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Convolutional Neural Networks

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Abstract

Convolutional neural networks are designed to work with grid-structured inputs, which have strong spatial dependencies in local regions of the grid. The most obvious example of grid-structured data is a 2-dimensional image. This type of data also exhibits spatial dependencies, because adjacent spatial locations in an image often have similar color values of the individual pixels. An additional dimension captures the different colors, which creates a 3-dimensional input volume. Therefore, the features in a convolutional neural network have dependencies among one another based on spatial distances.

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Notes

  1. 1.

    Here, it is assumed that (L q − F q) is exactly divisible by S q in order to obtain a clean fit of the convolution filter with the original image. Otherwise, some ad hoc modifications are needed to handle edge effects. In general, this is not a desirable solution.

  2. 2.

    In recent years, subsampling also refers to other operations that reduce the spatial footprint. Therefore, there is some difference between the classical usage of this term and modern usage.

  3. 3.

    The top-5 error rate makes more sense in image data where a single image might contain objects of multiple classes. Throughout this chapter, we use the term “error rate” to refer to the top-5 error rate.

  4. 4.

    http://www.clarifai.com

  5. 5.

    Personal communication from Matthew Zeiler.

  6. 6.

    The original architecture also contained auxiliary classifiers, which have been ignored in recent years.

  7. 7.

    Typically, a 3 × 3 filter is used at a stride/padding of 1. This trend started with the principles in VGG, and was adopted by ResNet.

  8. 8.

    Under normal circumstances, one only backpropagates to hidden layers as an intermediate step to compute gradients with respect to incoming weights in that hidden layer. Therefore, backpropagation to input layer is never really needed in traditional training. However, backpropagation to the input layer is identical to that with respect to the hidden layers.

  9. 9.

    Example available at http://deeplearning.net/software/theano/tutorial/conv_arithmetic.html.

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    Charu C. Aggarwal

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Aggarwal, C.C. (2018). Convolutional Neural Networks. In: Neural Networks and Deep Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-94463-0_8

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