Basic Reasoning with Tensor Product Representations
This work provides a theoretical foundation for using TPRs in logical reasoning, potentially benefiting AI researchers working on symbolic reasoning and neural-symbolic integration, though it appears incremental as it builds on existing TPR frameworks.
The paper tackles the problem of mapping inference in predicate logic to computation over Tensor Product Representations (TPRs), demonstrating this through examples in the bAbI question-answering task and extending simplified methods to more general reasoning tasks.
In this paper we present the initial development of a general theory for mapping inference in predicate logic to computation over Tensor Product Representations (TPRs; Smolensky (1990), Smolensky & Legendre (2006)). After an initial brief synopsis of TPRs (Section 0), we begin with particular examples of inference with TPRs in the 'bAbI' question-answering task of Weston et al. (2015) (Section 1). We then present a simplification of the general analysis that suffices for the bAbI task (Section 2). Finally, we lay out the general treatment of inference over TPRs (Section 3). We also show the simplification in Section 2 derives the inference methods described in Lee et al. (2016); this shows how the simple methods of Lee et al. (2016) can be formally extended to more general reasoning tasks.