Digital neural networks, matched filters and optical implementations

There has been much interest in the possibility of implementing associative memories using optical techniques, much of it centred recently around implementations of the Hopfield model of a neural network. In this chapter, we show how this model can be recast in terms of ‘matched filters’ whose properties have been well studied in electrical engineering. From this observation, we are then able to present the Hopfield neural network as a bank of filters and a thresholding stage. This formalism allows one to analyse the operation of the filter bank and its associated threshold without resort to digital simulation. A prime purpose of this approach has been to set the foundations in place for a detailed analysis of the scale-ability of an optical implementation and to allow some specification to be placed upon the requirements of the thresholding elements to be used since the signal-to-noise performance and memory size requirements to meet any reasonably complex network requirement remain uncertain. To our knowledge, this latter work remains incomplete, so that here we outline the problem and indicate why optical elements offer some new opportunities over and above electronic implementations.