Neural Network Models

The Artificial Neural Network (ANN) models gained a wide popularity owing to a number of claimed advantages such as biological plausibility, tolerance with respect to errors or noise in the input data, learning ability allowing an adaptability to environmental constraints. Notwithstanding the fact that most of these advantages are not typical only of ANNs, engineers, psychologists and neuroscientists made an extended use of ANN models in a large number of scientific investigations. In most cases, however, these models have been introduced in order to provide optimization tools more useful than the ones commonly used by traditional Optimization Theory. Unfortunately, just the successful performance of ANN models in optimization tasks produced a widespread neglect of the true – and important – objectives pursued by the first promoters of these models. These objectives can be shortly summarized by the manifesto of connectionist psychology, stating that mental processes are nothing but macroscopic phenomena, emergent from the cooperative interaction of a large number of microscopic knowledge units. This statement – wholly in line with the goal of statistical mechanics – can be readily extended to other processes, beyond the mental ones, including social, economic, and, in general, organizational ones. Therefore this chapter has been designed in order to answer a number of related questions, such as: are the ANN models able to grant for the occurrence of this sort of emergence? How can the occurrence of this emergence be empirically detected? How can the emergence produced by ANN models be controlled? In which sense the ANN emergence could offer a new paradigm for the explanation of macroscopic phenomena? Answering these questions induces to focus the chapter on less popular ANNs, such as the recurrent ones, while neglecting more popular models, such as perceptrons, and on less used units, such as spiking neurons, rather than on McCulloch-Pitts neurons. Moreover, the chapter must mention a number of strategies of emergence detection, useful for researchers performing computer simulations of ANN behaviours. Among these strategies it is possible to quote the reduction of ANN models to continuous models, such as the neural field models or the neural mass models, the recourse to the methods of Network Theory and the employment of techniques borrowed by Statistical Physics, like the one based on the Renormalization Group. Of course, owing to space (and mathematical expertise) requirements, most mathematical details of the proposed arguments are neglected, and, to gain more information, the reader is deferred to the quoted literature.