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Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

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Transition to chaos in extended systems and their quantum impurity models

Anomalous dissipation and other non-smooth phenomena in fluids

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Validation of short-pulse reflectometry turbulence measurements with a synthetic diagnostic

From low-rank retractions to dynamical low-rank approximation and back

A ride time-oriented scheduling algorithm for dial-a-ride problems

A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces

A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Stability: a search for structure

Transition to chaos in extended systems and their quantum impurity models

A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

A ride time-oriented scheduling algorithm for dial-a-ride problems

Anomalous dissipation and other non-smooth phenomena in fluids

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Stability: a search for structure

From low-rank retractions to dynamical low-rank approximation and back

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Validation of short-pulse reflectometry turbulence measurements with a synthetic diagnostic

A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces