Capacity of k-gridgraphs as associative memory

Bienenstock and C. von der Malsberg propose a graph based method to model memory and visual pattern recognition. It involves modeling each remembered picture as a subgraph of global memory, where each of these subgraphs is a simple grid, each vertex with four neighbors; above, below, to the right and to the left, with each vertex labeled either black or white. Each vertex can be in many different subgraphs. In this paper we calculate the capacity of a given memory (vertex size) that will still allow good pattern recognition. We give this as a function of the allowed degradation of matched input. This is done using probabilistic and graph theoretical methods.