Feedforward Neural Networks: Algorithms and Optimization Approaches

The backpropagation neural network algorithm represents one of the most advanced optimization solutions. This paper examines the widely-used feedforward neural networks and discusses key algorithmic improvements. While the error backpropagation (BP) algorithm dominates weight learning approaches, it suffers from limitations like local minima and slow convergence. The Levenberg-Marquardt optimization-based algorithm addresses some issues but neglects second-order terms. This research explores approximate Hessian matrix computation when error functions are nonlinear and second-order term S(W) becomes significant, providing enhanced network training methodology with implementation insights.

The Conjugate Gradient Method: Bridging Gradient Descent and Newton's Method

The Conjugate Gradient (CG) method serves as an intermediate approach between Steepest Descent and Newton's Method. It leverages only first-order derivative information while overcoming the slow convergence of Steepest Descent and avoiding the computational burden of storing, computing, and inverting the Hessian matrix required by Newton's Method. The CG method is not only one of the most useful techniques for solving large linear systems but also stands as one of the most efficient algorithms for large-scale nonlinear optimization problems. In implementation, CG typically uses iterative updates with conjugate directions computed through recurrence relations rather than matrix operations.