Projects per year
Abstract
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of stateofthe art software on a large scale image classification problem. We finish with references to the current literature.
Original language  English 

Pages (fromto)  860–891 
Number of pages  32 
Journal  SIAM Review 
Volume  61 
Issue number  4 
DOIs  
Publication status  Published  6 Nov 2019 
Keywords
 back progagation
 chain rule
 convolution
 image classification
 neural network
 overfitting
 sigmoid
 stochastic gradient method
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Projects
 2 Finished

Data Analytics for Future Cities
Higham, D.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/15 → 31/12/19
Project: Research Fellowship

UK Quantum Technology Hub in Quantum Enhanced Imaging (Quantic)
Birch, D., Dawson, M., Dawson, M., Strain, M., Chen, Y., Gu, E., Li, D., Strain, M., Watson, I., Jeffers, J., Oppo, G. & Yao, A.
EPSRC (Engineering and Physical Sciences Research Council), HORIBA Jobin Yvon IBH Ltd
1/10/14 → 31/10/19
Project: Research