You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We study the problem of inducing interpretability in KG embeddings. Specifically, we explore the Universal Schema (, 2013) and propose a method to induce interpretability. There have been many vector space models proposed for the problem, however, most of these methods don't address the interpretability (semantics) of individual dimensions. In this work, we study this problem and propose a method for inducing interpretability in KG embeddings using entity co-occurrence statistics. The proposed method significantly improves the interpretability, while maintaining comparable performance in other KG tasks.

Cited Abstract(s):
[1]: 

[2]: Recently, knowledge graph embedding, which projects symbolic entities and relations into continuous vector space, has become a new, hot topic in artificial intelligence. This paper addresses a new issue of multiple relation semantics that a relation may have multiple meanings revealed by the entity pairs associated with the corresponding triples, and proposes a novel Gaussian mixture model for embedding, TransG. The new model can discover latent semantics for a relation and leverage a mixture of relation component vectors for embedding a fact triple. To the best of our knowledge, this is the first generative model for knowledge graph embedding, which is able to deal with multiple relation semantics. Extensive experiments show that the proposed model achieves substantial improvements against the state-of-the-art baselines.

[3]: 

[4]: Knowledge representation is a major topic in AI, and many studies attempt to represent entities and relations of knowledge base in a continuous vector space. Among these attempts, translation-based methods build entity and relation vectors by minimizing the translation loss from a head entity to a tail one. In spite of the success of these methods, translation-based methods also suffer from the oversimplified loss metric, and are not competitive enough to model various and complex entities relations in knowledge bases. To address this issue, we propose , an adaptive metric approach for embedding, utilizing the metric learning ideas to provide a more flexible embedding method. Experiments are conducted on the benchmark datasets and our proposed method makes significant and consistent improvements over the state-of-the-art baselines.

[5]: 

[6]: 

[7]: © 2013 Association for Computational Linguistics. Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of the same schema. The need for existing datasets can be avoided by using a universal schema: the union of all involved schemas (surface form predicates as in OpenIE, and relations in the schemas of preexisting databases). This schema has an almost unlimited set of relations (due to surface forms), and supports integration with existing structured data (through the relation types of existing databases). To populate a database of such schema we present matrix factorization models that learn latent feature vectors for entity tuples and relations. We show that such latent models achieve substantially higher accuracy than a traditional classification approach. More importantly, by operating simultaneously on relations observed in text and in pre-existing structured DBs such as Freebase, we are able to reason about unstructured and structured data in mutually-supporting ways. By doing so our approach outperforms stateof- the-Art distant supervision.

[8]: Many knowledge repositories nowadays contain billions of triplets, i.e. (head-entity, relationship, tail-entity), as relation instances. These triplets form a directed graph with entities as nodes and relationships as edges. However, this kind of symbolic and discrete storage structure makes it difficult for us to exploit the knowledge to enhance other intelligenceacquired applications (e.g. the QuestionAnswering System), as many AI-related algorithms prefer conducting computation on continuous data. Therefore, a series of emerging approaches have been proposed to facilitate knowledge computing via encoding the knowledge graph into a low-dimensional embedding space. TransE is the latest and most promising approach among them, and can achieve a higher performance with fewer parameters by modeling the relationship as a transitional vector from the head entity to the tail entity. Unfortunately, it is not flexible enough to tackle well with the various mapping properties of triplets, even though its authors spot the harm on performance. In this paper, we thus propose a superior model called TransM to leverage the structure of the knowledge graph via pre-calculating the distinct weight for each training triplet according to its relational mapping property. In this way, the optimal function deals with each triplet depending on its own weight. We carry out extensive experiments to compare TransM with the state-of-the-art method TransE and other prior arts. The performance of each approach is evaluated within two different application scenarios on several benchmark datasets. Results show that the model we proposed significantly outperforms the former ones with lower parameter complexity as TransE.

[9]: Models that learn to represent textual and knowledge base relations in the same continuous latent space are able to perform joint inferences among the two kinds of relations and obtain high accuracy on knowledge base completion (, 2013). In this paper we propose a model that captures the compositional structure of textual relations, and jointly optimizes entity, knowledge base, and textual relation representations. The proposed model significantly improves performance over a model that does not share parameters among textual relations with common sub-structure.
A very effective and powerful set of models are based on translation vectors. These models represent entities as vectors in @math -dimensional space, @math and relations as translation vectors from head entity to tail entity, in either same or a projected space. TransE [3] is one of the initial works, which was later improved by many works [ [1] , [5] , [2] , [4] , [6] , [4]0 ]. Also, there are methods which are able to incorporate text data while learning KG embeddings. [7] is one such method, which assumes a combined universal schema of relations from KG as well as text. [4]1 further improves the performance by sharing parameters among similar textual relations.