CAM Storage of Analog Patterns and Continuous Sequences with 3n2 Weights

Abstract

A simple architecture and algorithm for analytically guaranteed associa(cid:173) tive memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N 2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and four per chaotic attractor. There are no spurious attractors, and there is a Lia(cid:173) punov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incre(cid:173) mental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The archi(cid:173) tecture can be "folded" into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Hierarchical sensory-motor control networks may be constructed of interconnected "cortical patches" of these network modules. Network performance is being investigated by application to the problem of real time handwritten digit recognition.