Putting a Spin on Language: A Quantum Interpretation of Ambiguous Sentence Readings

One of the biggest challenges in Artificial Intelligence (AI) is to understand and formulate coherent and meaningful discourse in natural language. Words are traditionally represented as vectors, agnostic to their syntactical role, and used in specific tasks such as word similarity. Once we wish to represent the meanings of well-formed larger fragments, we have to deal with the complexity of sentence structure.
On a sentence, words can be seen as having a function-argument relationship. Basic words, like nouns, are arguments of complex words, like verbs and adjectives, taken as functions. Such a grammar, formalized by Lambek, is mirrored in vector space representations of meaning, originally introduced by Coecke et al. Basic words are still described as vectors, but complex words are now interpreted as higher order linear maps. By mapping the first to quantum states and the latter to quantum operators, we can describe the meaning of a grammatical string of words as a quantum process.
The complexity of this process is further increased by the many ambiguities that arise at different levels. Words can be ambiguous in their meanings (“bank”, financial or of a river) or their grammatical roles (“bite” as a noun or a verb), forming conflicting interpretations of sentences (“I saw a boy by the bank”, “Man helps dog bite victim”). Lastly, different words taken as argument of the same complex word give rise to different readings of the same sentence (“I shot an elephant in my pajamas” is ambiguous about who wears the pajamas; in Dutch, “Man die de hond bijt” can either mean “man that bites the dog” or “man that the dog bites”).
In our work, we raise the building blocks of meaning to density matrices, leveraging their treatment of meaning ambiguity and including the directionality the information in the function-argument structure of the original Lambek grammar. We deal with higher-level ambiguous readings by extending this grammar with unary operators, which trace structural and syntactic variations. We interpret them by attaching an extra spin state to each word, encoding multiple readings on a parallel quantum process. Our method contributes to a growing field of complexity research at the intersection of AI, Linguistics and Quantum Computation.