Quantum logic inspired embedding (aka Quantum Embedding (QE)) of a Knowledge-Base (KB) was proposed recently by Garg:2019. It is claimed that the QE preserves the logical structure of the input KB given in the form of unary and binary predicates hierarchy. Such structure preservation allows one to perform Boolean logic style deductive reasoning directly over these embedding vectors. The original QE idea, however, is limited to the transductive (not inductive) setting. Moreover, the original QE scheme runs quite slow on real applications involving millions of entities. This paper alleviates both of these key limitations. We start by reformulating the original QE problem to allow for the induction. On the way, we also underscore some interesting analytic and geometric properties of the solution and leverage them to design a faster training scheme. As an application, we show that one can achieve state-of-the-art performance on the well-known NLP task of fine-grained entity type classification by using the inductive QE approach. Our training runs 9-times faster than the original QE scheme on this task.

Statistical Relational Learning (SRL) methods are the most widely used techniques to generate distributional representations of the symbolic Knowledge Bases (KBs). These methods embed any given KB into a vector space by exploiting statistical similarities among its entities and predicates but without any guarantee of preserving the underlying logical structure of the KB. This, in turn, results in poor performance of logical reasoning tasks that are solved using such distributional representations. We present a novel approach called Embed2Reason (E2R) that embeds a symbolic KB into a vector space in a logical structure preserving manner. This approach is inspired by the theory of Quantum Logic. Such an embedding allows answering membership based complex logical reasoning queries with impressive accuracy improvements over popular SRL baselines.