Artificial Neural Networks and Classification

In models of large networks of neurons, the behavior of individual neurons is treated in much simpler ways than in the Hodgkin–Huxley theory presented in Chap. 1 . Activity is usually represented by a binary variable (1 \(=\) firing and 0 \(=\) silent), and time is modeled by a discrete sequence of time steps running in synchrony for all neurons in the net. Besides activity, the most interesting state variable of such networks is synaptic strength, or weight, which determines the influence of each neuron on its neighbors in the network. Synaptic weights may change according to so-called learning rules, which create network connectivities optimized for the performance of various tasks. The networks are thus characterized by two state variables, a vector of neuron activities per time step and a matrix of neuron-to-neuron transmission weights describing the connectivity, which also depends on time. In this chapter, we will discuss the basic approach and apply it to an important network architecture used for pattern recognition tasks. Other problems of neural information processing will be addressed in Chap. 6 . The mathematical treatment is largely based on linear algebra (vectors and matrices) and, as in the other chapters, will be explained “on the fly.”