Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits -- constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design. Furthermore, our models scale more gracefully than the original KGEs on graphs with millions of entities.

翻译：一些最成功的用于链接预测的知识图谱嵌入（KGE）模型——CP、RESCAL、TuckER、ComplEx——可以解释为基于能量的模型。在这种视角下，它们不适用于精确的最大似然估计（MLE）、采样，并且难以整合逻辑约束。本工作将这些KGE的得分函数重新解释为电路——一种允许高效边际化的约束计算图。随后，我们设计了两种方法，通过限制其激活值为非负或对输出进行平方，来获得高效的生成电路模型。我们的解释在链接预测方面几乎没有性能损失，而电路框架则解锁了通过MLE进行精确学习、高效采样新三元组以及确保逻辑约束在设计上得到满足的能力。此外，在包含数百万实体的图上，我们的模型比原始KGE具有更优越的可扩展性。