JANUARY2017

I. Goodfellow, Y. Bengio, A. Courville. *Deep Learning*. Chapter 9, MIT Press, 2016.

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In chapter 9, Goodfellow et al. discuss convolutional networks in quite some detail. However, instead of focussing on the technical details, they discuss the high-level interpretations and ideas.

For example, they motivate the convolutional layer by sparse interactions, parameter sharing and equivariant representations. With sparse interactions, they refer to the local receptive field of individual units within convolutional networks (as the used kernels are usually small compared to the input size). Parameter sharing is achieved by using the same kernel at different spatial locations, such that neighboring units use the same weights. In this regard, some of the discussed alternative uses of convolution in neural networks are interesting. For example tiled convolution where different kernels are used for neighboring units by cycling through a fixed number of different kernels. Unshared convolution is also briefly discussed. Finally, equivariant representation refers to the translation invariance of the convolution operation.

Regarding pooling, they focus on the invariance introduced through pooling. However, they do not discuss the different pooling approaches used in practice. Unfortunately, They also don't give recommendations of when to use pooling and which pooling scheme to use. In contrast, they discuss the interpretation of pooling as infinitely strong prior. An interesting interpretation where pooling is assumed to place an infinitely strong prior on units invariant to local variations (like small translations or noise). In the same sense, convolutional layers place an infinitely strong prior on neighboring units having the same weights.

Finally, the importance of random and unsupervised features is briefly discusses. Here, an interesting reference is [1] where it is shown that random features work surprisingly well.

They conclude with a longer discussion of the biological motivation of convolutional networks given by neuroscience. While most of the discussed aspects are well-known, it is an interesting summary of different aspects motivating research in convolutional networks. Some of the main points is to distinguish simple and complex cells, and the simple cells in particular can often be modeled using Gabor filters. Another interesting insight is the low resolution used by the human eye. Only individual locations are available in higher resolution. Unfortunately, Goodfellow et al. do not provide many references how this model of attention can be implemented in modern convolutional networks.

On random weights and unsupervised feature learning. ICML, 2011.