B Atch G Radient M Ethod for T Raining of P I - Sigma N Eural N Etwork with P Enalty

In this letter, we describe a convergence of batch gradient method with a penalty condition term for a narration feed forward neural network called pi-sigma neural network, which employ product cells as the output units to inexplicit amalgamate the capabilities of higher-order neural networks while using a minimal number of weights and processing units. As a rule, the penalty term is condition proportional to the norm of the weights. The monotonicity of the error function with the penalty condition term in the training iteration is firstly proved and the weight sequence is uniformly bounded. The algorithm is applied to carry out for 4-dimensional parity problem and Gabor function problem to support our theoretical findings.