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Training Deep Neural Networks

Abstract

The procedure for training neural networks with backpropagation is briefly introduced in Chapter 1 This chapter will expand on the description on Chapter 1 in several ways

“I hated every minute of training, but I said, ‘Don’t quit. Suffer now and live the rest of your life as a champion.”—Muhammad Ali

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Notes

  1. 1.

    Although the backpropagation algorithm was popularized by the Rumelhart et al. papers [408, 409], it had been studied earlier in the context of control theory. Crucially, Paul Werbos’s forgotten (and eventually rediscovered) thesis in 1974 discussed how these backpropagation methods could be used in neural networks. This was well before Rumelhart et al.’s papers in 1986, which were nevertheless significant because the style of presentation contributed to a better understanding of why backpropagation might work.

  2. 2.

    A different type of manifestation occurs in cases where the parameters in earlier and later layers are shared. In such cases, the effect of an update can be highly unpredictable because of the combined effect of different layers. Such scenarios occur in recurrent neural networks in which the parameters in later temporal layers are tied to those of earlier temporal layers. In such cases, small changes in the parameters can cause large changes in the loss function in very localized regions without any gradient-based indication in nearby regions. Such topological characteristics of the loss function are referred to as cliffs (cf. Section 3.5.4), and they make the problem harder to optimize because the gradient descent tends to either overshoot or undershoot.

  3. 3.

    In most of this book, we have worked with \(\overline{W}\) as a row-vector. However, it is notationally convenient here to work with \(\overline{W}\) as a column-vector.

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Aggarwal, C.C. (2018). Training Deep Neural Networks. In: Neural Networks and Deep Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-94463-0_3

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