ABSTRACT
A neural network is a collection of interconnected elements or units. Beyond that nearly trivial characterization, the phrase neural network means an amazing variety of things to a remarkable diversity of researchers. For biologists, of course, it refers to a mass of grey matter or, perhaps, a biologically faithful model of some part of the brain. For psychologists and other cognitive scientists, ‘neural’ (or ‘connectionist’) network denotes a virtual machine architecture that has come to be seriously considered as a model of the mind. In this book, however, we put aside neuroscience and cognitive science, and regard a neural network as a purely formal object—or better, as a rich family of formal objects. For even narrowing our scope to purely mathematical perspectives, ‘neural network’ still has a striking diversity of construals. For example, the following perspectives are all represented in this book (the terms used will all be defined several times throughout the book, at multiple levels of detail).
