Lexical semantic models provide robust performance for question answering, but, in general, can only capitalize on direct evidence seen during training. For example, monolingual alignment models acquire term alignment probabilities from semi-structured data such as question-answer pairs; neural network language models learn term embeddings from unstructured text. All this knowledge is then used to estimate the semantic similarity between question and answer candidates. We introduce a higher-order formalism that allows all these lexical semantic models to chain direct evidence to construct indirect associations between question and answer texts, by casting the task as the traversal of graphs that encode direct term associations. Using a corpus of 10,000 questions from Yahoo! Answers, we experimentally demonstrate that higher-order methods are broadly applicable to alignment and language models, across both word and syntactic representations. We show that an important criterion for success is controlling for the semantic drift that accumulates during graph traversal. All in all, the proposed higher-order approach improves five out of the six lexical semantic models investigated, with relative gains of up to +13% over their first-order variants.

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