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Additional resources for Raptors of the World: An Identification Guide to the Birds of Prey of the World
Drawn from a standard normal distribution. 18) 0 otherwise where σ is a positive number that regulates the importance of randomness. Output to x is now variable because ε is drawn anew each time x is presented. 18), the probability of responding to x increases steadily as the input y = W · x increases. 18). In the former case, perceptron output is interpreted directly as the probability of responding. This is handy in theoretical analyses and to compare a model with data about average behavior.
For instance, we can add more layers of nodes, recurrent connections and more complex node dynamics. We thus can obtain complex models gradually from simple ones and study how their properties change in the process. This is also relevant when studying the evolution from simple to complex behavior (Chapter 5). In practice, our approach means that multilayer feedforward networks operating in discrete time are our first choice of model. Indeed, most applications of neu- 28 CHAPTER 1 ral networks are of this kind.
Reprinted by permission from Minsky and Papert (1969). Perceptrons. The MIT Press. els, however, are also rooted in mathematics, theories for intelligent machines and philosophy (Crevier 1993; Minsky 1969; Wang 1995). The development of neural network models started in earnest in 1943 when Warren McCulloch and Walter Pitts described how arbitrary logical operations could be carried out by networks of nodes (so-called formal neurons) that could either respond or not respond to an input, computed as the weighted sum of the activation state of other nodes in the network (McCulloch & Pitts 1943).