Methods for knowledge graph (KG) completion need to capture semantic
regularities and use these regularities to infer plausible knowledge that is
not explicitly stated. Most embedding-based methods are opaque in the kinds of
regularities they can capture, although region-based KG embedding models have
emerged as a more transparent alternative. By modeling relations as geometric
regions in high-dimensional vector spaces, such models can explicitly capture
semantic regularities in terms of the spatial arrangement of these regions.
Unfortunately, existing region-based approaches are severely limited in the
kinds of rules they can capture. We argue that this limitation arises because
the considered regions are defined as the Cartesian product of two-dimensional
regions. As an alternative, in this paper, we propose RESHUFFLE, a simple model
based on ordering constraints that can faithfully capture a much larger class
of rule bases than existing approaches. Moreover, the embeddings in our
framework can be learned by a monotonic Graph Neural Network (GNN), which
effectively acts as a differentiable rule base. This approach has the important
advantage that embeddings can be easily updated as new knowledge is added to
the KG. At the same time, since the resulting representations can be used
similarly to standard KG embeddings, our approach is significantly more
efficient than existing approaches to differentiable reasoning.

在这篇论文中，我们提出了一种基于顺序约束的简单模型 RESHUFFLE，能够比现有方法更好地捕捉规则，同时在我们的框架中嵌入可以通过可微分的图神经网络（GNN）进行学习，从而具有更高的效率。

利用基于区域的图神经网络进行知识图谱的可微分推理

Differentiable Reasoning about Knowledge Graphs with Region-based Graph  Neural Networks

Many known planning tasks have inherent constraints concerning the best order
in which to achieve the goals. A number of research efforts have been made to
detect such constraints and to use them for guiding search, in the hope of
speeding up the planning process. We go beyond the previous approaches by
considering ordering constraints not only over the (top-level) goals, but also
over the sub-goals that will necessarily arise during planning. Landmarks are
facts that must be true at some point in every valid solution plan. We extend
Koehler and Hoffmann's definition of reasonable orders between top level goals
to the more general case of landmarks. We show how landmarks can be found, how
their reasonable orders can be approximated, and how this information can be
used to decompose a given planning task into several smaller sub-tasks. Our
methodology is completely domain- and planner-independent. The implementation
demonstrates that the approach can yield significant runtime performance
improvements when used as a control loop around state-of-the-art sub-optimal
planning systems, as exemplified by FF and LPG.

本文提出一种新的方法，在规划中利用排序约束来指导搜索，使用工具扩展 Koehler 和 Hoffmann 的合理顺序，找到 Landmarks 并将规划任务分解为多个子任务从而提高运行时间性能。