Weight Initialization for Simultaneous Recurrent Neural Network Trained with a Fixed-point Learning Algorithm

Abstract

This letter presents a study of the Simultaneous Recurrent Neural network, an adaptive algorithm, as a nonlinear dynamic system for static optimization. Empirical findings, which were recently reported in the literature, suggest that the Simultaneous Recurrent Neural network offers superior performance for large-scale instances of combinatorial optimization problems in terms of desirable convergence characteristics improved solution quality and computational complexity measures. A theoretical study that encompasses exploration of initialization properties of the Simultaneous Recurrent Neural network dynamics to facilitate application of a fixed-point training algorithm is carried out. Specifically, initialization of the weight matrix entries to induce one or more stable equilibrium points in the state space of the nonlinear network dynamics is investigated and applicable theoretical bounds are derived. A simulation study to confirm the theoretical bounds on initial values of weights is realized. Theoretical findings and correlating simulation study performed suggest that the Simultaneous Recurrent Neural network dynamics possesses desirable stability characteristics as an adaptive recurrent neural network for addressing static optimization problems.