Learning capability and storage capacity of two-hidden-layer feedforward networks

In this paper, we present a new class of quasi-Newton methods for an effective learning in large multilayer perceptron (MLP)-networks. The algorithms introduced in this work, named LQN, utilize an iterative scheme of a generalized BFGS-type method, involving a suitable family of matrix algebras L. The main advantages of these innovative methods are based upon the fact that they have an O(nlogn) complexity per step and that they require O(n) memory allocations. Numerical experiences, performed on a set of standard benchmarks of MLP-networks, show the competitivity of the LQN methods, especially for large values of n.