Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706449 |
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Title: | Dynamical systems theory for transparent symbolic computation in neuronal networks | ||||||
Author: | Carmantini, Giovanni Sirio |
ISNI:
0000 0004 6057 4209
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Awarding Body: | University of Plymouth | ||||||
Current Institution: | University of Plymouth | ||||||
Date of Award: | 2017 | ||||||
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Abstract: | |||||||
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.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.706449 | DOI: | Not available | ||||
Keywords: | Automata Theory ; Recurrent Neural Networks ; Representation Theory ; Neural Symbolic Computation ; Dynamical Systems ; Symbolic Dynamics | ||||||
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