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If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model.
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For a single-layer perceptron with multiple output units, since the weights of one output unit are completely separate from all the others', the same algorithm can be run for each output unit. For multilayer perceptrons, where a hidden layer exists, more sophisticated algorithms such as backpropagation must be used.
The third covers multi-layer and cross-coupled perceptrons, and the fourth back-coupled perceptrons and problems for future study. Rosenblatt used the book to teach an interdisciplinary course entitled "Theory of Brain Mechanisms" that drew students from Cornell's Engineering and Liberal Arts colleges.
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