English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Neural network models are one of the most successful approaches to machinelearning, enjoying an enormous amount of development and research over recentyears and finding concrete real-world applications in almost any conceivablearea of science, engineering and modern life in general. The theoreticalunderstanding of neural networks trails significantly behind their practicalsuccess and the engineering heuristics that have grown up around them. Randommatrix theory provides a rich framework of tools with which aspects of neuralnetwork phenomenology can be explored theoretically. In this thesis, weestablish significant extensions of prior work using random matrix theory tounderstand and describe the loss surfaces of large neural networks,particularly generalising to different architectures. Informed by thehistorical applications of random matrix theory in physics and elsewhere, weestablish the presence of local random matrix universality in real neuralnetworks and then utilise this as a modeling assumption to derive powerful andnovel results about the Hessians of neural network loss surfaces and theirspectra. In addition to these major contributions, we make use of random matrixmodels for neural network loss surfaces to shed light on modern neural networktraining approaches and even to derive a novel and effective variant of apopular optimisation algorithm.  Overall, this thesis provides important contributions to cement the place ofrandom matrix theory in the theoretical study of modern neural networks,reveals some of the limits of existing approaches and begins the study of anentirely new role for random matrix theory in the theory of deep learning withimportant experimental discoveries and novel theoretical results based on localrandom matrix universality.

Random matrix theory and the loss surfaces of neural networks