Learning effective representations of entities and relations for knowledge graphs (KGs) is critical to the success of many multi-relational learning tasks. Existing methods based on graph neural networks learn a deterministic embedding function, which lacks sufficient flexibility to explore better choices when dealing with the imperfect and noisy KGs such as the scarce labeled nodes and noisy graph structure. To this end, we propose a novel multi-relational graph Gaussian Process network (GGPN), which aims to improve the flexibility of deterministic methods by simultaneously learning a family of embedding functions, i.e., a stochastic embedding function. Specifically, a Bayesian Gaussian Process (GP) is proposed to model the distribution of this stochastic function and the resulting representations are obtained by aggregating stochastic function values, i.e., messages, from neighboring entities. The two problems incurred when leveraging GP in GGPN are the proper choice of kernel function and the cubic computational complexity. To address the first problem, we further propose a novel kernel function that can explicitly take the diverse relations between each pair of entities into account and be adaptively learned in a data-driven way. We address the second problem by reformulating GP as a Bayesian linear model, resulting in a linear computational complexity. With these two solutions, our GGPN can be efficiently trained in an end-to-end manner. We evaluate our GGPN in link prediction and entity classification tasks, and the experimental results demonstrate the superiority of our method. Our code is available at https://github.com/sysu-gzchen/GGPN.
Abstruct-This letter presents a derivation of the closedform expression of numerical reflection at interfaces of perfectly matched layer (PML). Reflection coefficients at singleinterfaces and of finite-thickness absorbers are presented. The derived closed-form expression is found to match identically with the reflection coefficient obtained directly through finitedifference time-domain computation. The closed-form expression of numerical reflection coefficient can significantly facilitate the optimization of PML performance.
This paper focuses on the task of cross domain few-shot named entity recognition (NER), which aims to adapt the knowledge learned from source domain to recognize named entities in target domain with only a few labeled examples. To address this challenging task, we propose MANNER, a variational memoryaugmented few-shot NER model. Specifically, MANNER uses a memory module to store information from the source domain and then retrieve relevant information from the memory to augment few-shot tasks in the target domain. In order to effectively utilize the information from memory, MANNER uses optimal transport to retrieve and process information from memory, which can explicitly adapt the retrieved information from source domain to target domain and improve the performance in the cross domain few-shot setting. We conduct experiments on both English and Chinese cross domain fewshot NER datasets, and the experimental results demonstrate that MANNER can achieve superior performance 1 .
Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.
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