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]: In this paper, we introduce an application of matrix factorization to produce corpus-derived, distributional models of semantics that demonstrate cognitive plausibility. We find that word representations learned by Non-Negative Sparse Embedding (NNSE), a variant of matrix factorization, are sparse, effective, and highly interpretable. To the best of our knowledge, this is the first approach which yields semantic representation of words satisfying these three desirable properties. Though extensive experimental evaluations on multiple real-world tasks and datasets, we demonstrate the superiority of semantic models learned by NNSE over other state-of-the-art baselines.

[2]: Knowledge representation is a long-history topic in AI, which is very important. A variety of models have been proposed for knowledge graph embedding, which projects symbolic entities and relations into continuous vector space. However, most related methods merely focus on the data-fitting of knowledge graph, and ignore the interpretable semantic expression. Thus, traditional embedding methods are not friendly for applications that require semantic analysis, such as question answering and entity retrieval. To this end, this paper proposes a semantic representation method for knowledge graph , which imposes a two-level hierarchical generative process that globally extracts many aspects and then locally assigns a specific category in each aspect for every triple. Since both aspects and categories are semantics-relevant, the collection of categories in each aspect is treated as the semantic representation of this triple. Extensive experiments show that our model outperforms other state-of-the-art baselines substantially.
While the vector space models perform well in many tasks, the semantics of learned representations are not directly clear. This problem for word embeddings was addressed by [1] where they proposed a set of constraints inducing interpretability. However, its adaptation for KG embeddings hasn't been addressed. A recent work [2] addressed a similar problem, where they learn coherent semantic features for entities and relations in KG. Our method differs from theirs in the following two aspects. Firstly, we use vector space modeling leading directly to KG embeddings while they need to infer KG embeddings from their probabilistic model. Second, we incorporate additional information about entities which helps in learning interpretable embeddings.