of ComplEx [18] managed to preserveantisymmetric relations, but involves redundant compu-tations [41]. ComplEx [18], SimplE [41], and TuckER [45]can guarantee full expressiveness under specific embeddingdimensionality bounds. Neural network-based encodingmodels start from distributed representation of entities andrelations, and some utilizes complex neural structures such astensor networks [14], graph convolution networks [38], [53],[55], recurrent networks [39] and transformers [51], [52] tolearn richer representation. These deep models have achievedvery competitive results, but they are not transparent, andlack of interpretability. As deep learning techniques aregrowing prosperity and gaining extensive superiority inmany tasks, the recent trend is still likely to focus on morepowerful neural architectures or large-scale pre-training,while interpretable deep models remains a challenge.

APPENDIX DKRL MODEL TRAINING

To train knowledge representation learning models, openworld assumption (OWA) and closed world assumption(CWA) [176] are considered. During training, negative sam-ple set F ′ is randomly generated by corrupting a goldentriple set F under the OWA. Mini-batch optimization andStochastic Gradient Descent (SGD) are carried out to min-imize a certain loss function. Under the OWA, negativesamples are generated with specific sampling strategiesdesigned to reduce the number of false negatives.

D.1 Open and Closed World Assumption

The CWA assumes that unobserved facts are false. Bycontrast, the OWA has a relaxed assumption that unobservedones can be either missing or false. Generally, OWA hasadvantage over CWA because of the incompleteness natureof knowledge graphs. RESCAL [42] is a typical model trainedunder the CWA, while more models are formulated underthe OWA.

D.2 Loss Function

Several families of loss function are introduced for KRLmodel optimization. First, margin-based loss is optimizedto learn representations that positive samples have higherscores than negative ones. Some literature also called it aspairwise ranking loss. As shown in Eq. 42 , the rank-based

hinge loss maximizes the discriminative margin between agolden triple (h, r, t) and an invalid triple (h′, r, t′).

minΘ

∑(h,r,t)∈F

∑(h′,r,t′)∈F′

max(0, fr(h, t) + γ − fr

(h′, t′

))(42)

here γ is a margin. The invalid triple (h′, r, t′) is constructedby randomly changing a head or tail entity or both entitiesin the knowledge graph. Most translation-based embeddingmethods use margin-based loss [177]. The second kind of lossfunction is logistic-based loss in Eq. 43, which is to minimizenegative log-likelihood of logistic models.

minΘ

∑(h,r,t)∈F∪F′

log (1 + exp (−yhrt · fr(h, t))) (43)

here yhrt is the label of triple instance. Some methods alsouse other kinds of loss functions. For example, ConvE andTuckER use binary cross-entropy or the so-called Bernoullinegative log-likelihood loss function defined as:

− 1

Ne

Ne∑i

(yi · log (pi) + (1− yi) · log (1− pi)) , (44)

where p is the prediction and y is the ground label. AndRotatE uses the form of loss function in Eq. 45.

− log σ (γ − fr(h, t))−n∑i=1

1

klog σ

(fr(h′i, t

′i

)− γ)

(45)

For all those kinds of loss functions, specific regularizationlike L2 on parameters or constraints can also be applied, aswell as combined with the joint learning paradigm.

D.3 Negative Sampling

Facing the nature of incompleteness of knowledge graphs,several heuristics of sampling distribution are proposedto corrupt the head or tail entities. The widest appliedone is uniform sampling [12], [13], [34] that uniformlyreplaces entities. But it leads to sampling false negative labels.More effective negative sampling strategies are required tolearn semantic representation and improve the predictiveperformance.

Considering the mapping property of relations, Bernoullisampling [15] introduces a heuristic of sampling distributionas tph

tph+hpt , where tph and hpt denote the average number oftail entities per head entity and the average number of headentities per tail entity respectively. Domain sampling [31]chooses corrupted samples from entities in the same domainor from the whole entity set with a relation-dependent

19

TABLE 5: A comprehensive summary of knowledge representation learning models

Category Model Ent. embed. Rel. embed. Scoring Function fr(h, t)

Complexvector

ComplEx [18] h, t ∈ Cd r ∈ Cd Re(< r,h, t >

)= Re

(∑Kk=1 rkhktk

)RotatE [19] h, t ∈ Cd r ∈ Cd ‖h ◦ r− t‖QuatE [20] h, t ∈ Hd r ∈ Hd h⊗ r

|r| · t

Manifold& Group

ManifoldE [23] h, t ∈ Rd r ∈ Rd∥∥M(h, r, t)−D2

r

∥∥2TorusE [24] [h], [t] ∈ Tn [r] ∈ Tn min(x,y)∈([h]+[r])×[t] ‖x− y‖iDihEdral [25] h(l), t(l) ∈ R2 R(l) ∈ DK

∑Ll=1 h(l)>R(l)t(l)

Gaussian

KG2E [21]

h ∼ N (µh,Σh)r ∼ N (µr,Σr)

∫x∈Rke N (x;µr,Σr) log

N(x;µe,Σe)N(x;µr,Σr)

dxt ∼ N (µt,Σt)

µh,µt ∈ Rdµr ∈ Rd,Σr ∈ Rd×d log

∫x∈Rke N (x;µe,Σe)N (x;µr,Σr) dx

Σh,Σt ∈ Rd×d

TransG [22]h ∼ N

(µh,σ

2hI)

µir ∼ N(µt − µh,

(σ2h + σ2

t

)I) ∑

i πir exp

(−∥∥∥µh+µir−µt

∥∥∥22

σ2h+σ2t

)t ∼ N (µt,Σt) r =

∑i π

irµ

ir ∈ Rd

µh,µt ∈ Rd

Translationaldistance

TransE [12] h, t ∈ Rd r ∈ Rd −‖h + r− t‖1/2TransR [13] h, t ∈ Rd r ∈ Rk,Mr ∈ Rk×d −‖Mrh + r−Mrt‖22TransH [15] h, t ∈ Rd r,wr ∈ Rd −

∥∥∥(h−w>r hwr

)+ r−

(t−w>r twr

)∥∥∥22

TransA [29] h, t ∈ Rd r ∈ Rd,Mr ∈ Rd×d (|h + r− t|)>Wr(|h + r− t|)TransF [30] h, t ∈ Rd r ∈ Rd (h + r)>t + (t− r)>h

ITransF [31] h, t ∈ Rd r ∈ Rd∥∥∥αHr ·D · h + r− αTr ·D · t

∥∥∥`

TransAt [32] h, t ∈ Rd r ∈ Rd Pr (σ (rh) h) + r− Pr (σ (rt) t)

TransD [28] h, t,whwt ∈ Rd r,wr ∈ Rk −∥∥∥(wrw

>h + I

)h + r−

(wrw

>t + I

)t∥∥∥22

TransM [173] h, t ∈ Rd r ∈ Rd −θr‖h + r− t‖1/2TranSparse [174] h, t ∈ Rd

r ∈ Rk,Mr (θr) ∈ Rk×d −‖Mr (θr) h + r−Mr (θr) t‖21/2M1r

(θ1r),M2

r

(θ2r)∈ Rk×d −

∥∥M1r

(θ1r)

h + r−M2r

(θ2r)

t∥∥21/2

Semanticmatching

TATEC [175] h, t ∈ Rd r ∈ Rd,Mr ∈ Rd×d h>Mrt + h>r + t>r + h>Dt

ANALOGY [17] h, t ∈ Rd Mr ∈ Rd×d h>Mrt

CrossE [36] h, t ∈ Rd r ∈ Rd σ(

tanh (cr ◦ h + cr ◦ h ◦ r + b) t>)

SME [34] h, t ∈ Rd r ∈ Rd gleft(h, r)>gright(r, t)

DistMult [26] h, t ∈ Rd r ∈ Rd h> diag(Mr)t

HolE [16] h, t ∈ Rd r ∈ Rd r>(h ? t)

HolEx [35] h, t ∈ Rd r ∈ Rd∑lj=0 p (h, r; cj) · t

SE [27] h, t ∈ Rd M1r,M

2r ∈ Rd×d −

∥∥M1rh−M2

rt∥∥1

SimplE [41] h, t ∈ Rd r, r′ ∈ Rd 12

(h ◦ rt + t ◦ r′t

)RESCAL [42] h, t ∈ Rd Mr ∈ Rd×d h>Mrt

LFM [44] h, t ∈ Rd ur,vr ∈ Rp h>∑di=1 α

riuiv

>i t

TuckER [45] h, t ∈ Rde r ∈ Rdr W ×1 h×2 r×3 t

NeuralNetworks

MLP [5] h, t ∈ Rd r ∈ Rd σ(w> σ(W[h, r, t]))

NAM [46] h, t ∈ Rd r ∈ Rd σ(z(L) · t + B(L+1)r

)ConvE [47] Mh ∈ Rdw×dh , t ∈ Rd Mr ∈ Rdw×dh σ (vec (σ ([Mh; Mr] ∗ ω)) W) t

ConvKB [37] h, t ∈ Rd r ∈ Rd concat (σ ([h, r, t] ∗ ω)) ·wHypER [48] h, t ∈ Rd wr ∈ Rdr σ

(vec(h ∗ vec−1 (wrH)

)W)

t

SACN [38] h, t ∈ Rd r ∈ Rd g (vec (M (h, r))W ) t

NTN [14] h, t ∈ Rdr,br ∈ Rk, M ∈ Rd×d×k

r>σ(hT Mt + Mr,1h + Mr,2t + br

)Mr,1,Mr,2 ∈ Rk×d

probability pr or 1− pr respectively, with the head and taildomain of relation r denoted as MH

r = {h | ∃ t(h, r, t) ∈ P}and MT

r = {t | ∃ h(h, r, t) ∈ P}, and induced relational setdenoted as Nr = {(h, r, t) ∈ P}.

Recently, two adversarial sampling are further proposed.KBGAN [177] introduces adversarial learning for negativesampling, where the generator uses probability-based log-loss embedding models. The probability of generating nega-tive samples p

(h′j , r, t

′j | {(hi, ri, ti)}

)is defined as

exp fG (h′i, r, t′i)∑

j=1 exp fG(h′j , r, t

′j

) , (46)

where fG(h, r, t) is the scoring function of generator. Sim-ilarly, Sun et al. [19] proposed self-adversarial negative

sampling based on self scoring function by sampling negativetriples from the distribution in Eq. 47, where α is thetemperature of sampling.

p(h′j , r, t

′j | {(hi, ri, ti)}

)=

expαf(h′j , r, t

′j

)∑i expαf (h

′i, r, t

′i)

(47)

Negative sampling strategies are summarized in Table 6.Trouillon et al. [18] studied the number of negative samplesgenerated per positive training sample, and found a trade-offbetween accuracy and training time.

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TABLE 6: A summary of negative sampling

Sampling Mechanism Sampling probability

Uniform [34] uniform distribution 1n

Bernoulli [15] mapping property tphtph+hpt

Domain [31] relation-depend domain min

(λ∣∣∣MTr ∣∣∣∣∣∣MHr ∣∣∣|Nr|

, 0.5

)Adversarial [177] generator embedding

exp fG(h′i,r,t′i)∑

j=1 exp fG

(h′j,r,t′

j

)Self-adversarial [19] current embedding

expαf(h′j ,r,t

′j

)∑i expαf(h′i,r,t

′i)

APPENDIX EMORE KNOWLEDGE-AWARE APPLICATIONS

There are also many other applications that utilizeknowledge-driven methods. 1) Question generation focuseson generating natural language questions. Seyler et al. [178]studied quiz-style knowledge question generation by gener-ating a structured triple-pattern query over the knowledgegraph while estimating how difficult the questions are. Butfor verbalizing the question, the authors used a template-based method, which may have a limitation on generatingmore natural expression. 2) Academic search engine helpsresearch to find relevant academic papers. Xiong et al. [179]proposed explicit semantic ranking with knowledge graphembedding to help academic search better understand themeaning of query concepts. 3) Medical applications involvewith domain-specific knowledge graph of medical concepts.Li et al. [180] formulated medical image report generation bythree steps of encoding, retrieval and paraphrasing, wheremedical image is encoded by the abnormality graph. 4)Mental healthcare with knowledge graph facilitates a good un-derstanding of mental conditions and risk factors of mentaldisorders, and is applied to effective prevention of mentalhealth leaded suicide. Gaurs et al. [181] developed a rule-based classifier for knowledge-aware suicide risk assessmentwith a suicide risk severity lexicon incorporating medicalknowledge bases and suicide ontology. 5) Zero-shot imageclassification gets benefits from knowledge graph propagationwith semantic descriptions of classes. Wang et al. [182]proposed a multi-layer GCN to learn zero-shot classifiersusing semantic embeddings of categories and categoricalrelationship. 6) Text generation synthesizes and composescoherent multi-sentence texts. Koncel-Kedziorski et al. [183]studied text generation for information extraction systems,and proposed a graph transforming encoder for graph-to-textgeneration from the knowledge graph. 7) Sentiment analysisintegrated with sentiment-related concepts can better un-derstand people’s opinions and sentiments. SenticNet [184]learns conceptual primitives for sentiment analysis, whichcan also be used as a commonsense knowledge source.To enable sentiment-related information filtering, SenticLSTM [185] injects knowledge concepts to the vanilla LSTM,and designs a knowledge output gate for concept-leveloutput as a complement to the token level.

E.1 Dialogue Systems

QA can also be viewed as a single-turn dialogue system bygenerating the correct answer as response, while dialogue

systems consider conversational sequences and aim to gener-ate fluent responses to enable multi-round conversationsvia semantic augmentation and knowledge graph walk.Liu et al. [186] encoded knowledge to augment semanticrepresentation and generated knowledge aware response byknowledge graph retrieval and graph attention mechanismunder an encoder-decoder framework. DialKG Walker [187]traverses symbolic knowledge graph to learn contextualtransition in dialogue, and predicts entity responses withattentive graph path decoder.

Semantic parsing via formal logical representation isanother direction for dialog systems. By predefining a set ofbase actions, Dialog-to-Action [188] is an encoder-decoderapproach that maps executable logical forms from utterancein conversation, to generate action sequence under thecontrol of a grammar-guided decoder.

APPENDIX FDATASETS AND LIBRARIES

In this section, we introduce and list useful resources ofknowledge graph datasets and open-source libraries.

F.1 DatasetsMany public datasets have been released. We conduct anintroduction and a summary of general, domain-specific,task-specific and temporal datasets.

F.1.1 General DatasetsDatasets with general ontological knowledge include Word-Net [189], Cyc [190], DBpedia [191], YAGO [192], Free-base [193], NELL [194] and Wikidata [195]. It is hard tocompare them within a table as their ontologies are different.Thus, only an informal comparison is illustrated in Table 7,where their volumes kept going after their release.

WordNet, firstly released in 1995, is a lexical databasethat contains about 117,000 synsets. DBpedia is a community-driven dataset extracted from Wikipedia. It contains 103million triples and can be enlarged when interlinked withother open datasets. To solve the problems of low coverageand low quality of single-source ontological knowledge,YAGO utilized the concept information in the category pageof Wikipedia and the hierarchy information of concepts inWordNet to build a multi-source dataset with high coverageand quality. Moreover, it is extendable by other knowledgesources. It is available online with more than 10 millionentities and 120 million facts currently. Freebase, a scalableknowledge base, came up for the storage of the world’sknowledge in 2008. Its current number of triples is 1.9 billion.NELL is built from the Web via an intelligent agent calledNever-Ending Language Learner. It has 2,810,379 beliefswith high confidence by far. Wikidata is a free structuredknowledge base, which is created and maintained by humaneditors to facilitate the management of Wikipedia data. It ismulti-lingual with 358 different language.

The aforementioned datasets are openly published andmaintained by communities or research institutions. Thereare also some commercial datasets. The Cyc knowledge basefrom Cycorp contains about 1.5 million general concepts andmore than 20 million general rules, with an accessible version

21

called OpenCyc deprecated sine 2017. Google knowledgegraph hosts more than 500 million entities and 3.5 billionfacts and relations. Microsoft builds a probabilistic taxonomycalled Probase [196] with 2.7 million concepts.

F.1.2 Domain-Specific Datasets

To solve domain-specific tasks, some knowledge bases onspecific domains are designed and collected. Some notabledomains include life science, health care, and scientificresearch, covering complex domain and relations such ascompounds, diseases and tissues. Examples of domain-specific knowledge graphs are ResearchSpace6, a culturalheritage knowledge graph; UMLS [197], a unified medicallanguage system; GeneOntology7, a gene ontology resource;SNOMED CT8, a commercial clinical terminology; and amedical knowledge graph from Yidu Research9.

F.1.3 Task-Specific Datasets

A popular way for generating task-specific datasets is tosample subsets from large general datasets. Statistics ofseveral datasets for tasks on knowledge graph itself arelisted in Table 8. Notice that WN18 and FB15k suffer fromtest set leakage [47]. For KRL with auxiliary informationand other downstream knowledge-aware applications, textsand images are also collected, for example, WN18-IMG [63]with sampled images and textual relation extraction datasetincluding SemEval 2010 dataset, NYT [198] and Google-RE10. IsaCore [199], an analogical closure of Probase foropinion mining and sentiment analysis, is built by commonknowledge base blending and multi-dimensional scaling.Recently, the FewRel dataset [200] was built to evaluatethe emerging few-shot relation classification task. There arealso more datasets for specific tasks such as cross-lingualDBP15K [101] and DWY100K [100] for entity alignment,multi-view knowledge graphs of YAGO26K-906 and DB111K-174 [201] with instances and ontologies.

Numerous downstream knowledge-aware applicationsalso come up with many datasets, for example, Wiki-Facts [203] for language modeling; SimpleQuestions [155]and LC-QuAD [204] for question answering; and FreebaseSemantic Scholar [179] for academic search.

F.2 Open-Source Libraries

Recent research has boosted open source campaign, withseveral libraries listed in Table 9. They are AmpliGraph [205]for knowledge representation learning, Grakn for integra-tion knowledge graph with machine learning techniques,and Akutan for knowledge graph store and query. Theresearch community has also released codes to facilitatefurther research. Notably, there are three useful toolkits,namely scikit-kge and OpenKE [206] for knowledge graphembedding, and OpenNRE [207] for relation extraction. We

6. https://www.researchspace.org/index.html7. http://geneontology.org8. http://www.snomed.org/snomed-ct/five-step-briefing9. https://www.yiducloud.com.cn/en/academy.html10. https://code.google.com/archive/p/

relation-extraction-corpus/

provide an online collection of knowledge graph publica-tions, together with links to some open-source implemen-tations of them, hosted at https://github.com/shaoxiongji/awesome-knowledge-graph.

ACKNOWLEDGMENTS

We acknowledge the Australian Research Council (ARC)Linkage Project (LP150100671), the UQ Candidate TravelAward, and the Aalto Science-IT project.

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TABLE 7: Statistics of datasets with general knowledge when originally released

Dataset # entities # facts Website

WordNet [189] 117,597 207,016 https://wordnet.princeton.eduOpenCyc [190] 47,000 306,000 https://www.cyc.com/opencyc/Cyc [190] ∼250,000 ∼2,200,000 https://www.cyc.comYAGO [192] 1,056,638 ∼5,000,000 http://www.mpii.mpg.de/∼suchanek/yagoDBpedia [191] ∼1,950,000 ∼103,000,000 https://wiki.dbpedia.org/develop/datasetsFreebase [193] - ∼125,000,000 https://developers.google.com/freebase/NELL [194] - 242,453 http://rtw.ml.cmu.edu/rtw/Wikidata [195] 14,449,300 - https://www.wikidata.org/wikiProbase IsA 12,501,527 85,101,174 https://concept.research.microsoft.com/Home/DownloadGoogle KG > 500 million > 3.5 billion https://developers.google.com/knowledge-graph

TABLE 8: A summary of datasets for tasks on knowledgegraph itself

Dataset # Rel. #Ent. # Train # Valid. # Test

WN18 [12] 18 40,943 141,442 5,000 5,000FB15K [12] 1,345 14,951 483,142 50,000 59,071WN11 [14] 11 38,696 112,581 2,609 10,544FB13 [14] 13 75,043 316,232 5,908 23,733WN18RR [47] 11 40,943 86,835 3,034 3,134FB15k-237 [202] 237 14,541 272,115 17,535 20,466FB5M [15] 1,192 5,385,322 19,193,556 50,000 59,071FB40K [13] 1,336 39,528 370,648 67,946 96,678

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