Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.
Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.
Quantum computing has demonstrated computational advantages over classical computing, yet its applications to natural language processing (NLP) remain in their early stages. Quantum contextuality, a fundamental feature of quantum mechanics, has been identified as a resource for achieving these advantages. Meanwhile, ambiguities in human languages present challenges in building systems capable of understanding and generating natural language. Many of these ambiguities can be addressed by considering the context in which they arise. This thesis investigates the connection between quantum contextuality and ambiguities in natural language. It introduces a framework that models ambiguities in language as a form of measurement, analogous to physical experiments. The findings reveal that contextuality is present in natural language and that its degree is linked to the reasoning capabilities of large language models (LLMs).
Contextuality is a distinguishing feature of quantum mechanics, and there is evidence that it is a necessary condition for quantum advantage in the context of magic state distillation. To harness it, researchers have been asking whether similar phenomena arise in other domains. The answer has been affirmative, e.g. in behavioural sciences. However, one has to adopt frameworks that take some degree of signalling into account. Two such frameworks exist: (i) a signalling-corrected sheaf-theoretic model and (ii) the Contextuality-by-Default (CbD) framework. This paper provides the first large-scale experimental evidence for contextuality in the large language model BERT. We constructed a linguistic schema modelled over a contextual quantum scenario, instantiated it in the Simple English Wikipedia, and extracted probability distributions for the instances. This led to the discovery of 77 118 sheaf-contextual and 36 938 948 CbD contextual instances. We prove that these contextual instances arise from semantically similar words by deriving an equation that relates degrees of contextuality to the Euclidean distance of BERT’s embedding vectors. Our linguistic schema is a variant of the coreference resolution challenge. These results suggest that quantum methods may be advantageous in the field of natural language processing.
Ambiguities of natural language do not preclude us from using it and context helps in getting ideas across. They, nonetheless, pose a key challenge to the development of competent machines to understand natural language and use it as humans do. Contextuality is an unparalleled phenomenon in quantum mechanics, where different mathematical formalisms have been put forwards to understand and reason about it. In this paper, we construct a schema for anaphoric ambiguities that exhibits quantum-like contextuality. We use a recently developed criterion of sheaf-theoretic contextuality that is applicable to signalling models. We then take advantage of the neural word embedding engine BERT to instantiate the schema to natural language examples and extract probability distributions for the instances. As a result, plenty of sheaf-contextual examples were discovered in the natural language corpora BERT utilises. Our hope is that these examples will pave the way for future research and for finding ways to extend applications of quantum computing to natural language processing.
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent.Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities.In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability.In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same.We will discuss how the consequences of this move may help us understand quantum contextuality.
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen–Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.
Since Bell, Kochen and Specker formulated the first notions of contextuality, a number of frameworks have been created to help make philosophical and mathematical sense of the concept. Two of the most common are the Equivalence-based approach due to Spekkens, and the Sheaf-theoretic framework of Abramsky and Brandenburger. Each of these can support a hierarchy of strengths of contextuality, which can include possibilistic concepts. This thesis will explore the differences between the two approaches, and explore what can be demonstrated by using weaker notions of noncontextuality. Notions of noncontextuality are important for proving no-go theorems which highlight that many properties that are true of classical mechanics fail to be compatible with quantum predictions. Often, the notions of noncontextuality used are very strong assumptions, and even weaker flavours of noncontextuality can be used to draw the same, or similar conclusions. An important class of such notions are, possibilistic assumptions that only care about whether or not events are possible or impossible, rather than the exact Born rule probabilities that are applied to events. Even these weaker notions are often impossible to resolve with the logical structure and predictions of quantum theory. Contextuality has been demonstrated to be a resource for many quantum computational operations, and the contextual fraction has been shown to be an important resource. We introduce a metric that can differentiate between different quantum mechanical scenarios with contextual fraction 1, and demonstrate analogues of CHSH and Tsirelson bounds for this quantity. We also investigate the computational complexity of calculating the values of some metrics for nonlocality and contextuality, completing the classification of possibilistic nonlocality scenarios, as well as other metrics of nonlocality analogous to our metric of maximal contextuality.