Convergence analysis of recurrent neural network with self-loops based on eigenvalues of a connection matrix

Nonlinear Computability Based on Chaos

“…Consequently, many other researchers have proposed improvements to the Hopfield network approach. These approaches consist of (i) using the steepest descent method [Tachibana et al, 1995], (ii) manipulating the self-feedback coefficients based on eigenvalue/eigenvector analysis to accelerate the convergence [Tomikawa & Nakayama, 1995], (iii) addition of numerically induced chaos [Wang & Smith, 1998], or, the use of chaotic neurons [Hasegawa et al, 1995;Chen, 1993;Hasegawa et al, 1996;Aihara, 1990;] to avoid local minima, (iv) a combination of the previous two ideas [Chao et al, 1994], (v) attempting to obtain a unique optimal equilibrium (globally stable neural networks) throughout the manipulation of the neural interconnections [Kaszkurewicz & Bhaya, 1994], (vi) using transformational methods and subsequent application of the Lagrange method [Lau et al, 1995]. All of these methods have given improved solutions without, unfortunately, giving a final answer to the problem.…”