Concrete Sentence Spaces for Compositional Distributional Models of Meaning

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a\ncompositional model of meaning for distributional semantics, in which each word\nin a sentence has a meaning vector and the distributional meaning of the\nsentence is a function of the tensor products of the word vectors. Abstractly\nspeaking, this function is the morphism corresponding to the grammatical\nstructure of the sentence in the category of finite dimensional vector spaces.\nIn this paper, we provide a concrete method for implementing this linear\nmeaning map, by constructing a corpus-based vector space for the type of\nsentence. Our construction method is based on structured vector spaces whereby\nmeaning vectors of all sentences, regardless of their grammatical structure,\nlive in the same vector space. Our proposed sentence space is the tensor\nproduct of two noun spaces, in which the basis vectors are pairs of words each\naugmented with a grammatical role. This enables us to compare meanings of\nsentences by simply taking the inner product of their vectors.\n

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