Design and analyses of computational neural networks

In this paper, we develop two approaches for designing computation neural networks to solve computational problems. Intuitively, the direct feedforward approach, which originated from the concept of power series expansions, can solve all computational problems. Indirectly, we propose a computation-by-search (CBS) scheme, which can effectively solve some types of complicated problems, when their search functions can be easily obtained from existing neural networks. The convergence of the CBS neural networks to achieve the true solution is discussed and analyzed. Both theoretical analyses and simulated results show that the proposed neural networks can effectively solve complicated computational problems and find the real roots of higher-order polynomials.