NALA : an Effective and Interpretable Entity Alignment Method (2024)

Abstract: Entity alignment (EA) aims to find equivalent entities between two Knowledge Graphs. Existing embedding-based EA methods usually encode entities as embeddings, triples as embeddings’ constraint and learn to align the embeddings. However, the details of the underlying logical inference steps among the alignment process are usually omitted, resulting in inadequate inference process. In this paper, we introduce NALA, an entity alignment method that captures three types of logical inference paths with Non-Axiomatic Logic (NAL). Type 1&2 align the entity pairs and type 3 aligns relations. NALA iteratively aligns entities and relations by integrating the conclusions of the inference paths. Our method is logically interpretable and extensible by introducing NAL, and thus suitable for various EA settings. Experimental results show that NALA outperforms state-of-the-art methods in terms of Hits@1, achieving 0.98+ on all three datasets of DBP15K with both supervised and unsupervised settings. We offer a pioneering in-depth analysis of the fundamental principles of entity alignment, approaching the subject from a unified and logical perspective. Our code is available at https://github.com/13998151318/NALA.

## introduction knowledge graphs (kgs), which store massive facts about the real world, expresses massive information in a form closer to human cognition. kgs can be used by various application domains, such as question answering, recommender systems and language representation learning (knowledge graph enhanced language model) @xcite . the information contained in each individual kg project, such as dbpedia @xcite and yago @xcite (ea) is proposed to increase kg completeness. the ea task consists of integrating two or more kgs into a same kg by aligning nodes that refer to the same entity. there are many embedding-based ea methods @xcite that leverage deep learning techniques to represent entities with lowdimensional embeddings, and align entities with a similarity function on the embedding space. kgs' triples and seed alignments are usually seen as embeddings' constraint during the training process of such embedding model. the structural and side information of kgs are usually utilized via embedding propagation, aggregation or interaction. generally speaking, there are some crucial shortcomings of embedding-based ea methods: first, they possibly lack complex reasoning capability. some of them are enhanced by paths @xcite , however, due to the nature of vector repre-sentation, it is not easy to perform or approximate symbolic reasoning on such paths. second, they lack interpretability in the models, so they have to rely solely on numerical evaluation metrics to evaluate their performance. thus the cons and pros of their model design may not be properly evaluated. third, the absence of a unified framework explaining the mechanism of embedding learning and processing renders their semantic or structural learning capability quite mysterious. apart from embedding-based methods, pathbased methods directly estimates entity similarities from the contextual data (path) that are available in the two input kgs. a "path" usually refers to an interconnected sequence of edges that links two entities of different kgs. the edges can be either relations or entity similarities. we refer to the estimation of entity similarities by processing and aggregating the paths as "similarity inference". there is a potential advantage that pathbased methods can capture fine-grained matches of neighbors while the traditional embedding-based methods can't. there are also emerging methods that combine the idea of embedding learning and path reasoning. more recently, path-based (such as paris+ @xcite ) and combined methods (such as bert-int @xcite and fgwea @xcite ) are starting to surpass the performance of traditional embeddingbased methods. however, they failed to handle the similarity inference appropriately to some extent, possibly due to the lack of proper formalization of the inference paths and steps. to address the aforementioned issues of existing methods, we carefully examine the similarity inference of ea from the logical perspective. thus we propose a path-based ea method nala, where nal stands for non-axiomatic logic @xcite and "a" for align. nal is a term logic with a specific semantic theory and its design suits kg tasks (see section 2.3). as illustrated in figure 1 , nala adopts an iterative entity alignment strategy with two modules, namely similarity inference module and matching module. for each iteration, it first performs the similarity inference module. the module has three functions: 1) search for three types of paths across the kgs. 2) inference on the path instances with fixed inference rules defined by nal. 3) aggregate the conclusions of the paths. type i&ii paths yield conclusions on similarities of entity pairs. type iii paths yield conclusions on substitutability (or, inheritance) of relation or attribute pairs. we use bert embedding to assist path inference by obtaining similarity among entity names and attribute values, which constitutes some premises of the paths. then nala uses the matching module to obtain 1-to-1 ea results of the current iteration. we propose an algorithm, namely rbmat algorithm with swapping step (see section 3.2) for the matching module. experiments on cross-lingual ea dataset dbp15k demonstrate that nala outperforms sota ea methods in 5 different setting groups (including both supervised and unsupervised scenarios), showcasing the effectiveness of our proposed logical similarity inference module and matching module. ablation study shows that our design choices jointly boost the overall performance of nala. our contributions can be summarized as: various types of logical paths are formalized within the similarity inference phase. ea. the entity alignment (ea) problem is typically defined between two kgs, kg 1 and kg 2 , where the task consists of finding equivalences (socalled alignment) between the set of entities e 1 and e 2 of the two kgs. sometimes there exists a set of given equivalences that can be used as supervision. this set s is known as seed alignment set. we assume that there exists a ground truth set ## the proposed method the overall structure of nala (as illustrated in figure 1 and algorithm 3) adopts an iterative aligning strategy, and for each iteration it first performs similarity inference, then it uses the matching module (rbmat algorithm with swapping step in section 3.2) to obtain ea results. the inference within each iteration benefits from the alignment results (both entities and relations) of the previous iteration. ## interpretability of nala following @xcite , interpretable ml (machine learning) focuses on designing models that are inherently interpretable, while explainable ml tries to provide post hoc explanations for existing black box models. nala is highly interpretable and self-explanatory. it is arguably more interpretable than paris for the following two reasons. first, with the introduction of evidence amount (confidence) and logical inference rules, nala processes data with more information and generates a more informative explanation. second, nala manages value similarity, name similarity and structural similarity in a unified logical framework, while paris doesn't leverage such side information. nala is self-explanatory in the sense that it generates a log file of evidences for the alignments so we can inspect the file after an iteration. this feature enhances the troubleshooting capacity of us to some extent during the development process of nala. for example, inspecting the faulty alignments in the evidence file inspired many decision choices in this paper. the generated evidences are displayed in our github repository. using the neural bert model does not weaken the interpretability of type i path because utilizing literal value similarity does not affect the interpretable inference steps. moreover, as we only keep the attribute value similarities with a score above the threshold, most of these similarities are easily understood and self-explanatory, except the wrong ones. our method tolerates faulty attribute value similarity because type i path needs a conjunction of all premises, while faulty similarities usually can't form a complete premise set. we discuss nala's relation with other methods and help explain the mechanism of those methods in appendix d.4. ## conclusion and future work in this paper, we propose an entity alignment method named nala, tackling the ea problem by modeling similarity inference and performing a matching algorithm. similarity inference obtains similarity through paths that connect the entities. nala leverages three type of paths, exploiting both structural and side information of kgs. using the similarities, nala matches the entities by the proposed rbmat algorithm. nala is also successfully adapted to the unsupervised scenario and a scenario without attribute triples. compared with up-to-date ea methods, nala attains competitive result on openea benchmark datasets and various settings of dbp15k, indicating that it successfully handles the most effective part of similarity inference. we also take a step in re-evaluating the design choices of different ea models, by providing some interesting insights (explanations) of different methods and competitive results compared with them. hopefully, our approach may broaden the view and deepen the understanding of the ea research community. how to combine embedding models with path inference and facilitate its full potential is a research question to be further studied. nal can express and process many different reasoning patterns and logical structures, so nala can be extended to tackle other challenges in the ea process in future research, such as integrating ontological information.