Deep Neural Networks in a Mathematical Framework

  • Anthony L. Caterini
  • Dong Eui Chang

Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Anthony L. Caterini, Dong Eui Chang
    Pages 1-10
  3. Anthony L. Caterini, Dong Eui Chang
    Pages 11-22
  4. Anthony L. Caterini, Dong Eui Chang
    Pages 23-34
  5. Anthony L. Caterini, Dong Eui Chang
    Pages 35-58
  6. Anthony L. Caterini, Dong Eui Chang
    Pages 59-79
  7. Anthony L. Caterini, Dong Eui Chang
    Pages 81-82
  8. Back Matter
    Pages 83-84

About this book


This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks.

This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.


deep learning machine learning neural networks multilayer perceptron convolutional neural networks recurrent neural network autoencoder backpropagation artificial intelligence gradient descent

Authors and affiliations

  • Anthony L. Caterini
    • 1
  • Dong Eui Chang
    • 2
  1. 1.Department of StatisticsUniversity of OxfordOxfordUnited Kingdom
  2. 2.School of Electrical EngineeringKorea Advanced Institute of Science and TechnologyDaejeonKorea (Republic of)

Bibliographic information