Skip to main content

Artificial Neural Networks and Backpropagation

Part of the Mathematics in Industry book series (MATHINDUSTRY,volume 37)

Abstract

Inspired by the biological neural network, here we discuss its mathematical abstraction known as the artificial neural network (ANN). Although efforts have been made to model all aspects of the biological neuron using a mathematical model, all of them may not be necessary: rather, there are some key aspects that should not be neglected when modeling a neuron. This includes the weight adaptation and the nonlinearity.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-981-16-6046-7_6
  • Chapter length: 22 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   69.99
Price excludes VAT (USA)
  • ISBN: 978-981-16-6046-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   89.99
Price excludes VAT (USA)
Fig. 6.1
Fig. 6.2
Fig. 6.3
Fig. 6.4
Fig. 6.5
Fig. 6.6
Fig. 6.7
Fig. 6.8

References

  1. V. Nair and G. E. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proceedings of the 27th International Conference on Machine Learning (ICML-10), 2010, pp. 807–814.

    Google Scholar 

  2. J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” Journal of Machine Learning Research, vol. 12, no. 7, pp. 2121–2159, 2011.

    MathSciNet  MATH  Google Scholar 

  3. T. Tieleman and G. Hinton, “Lecture 6.5-RMSprop: Divide the gradient by a running average of its recent magnitude,” COURSERA: Neural Networks for Machine Learning, vol. 4, no. 2, pp. 26–31, 2012.

    Google Scholar 

  4. D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.

    Google Scholar 

  5. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, no. 6088, pp. 533–536, 1986.

    CrossRef  Google Scholar 

  6. I. M. Gelfand, R. A. Silverman et al., Calculus of variations. Courier Corporation, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Ye, J.C. (2022). Artificial Neural Networks and Backpropagation. In: Geometry of Deep Learning. Mathematics in Industry, vol 37. Springer, Singapore. https://doi.org/10.1007/978-981-16-6046-7_6

Download citation