Quantum Structures for Cognition, Linguistics and Artificial Intelligence

This project falls within the EPSRC Artificial Intelligence research area, at the crossroad of the EPSRC themes "Mathematical Sciences" and "Quantum Technologies".

Following a recent line of work on Categorical Compositional Distributional (DisCoCat) models of meaning, we investigate how the mathematical tools developed in the context of quantum theory can apply to the study of human cognition and artificial intelligence. In the same way as Eilenberg and MacLane first formulated category theory as a language for the translation between geometry and algebra, DisCoCat models allow to translate between the statistical and the logical approaches to natural language semantics.

The overall aim of the project is to extend this duality to the interface between human and machine thinking: working towards a bridge from symbolic methods on one side, characterising intelligence in terms of abstract logical
processes; and the connectionnist approach on the other, which models thinking as the emerging behaviour of a complex network of basic processing units. In the first direction, this would allow to use methods from machine learning to
investigate models of human cognition; and in the opposite direction we can hope to design architectures for machine learning systems which are motivated from a cognitive perspective. Thus, the project aims at transdisciplinarity and we will make use of tools from modern mathematics in order to borrow concepts from and translate between computer science, linguistics, philosophy and physics. In particular, diagrammatic reasoning and related methods inspired from
categorical quantum mechanics will be used to translate human language into graphical representations, which can then be used to reason about natural language processing tasks such as reference resolution and question answering.
String diagrams in the category of relations, once generalised to account for cognitive structures, would allow to model database schema, neural network architectures and the translation between them as part of a unified framework,
driven by natural language syntax. Going beyond syntax and semantics into pragmatics, this line of work aims at understanding language and cognition in context.

Hence, we will explore two broad directions towards formalising contextual reasoning: on one hand, methods from game theory would naturally apply to the problem of question answering; on the other, reference resolution has been formulated using the computational tools developed for studying contextuality in quantum mechanics. This three-way connection between computation, games and quantum theory can be traced back to von Neumann as a common founding father to the three fields. It has ongoing developments in demonstrating quantum supremacy: players with access to the non-locality of shared quantum resources can outperform any classical strategy. We believe it should also play a role in getting a deeper structural understanding of recent developments in neural network architecture and their relation to human cognition, such as interhemispheric switching and generative adversarial networks.