Neural network based on the linear programming for associative memory

Almost all the continuous neural networks available now for associative memory are based on optimizing a quadratic function, and each pattern to be recognized is used as an initial point of the network. The disadvantage is that their structure is complicated and their implementation of circuit is difficult to coincide with the theoretical analysis. In this paper, all the patterns considered are on the surface of one ball. Optimizing problem about the distance is sometimes equivalent to that about the inner product. A continuous neural network, which is based on the optimization of a linear function, is thus presented for associative memory, and the pattern to be recognized is regarded as the parameter of the network. It is in fact a network for solving a special optimization problem with hybrid constraint. It is proved that the set of prototype patterns is the same as the set of asymptotically stable equilibrium points. The basin of attraction of each desired memory pattern is distributed reasonably (in the Hamming distance sense) and an equilibrium point that is not asymptotically stable is just the state that can not be recognized. The theoretic analysis demonstrates not only that the proposed network is an ideal model for associative memory, but also that each refused pattern can be explained very clearly, and that the recognition result can be predicted by the motion of the network. The circuit implementation of the proposed network is very much like that for optimization problems. It can easily coincide with theoretical analysis. From the viewpoint of hardware implementation, there is no difference between the pattern to be recognized and the initial point of the network, they can all be regarded as the out inputs. Two numerical simulations show that the exact result can be obtained, although the bigger step and shorter simulation time are taken. The network in this paper thus can reduce requirement for the precision of the hardware.