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1 - Formalizing Deep Neural Networks

from Part I - Theory of Deep Learning for Image Reconstruction

Published online by Cambridge University Press:  15 September 2023

Jong Chul Ye
Affiliation:
Korea Advanced Institute of Science and Technology (KAIST)
Yonina C. Eldar
Affiliation:
Weizmann Institute of Science, Israel
Michael Unser
Affiliation:
École Polytechnique Fédérale de Lausanne
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Summary

We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares and cross-entropy criteria, respectively.

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Publisher: Cambridge University Press
Print publication year: 2023

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