OPTIMAL MAPPING OF THE CONFIGURATION SPACE OF A NETWORK OF NEURONS.

Summary form only given. The authors have used simulated annealing to map the N dimensional configuration space of a network of N binary neurons into observation spaces of three or four dimensions. This mapping minimizes the difference between distances over a neighborhood in the configuration space and the corresponding distances in the observation space for a choice of a metric in each space. In one such mapping, the Hamming distance in the configuration space is represented by Euclidean distance in the observation space. The distribution of points on the resultant maps approximates a spherical surface, and shows a hierarchical organization which is a consequence of the approximate ultrametricity of the configuration space. Application of this mapping to the analysis of simulated and real networks are discussed.