EM-RBR: a reinforced framework for knowledge graph completion from reasoning perspective

Knowledge graph completion aims to predict the missing links among the knowledge graph ( KG ) , i.e. , predicting the possibility that a certain triple belongs to the knowledge graph . Most mainstream embedding methods focus on fact triplets contained in the given KG , however , ignoring the rich background information provided by logic rules driven from knowledge base implicitly . Limited to the modeling of algebraic space , contradictory in expressing certain relational patterns usually exists in the embedding models . Therefore , the representation of the knowledge graph is incomplete and inaccurate . To solve this problem , in this paper , we propose a general framework , named EM-RBR ( embedding and rulebased reasoning ) , capable of combining the advantages of reasoning based on rules and the state-of-the-art models of embedding . EM-RBR aims to utilize relational background knowledge contained in rules to conduct multi-relation reasoning link prediction . In this way , we can find the most reasonable explanation for a given triplet to obtain higher prediction accuracy . In experiments , we demonstrate that EM-RBR achieves better performance compared with previous models on FB15k , WN18 and our new dataset FB15k-R , especially the new dataset where our model perform futher better than those state-of-the-arts . We make the implementation of EM-RBR available at https : //github.com/1173710224/ link-prediction-with-rule-based-reasoning . 1 INTRODUCTION . Knowledge graph ( KG ) has the ability to convey knowledge about the world and express the knowledge in a structured representation . The rich structured information provided by knowledge graphs has become extremely useful resources for many Artificial Intelligence related applications like query expansion ( Graupmann et al. , 2005 ) , word sense disambiguation ( Wasserman Pritsker et al. , 2015 ) , information extraction ( Hoffmann et al. , 2011 ) , etc . A typical knowledge representation in KG is multi-relational data , stored in RDF format , e.g . ( Paris , Capital-Of , France ) . However , due to the discrete nature of the logic facts ( Wang & Cohen , 2016 ) , the knowledge contained in the KG is meant to be incomplete ( Sadeghian et al. , 2019 ) . Consequently , knowledge graph completion ( KGC ) has received more and more attention , which attempts to predict whether a new triplet is likely to belong to the knowledge graph ( KG ) by leveraging existing triplets of the KG . Currently , the popular embedding-based KGC methods aim at embedding entities and relations in knowledge graph to a low-dimensional latent feature space . The implicit relationships between entities can be inferred by comparing their representations in this vector space . These researchers ( Bordes et al. , 2013 ; Mikolov et al. , 2013 ; Wang et al. , 2014 ; Ji et al. , 2015 ; Lin et al. , 2015 ; Nguyen et al. , 2017 ) make their own contributions for more reasonable and competent embedding . But the overall effect is highly correlated with the density of the knowledge graph . Because embedding method always fails to predict weak and hidden relations which a low frequency . The embedding will converge to a solution that is not suitable for triplets owned weak relations , since the training set for embedding can not contain all factual triplets.However , reasoning over the hidden relations can covert the testing target to a easier one . For example , there is an existing triplet ( Paul , Leader-Of , SoccerTeam ) and a rule Leader-Of ( x , y ) =⇒ Member-Of ( x , y ) which indicates the leader of a soccer team is also a member of a sport team . Then we can apply the rule on the triplet to obtain a new triplet ( Paul , Member-of , SportTeam ) even if the relation Member-of is weak in knowledge graph . Besides , some innovative models try to harness rules for better prediction . Joint models ( Rocktäschel et al. , 2015 ; Wang et al. , 2019 ; Guo et al. , 2016 ) utilize the rules in loss functions of translation models and get a better embedding representation of entities and relations . An optimization based on ProPPR ( Wang & Cohen , 2016 ) embeds rules and then uses those embedding results to calculate the hyper-parameters of ProPPR . These efforts all end up on getting better embedding from rules and triplets , rather than solving completion through real rule-based reasoning , which is necessary to address weak relation prediction as mentioned before . Compared with them , EM-RBR can perform completion from the reasoning perspective . Usually , there are some contradictions in the mathematical space of existing embedding-based models . Take transE ( Bordes et al. , 2013 ) and RotatE ( Sun et al. , 2019 ) as examples . For the relation pattern R ( x , y ) ⇒ R ( y , x ) , i.e. , a symmetrical relation , transE can not model it as described in Sun et al . ( 2019 ) . While RotatE can not model some relation pattern . For example , transitive relation R , w.r.t R ( x , y ) ∧R ( y , z ) ⇒ R ( x , z ) . We assume that the embedding of the relation R under RotatE is eiθR , abbreviated as r. Formula 1 is necessary and sufficient to transitivity . So we will get r2 = r , which means that eiθR = 1 , so θR = 0 , θR ∈ [ 0 , 2π ) . θR = 0 denotes that R is a reflexive relation . That is all the embedding of the transitive relation will be trained to have the nature of the reflexive relation , which is out of our expect . x · r = y , y · r = z , x · r = z ( 1 ) In addition to the above problems , transE and RotatE models can not model data that has multiple relations between two entities . TransR ( Lin et al. , 2015 ) can solve this problem by training the relationship as a transformation matrix . But none of them can solve the problem that an entity has the same relation with multiple other entities . For example , there are two triples ( h , r , t1 ) , ( h , r , t2 ) in the knowledge graph ( t1 6= t2 ) . For the transE model , h+ r is a fixed result . So a wrong equation r1 = r2 will exist under transE model . The other two mathematical models are no exception . The above-mentioned shortcomings can be solved by defining the relation pattern in a rule directly . Morivated by this , We propose a novel framework EM-RBR combing embedding and rule-based reasoning , which is a heuristic search essentially . In the development of the joint framework EMRBR , we meet two challenges . On the one hand , we use AMIE ( Galárraga et al. , 2013 ) to auto-mine large amount of rules but not manually . However , these rules automatically mined sometimes are not completely credible . Therefore , it is necessary to propose a reasonable way to measure rules to pick proper rules when reasoning . On the other hand , it is known that traditional reasoningbased methods will give only 0 or 1 to one triplet to indicate acceptance or rejection for the given knowledge graph . This conventional qualitative analysis lacks the quantitative information as the embedding models . So the result of EM-RBR need to reflect the probability one triplet belonging to the knowledge graph . Three main contributions in EM-RBR are summarized as follows : • EM-RBR is flexible and general enough to be combined with a lot of embedding models . • We propose a novel reasoning algorithm , which can distinguish a given triplet with other wrong triplets better . • We propose a novel rating mechanism for auto-mined reasoning rules and each rule will be measured properly in our framework . In the remaining of this paper , we will explain how our model works in Section 2 , experiments in Section 3 and related work in Section 4 . 2 METHOD . Our motivation is to use rules to make up for the shortcomings of embedding model . When the mathematical space of a certain embedding model is not enough to represent a certain relation pattern , the relation pattern can be declared through rules . For example , for the symmetric relationship R , we declare a rule R ( x , y ) ⇒ R ( y , x ) . When scoring a certain triple ( a , R , b ) under transE model , we can take min ( s ( a , R , b ) , s ( b , R , a ) ) as the The final score of the triple . This is equivalent to finding another triple that can explain the rationality of this triple through rules . Although the relation between the new triplet and the original triplet can not be expressed in the algebraic space of embedding , the most reasonable explanation can be found through rules to solve the defects of the model . The core idea of our framework is to conduct multi-relation path prediction in deeper context from reasoning perspective , that is in the form of heuristic search . Before explaining the concrete reasoning algorithm , let ’ s take an overview of our framework in Section 2.1 . 2.1 OVERVIEW . Definition 2.1 . Rule : A rule in our framework is in the form of B1 ( x , z ) ∧ B2 ( z , y ) =⇒ H ( x , y ) or B ( x , y ) =⇒ H ( x , y ) . We model a knowledge graph as a collection of facts G = { ( h , r , t ) |h , t ∈ E , r ∈ R } , where E and R represent the set of entities and relations in the knowledge graph , respectively . The steps of our framework are as follows corresponding to Figure 1 . Step 1 . We invoke an embedding model to get a set Ξ ∈ R ( |E|+|R| ) ×k containing the k-dimensional embedding of entities and relations in G. Step 2 . We apply AMIE ( Galárraga et al. , 2013 ) on G to get the reasoning rule set Ω , where each rule meets Definition 2.1 . Step 3 . The reasoning rules are measured based on the embedding of relations contained in the rule , which will explained in Secion 2.2.2 . Step 4 . Reasoning is conducted for a given triplet ( h , r , t ) , which will be described in Section 2.2 . 2.2 REASONING ALGORITHM . Definition 2.2. initial state : Initial state is represented as a set consisting of a single triplet , i.e . { ( h , r , t ) } . state : According to the initial state and the state ’ s expansion method described in Section 2.2.1 , each state is represented as a set a triples . This reasoning algorithm is the core of our framework and it ’ s a heuristic search . The input of this algorithm is a triplet ( h , r , t ) . State in the search space is as Definition 2.2 . Each state has two scores , i.e . H and L. H is the heuristic score of state and L is the score of the state . The calculation of scores is explained in Section 2.2.2 . The target of search is to compute Φ∼ ( h , r , t ) = minstate∈S { L∼state ( h , r , t ) } for a specific triple ( h , r , t ) . The score Φ of a triplet meets Φ ≥ 1 . The smaller Φ is , the triplet belongs to knowledge graph with greater probability . The pseudo code of search is as shown in Appendix B . We use a priority queue Q to store states in ascending order of H. The initial state is the target triplet itself , whose H is 1 . Push the initial state into Q and then begin the loop until Q is empty . During the search process , pop the top of Q as the current state scur . It will not be extended if Hscur ≥ Φ , otherwise we will extend it by matching rules to get new states . For each new state snew , compute its scoreHsnew and Lsnew . IfHsnew < Lscur , the state will then be pushed into Q .

Summary: The paper proposes a framework (EM-RBR) for doing Knowledge Base (KB) completion. Instead of the direct triple score from an embedding based method, EM-RBR allows the triple score to be calculated as a composition of the scores of the rules mined from the KB. EM-RBR uses a BFS type algorithm that recursively searches for reasoning paths connecting the triple while also updating the score.  The authors show that EM-RBR when used as an addendum to a translation-based embedding method (such as TrasnE, TransH) is able to outperform them. They show their results on FB15k and WN18.