Competitive and Cooperative Dynamics in Optical Neural Networks

Abstract

Real-time holographic materials are in many ways ideally suited to neural network implementation. In an associative memory, for example, information may be stored in a distributed manner so that, from a partial or distorted input, an entire pattern can be recalled. When several distinct items of information are stored together in a distributed memory, how do the various information chunks become separated again when something is to be recalled? In particular, if an input resembles more than one stored pattern, how does a system decide on a single output? Such questions lead us to consider decision making in neural networks as a dynamical process that involves a competitive and cooperative interaction among the stored items in the memory. The mathematics describing this mode interaction is familiar to several areas of physics. In particular, the competitive cooperative process is aptly described by general Lotka-Volterra equations. Photorefractive two-beam coupling can be employed to establish a wide array of dynamical mode interactions. I will discuss the photorefractive flip-flop as the prototype example of a competitive system. The mode interaction of the two-state flip-flop can be extended to a multimode system to establish what is known in neural network parlance as “winner take all” dynamics. Cooperation can also be implemented with photorefractive two-beam coupling. We demonstrate the application of cooperative dynamics to “playback” a time sequence of modes in an optical ring resonator.