Communicated by Christoph zyxwvu von der Malsburg zyxwv Parallel Activation of Memories in an Oscillatory Neural Network D. Horn M. Usher zyxwvut Sclrool of Physics and Astronomy, Raynioiid arid Bezwrly Sacklev Faculty zyxwvu of Exact Sciences, Tel Avizi University, Tel Aviv 69978, Israel We describe a feedback neural network whose elements possess dy- namic thresholds. This network has an oscillatory mode that we in- vestigate by measuring the activities of memory patterns as functions of time. We observe spontaneous and induced transitions between the different oscillating memories. Moreover, the network exhibits pat- tern segmentation, by oscillating between different memories that are included as a mixture in a constant input. The efficiency of pattern segmentation decreases strongly as the number of the input memories is increased. Using oscillatory inputs we observe resonance behavior. 1 Introduction Attractor neural networks perform the task of pattern retrieval. This is usually carried out in the following way. One incorporates the pattern in question as a memory in the connections of a feedback network. Starting the network dynamics from an initial condition that is a distorted ver- sion of one of the memories, the network should flow into a fixed point corresponding to that memory. Once the fixed point is reached, pattern retrieval is accomplished. In a recent article, Wang, Buhmann and von der Malsburg (1990) sug- gested a modification of this procedure that addresses a slightly different question. Suppose one is given an input that is a composition of sev- eral of the memories. How can the network recognize all the individual components in parallel? This requires the network to retrieve all memory components while conserving the holistic property of the input. Their solution is based on a network of oscillators that are constructed by ap- propriately connected neurons. Their network, when presented with a continuous input that is a superposition of memories, oscillates in pat- terns determined by the mixed input, shifting from one to another as time goes on. In other words, it achieves pattern segmentation. This new type of behavior can also be easily obtained in a model that we have proposed (Horn and Usher 1989). In fact, it is a special Neural Coinputation 3, 3143 (1991) zyxwvu @ 1991 Massachusetts Institute of Technology