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Deep Neural Networks in a Mathematical Framework

Part of the SpringerBriefs in Computer Science Book Series

DOI: 10.1007/978-3-319-75304-1

ISBN: 978-3-319-75303-4

Publisher: Springer International Publishing - Springer Journals

Mar 23, 2018

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Chapter 1Introduction and Motivation

Caterini, Anthony L.; Chang, Dong Eui

Pages: 1 –10

[This chapter serves as a basic introduction to neural networks, including their history and some applications in which they have achieved state-of-the-art results.]
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Chapter 2Mathematical Preliminaries

Caterini, Anthony L.; Chang, Dong Eui

Pages: 11 –22

[Current mathematical descriptions of neural networks are either exclusively based on scalars or with loosely-defined vector-valued derivatives, which needs to be improved upon. Thus, in this chapter we build up the framework by introducing prerequisite mathematical concepts and notation for...
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Chapter 3Generic Representation of Neural Networks

Caterini, Anthony L.; Chang, Dong Eui

Pages: 23 –34

[In the previous chapter, we took the first step towards creating a standard mathematical framework for neural networks by developing mathematical tools for vector-valued functions and their derivatives. We use these tools in this chapter to describe the operations employed in a generic layered...
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Chapter 4Specific Network Descriptions

Caterini, Anthony L.; Chang, Dong Eui

Pages: 35 –58

[We developed an algebraic framework for a generic layered network in the preceding chapter, including a method to express error backpropagation and loss function derivatives directly over the inner product space in which the network parameters are defined. We dedicate this chapter to expressing...
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Chapter 5Recurrent Neural Networks

Caterini, Anthony L.; Chang, Dong Eui

Pages: 59 –79

[We applied the generic neural network framework from Chap. 3 to specific network structures in the previous chapter. Multilayer Perceptrons and Convolutional Neural Networks fit squarely into that framework, and we were also able to modify it to capture Deep Auto-Encoders. We now extend the...
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Chapter 6Conclusion and Future Work

Caterini, Anthony L.; Chang, Dong Eui

Pages: 81 –82

[This chapter serves as a conclusion of this book and provides possible directions for future research.]

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