Inhibitory grids and the assignment problem.

A family of symmetric neural networks that solve a simple version of the assignment problem (AP) is analyzed. The authors analyze the suboptimal performance of these networks and compare the results to optimal answers obtained by linear programming techniques. They then use the interactive activation model to define the network dynamics-a model that is closely related to the Hopfield-Tank model. A systematic analysis of hypercube corner stability and eigenspaces of the connection strength matrix leads to network parameters that give feasible solutions 100% of the time and to a projection algorithm that significantly improves performance. Two formulations of the problem are discussed: (i) nearest corner: encode the assignment numbers as initial activations, and (ii) lowest energy corner: encode the assignment numbers as external inputs.

K-winner networks.

A special class of mutually inhibitory networks is analyzed, and parameters for reliable K-winner performance are presented. The network dynamics are modeled using interactive activation, and results are compared with the sigmoid model. For equal external inputs, network parameters that select the units with the larger initial activations (the network converges to the nearest stable state) are derived. Conversely, for equal initial activations, networks that select the units with larger external inputs (the network converges to the lowest energy stable state) are derived. When initial activations are mixed with external inputs, anomalous behavior results. These discrepancies are analyzed with several examples. Restrictions on initial states are derived which ensure accurate K-winner performance when unequal external inputs are used.