 requiring operational saving or driving new revenue growth. Deep learning is based on the perceptron model. The perceptron model, shown in Figure 8.7, was originally proposed in 1969 by Minsky and Papert [Min69]. A perceptron is a nonlinear computa- tional unit, which is capable of learning to partition simple patterns. It can accept both binary and continuous values. A single perceptron is represented by a set of parameters that include weights, W, and a bias. It is able to classify simple patterns into two classes by forming a half-plane decision region. A single perceptron, however, is unable to separate input patterns that require more complex decision bound- aries. For example, an exclusive OR problem cannot be solved by a single-layer perceptron. To overcome this restriction, one may introduce a hidden layer of neurons as shown in Figure 8.8. The three-layered network, which includes a set of M input features, two hidden layers, and an output layer of N nodes, is able to resolve arbitrary complex problems. Different applications may require adjusting the number of hidden layers and the number of respective neurons to attain a desired precision level. Multilayer perceptrons are feed-forward nets with neurons that are fully interconnected between adjacent layers, but which are separate within one layer. The weights associated with the arcs across all layers can be trained with a back-propagation algorithm, hence making these networks very attractive for classification problems. By expanding the number of neurons and layers used, one can classify very complex signals such as those used in speech, language, and video processing. For multidimensional signals, such as images, more advanced deep learners, known as convolutional networks [Lec98], have been commonly adopted. Those networks support multiple dimensions across each layer. One of the key advancements in deep learning is attributed to the discovery of the backpropaga- tion algorithm by Rumelhart et al. [Run86]. The algorithm enabled supervised training 