Abstract

Difficulties of the Hopfield-Tank (H-T) model reported by Wilson-Pawley [Bio-Cybern. 58, 63 (1988)] in a scale up Travelling Salesman Problem (TSP) have been clarified and repudiated. H-T [Bio-Cybern. 52, 141 (1985)] have successfully integrated the decaying Hamiltonian, H(Vi; a, b, c) equation dU_i/dt =(U_i/t) – [∂H(V_j; a, b, c)/∂V_i] for the neuron input U_i given the neuron output V_i by a sigmoid mapping V_i = g(U_i).An improvement is the conservative dynamics eliminating time-consuming computation for every iteration of each analog neuron (good for a buzz-booming real world) and the self-denying interconnect T_ii < 0 (necessary for VLSI resistive coupling). H-T dynamics is weakened by degenerate ground states due to those deliberately imprecise and inhibitory constraints (modeling the Mother Nature). In artificial problems, a hybrid neuron model consisting of a binary neuron with analog interconnects inputting intercity distances may be efficient. A decisive yes-visit-or-no-visit binary neuron may be better than a wishy-washy sigmoid neuron, for it can revive the ball-balancing game rolling over the energy landscape. The zero diagonal interconnect matrix means no self-talk (traceless T_ii = 0), which is best for the absolute convergence theorem (self-promoting T_ii > 0 may be OK, but self-denying T_ii < 0 is bad) for asynchronous and democratic voting updates by peer neurons excluding itself.

© 1988 Optical Society of America