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Neural Tensor Networks (NTNs), which are structured to encode the degree ofrelationship among pairs of entities, are used in Logic Tensor Networks (LTNs)to facilitate Statistical Relational Learning (SRL) in first-order logic. Inthis paper, we propose Randomly Weighted Tensor Networks (RWTNs), whichincorporate randomly drawn, untrained tensors into an NTN encoder network witha trained decoder network. We show that RWTNs meet or surpass the performanceof traditionally trained LTNs for Semantic Image Interpretation (SII) tasksthat have been used as a representative example of how LTNs utilize reasoningover first-order logic to exceed the performance of solely data-driven methods.We demonstrate that RWTNs outperform LTNs for the detection of the relevantpart-of relations between objects, and we show that RWTNs can achieve similarperformance as LTNs for object classification while using fewer parameters forlearning. Furthermore, we demonstrate that because the randomized weights donot depend on the data, several decoder networks can share a single NTN, givingRWTNs a unique economy of spatial scale for simultaneous classification tasks.

Randomly Weighted, Untrained Neural Tensor Networks Achieve Greater Relational Expressiveness