Knowledge graph reasoning aims at predicting the missing facts from the existing structural and semantic information contained in the graphs. A typical approach to infer new facts is reinforcement learning method, which demonstrates the reasoning process through multi-hop paths. However, previous works tacitly approve such reasoning paths make sense, neglecting the fact that the relational paths connecting two entities may lack explainable meaning. To address the above challenge, we propose a novel knowledge graph reasoning method that leverages logical rules to improve interpretability and reliability. It makes full use of logical rules through a two-stage training framework, where the rule memorization stage learn the reasoning patterns from rules, and then the strategy improvement stage to further enhance the inference policy to obtain correct answers. Experimental results on several real-world datasets show that our method achieves excellent performance, and logical rules help to improve the interpretability of reasoning results.

Graph contrastive learning defines a contrastive task to pull similar instances close and push dissimilar instances away. It learns discriminative node embeddings without supervised labels, which has aroused increasing attention in the past few years. Nevertheless, existing methods of graph contrastive learning ignore the differences between diverse semantics existed in graphs, which learn coarse-grained node embeddings and lead to sub-optimal performances on downstream tasks. To bridge this gap, we propose a novelFine-grainedSemantics enhancedGraphContrastiveLearning (FSGCL) in this paper. Concretely, FSGCL first introduces a motif-based graph construction, which employs graph motifs to extract diverse semantics existed in graphs from the perspective of input data. Then, the semantic-level contrastive task is explored to further enhance the utilization of fine-grained semantics from the perspective of model training. Experiments on five real-world datasets demonstrate the superiority of our proposed FSGCL over state-of-the-art methods. To make the results reproducible, we will make our codes public on GitHub after this paper is accepted.

Spline wavelets /spl psi//sub m/(t) are important in time-frequency localization due to (i) /spl psi//sub m/ can be arbitrarily close to the optimal case as m is sufficiently large, (ii) /spl psi//sub m/ has compact support and simple analytic expression, which lead to effective computation. Although the spline wavelet subspaces are so simple, Walter's well-known sampling theorem does not hold if the order of spline m is even. Moreover, when irregular sampling is considered in these spaces, it is hard to determine the sampling density, which is a serious problem in applications, in this correspondence, a general sampling theorem is obtained for m/spl ges/3 in the sense of iterative construction and the sampling density /spl delta//sub m/ is estimated.