The compact analog neural network-model of a new paradigm for neural based optimization, and its hardware realization

Hopfield and Tank (1985) showed how a network of neurons, now popularly termed the Hopfield net, could be used to solve combinatorial optimization tasks. However, the Hopfield net is expensive in terms of hardware complexity. In order to solve a problem of size N with the Hopfield net, one needs to use O(N²) neurons and O(N⁴ ) interconnection weights. We propose a new neural architecture, termed the compact analog neural network, or CANN, which can be used to solve optimization problems. In contrast with the Hopfield net, the CANN requires O(N) neurons and O(N²) neurons to solve a problem of size N. We illustrate the CANN through the use of an example, and derive the energy function for the neural network. We use sequential chaotic annealing, a newly proposed optimization method, to minimize the energy function and compare the results with those obtained by using a simple gradient based minimization approach. Finally, we show how the CANN may be realized efficiently in hardware form