ABSTRACT
Artificial neural networks are large, complex dynamic systems often constructed to perform a function of practical value. The behavior of a network is determined by rules prescribing how each unit evolves with time under the influence of other network elements and external inputs. On the basis of these rules, computer simulations can be used to determine how well a network performs a desired task. If we want to develop an analytic approach to evaluating and understanding network performance, however, a detailed microscopic description involving every network element may be too complex to be of much value. Instead, we need a macroscopic description using a small number of variables that are more directly related to the task being evaluated. By analogy, a person designing a system to handle gases does not want to deal with individual molecular positions and collisions, but rather needs to know about density and pressure. The statistical approach discussed here is a method for deriving, from the microscopic rules governing a network, a macroscopic description that is both simpler and more directly applicable to the evaluation of network function.
