Equilibration of deep neural networks and carrier chirality in Rashba systems
View / Open Files
Authors
Advisors
Conduit, Gareth J
Date
2021-12-02Awarding Institution
University of Cambridge
Qualification
Doctor of Philosophy (PhD)
Type
Thesis
Metadata
Show full item recordCitation
Verpoort, P. (2021). Equilibration of deep neural networks and carrier chirality in Rashba systems (Doctoral thesis). https://doi.org/10.17863/CAM.68669
Abstract
This thesis reports results of studies conducted on the equilibration of two systems and consists of two parts: the first part deals with the optimisation of deep neural networks, whereas the second part with the decay of non-equilibrium states in strongly Rashba-coupled systems at low temperature.
Deep learning is a conceptually simple, highly effective, and widely used tool, yet there remains insufficient understanding for why it works. The optimisation of deep neural networks with common algorithms such as stochastic gradient descent performs unexpectedly well given the complexity of the underlying high-dimensional non-convex minimisation problem. The first part of this thesis therefore looks at the optimisation procedure from the perspective of statistical physics. This allows us to interpret the loss function landscape of deep neural networks as the counterpart of the potential energy landscape in molecular systems and the optimisation of the network as its equilibration dynamics. Using landscape exploration tools developed in theoretical chemistry, we resolve the structure of the loss function landscape, from which we can draw conclusions for the relaxational dynamics of typical optimisers and, consequently, for deep learning.
The second part investigates how a non-equilibrium charge-carrier chirality distribution in a clean, strongly Rashba-coupled system at low temperatures decays over time. We first motivate this analysis based on experimental studies of transport properties in Rashba materials at low temperatures and subject to external magnetic fields. We investigate whether chirality imbalances could serve as the source for those experimental observations and develop a framework that models the behaviour of such a system. We then proceed with a more general theoretical study of the equilibration mechanisms of chirality in low-temperature strongly Rashba-coupled systems and compute the relaxation timescales of those mechanisms.
Keywords
Condensed-matter physics, Machine learning, Deep neural networks, Loss-function landscapes, Deep learning, Solid-state physics, Rashba effect, Non-equilibrium physics
Sponsorship
This thesis is the outcome of doctoral studies conducted at the University of Cambridge with the financial support of the Engineering and Physical Sciences Research Council of the UK.
Funder references
EPSRC (2138907)
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.68669
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Licence URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk