Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relations) that preserve task-relevant structure encoded within the underlying combinatorial object. Such knowledge graph embeddings can be modeled as an approximate global section of a cellular sheaf, an algebraic structure over the graph. Using the diffusion dynamics encoded by the corresponding sheaf Laplacian, we optimally propagate known embeddings of a subgraph to inductively represent new entities introduced into the knowledge graph at inference time. We implement this algorithm via an efficient iterative scheme and show that on a number of large-scale knowledge graph embedding benchmarks, our method is competitive with -- and in some scenarios outperforms -- more complex models derived explicitly for inductive knowledge graph reasoning tasks.

翻译：知识图谱上的许多推理任务，包括关系预测，都依赖于知识图谱嵌入——即顶点（实体）和边（关系）的向量表示，这些表示保留了底层组合对象中编码的与任务相关的结构。此类知识图谱嵌入可以建模为胞腔层（图上的一个代数结构）的近似全局截面。利用由相应层拉普拉斯算子编码的扩散动力学，我们将子图的已知嵌入最优地传播出去，以在推理时归纳地表示引入知识图谱的新实体。我们通过一种高效的迭代方案实现了该算法，并证明在多个大规模知识图谱嵌入基准测试中，我们的方法与那些为归纳式知识图谱推理任务显式设计的更复杂模型相比具有竞争力——在某些场景下甚至表现更优。