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Title: Dynamical systems theory for transparent symbolic computation in neuronal networks
Author: Carmantini, Giovanni Sirio
ISNI:       0000 0004 6057 4209
Awarding Body: University of Plymouth
Current Institution: University of Plymouth
Date of Award: 2017
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In this thesis, we explore the interface between symbolic and dynamical system computation, with particular regard to dynamical system models of neuronal networks. In doing so, we adhere to a definition of computation as the physical realization of a formal system, where we say that a dynamical system performs a computation if a correspondence can be found between its dynamics on a vectorial space and the formal system’s dynamics on a symbolic space. Guided by this definition, we characterize computation in a range of neuronal network models. We first present a constructive mapping between a range of formal systems and Recurrent Neural Networks (RNNs), through the introduction of a Versatile Shift and a modular network architecture supporting its real-time simulation. We then move on to more detailed models of neural dynamics, characterizing the computation performed by networks of delay-pulse-coupled oscillators supporting the emergence of heteroclinic dynamics. We show that a correspondence can be found between these networks and Finite-State Transducers, and use the derived abstraction to investigate how noise affects computation in this class of systems, unveiling a surprising facilitatory effect on information transmission. Finally, we present a new dynamical framework for computation in neuronal networks based on the slow-fast dynamics paradigm, and discuss the consequences of our results for future work, specifically for what concerns the fields of interactive computation and Artificial Intelligence.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Automata Theory ; Recurrent Neural Networks ; Representation Theory ; Neural Symbolic Computation ; Dynamical Systems ; Symbolic Dynamics