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Elman recurrent network is a representative model with feedback mechanism. Although gradient descent method has been widely used to train Elman network, it frequently leads to slow convergence. According to optimization theory, conjugate gradient method is an alternative strategy in searching the descent direction during training. In this paper, an efficient conjugate gradient method has been presented to reach the optimal solution in two ways: (1) constructing a more effective conjugate coefficient, (2) determining adaptive learning rates in terms of the generalized Armijo search method. Experiments show that the performance of the new algorithm is superior to traditional algorithms, such as gradient descent method and conjugate gradient method. In particular, the new algorithm has better performance than the evolutionary algorithm. Finally, we prove the weak and strong convergence of the presented algorithm, i.e., the gradient norm of the error function with respect to the weight vectors converges to zero and the weight sequence approaches a fixed optimal point. [ABSTRACT FROM AUTHOR]

Find the global optimal solution of the model is one promising research topic in computational intelligent community. Dependent on analogies to natural processes, the evolutionary swarm intelligent algorithms are widely used for solving global optimization problems which directed by the fitness values. In this paper, we propose one efficient fractional global learning machine (Fragmachine) which includes two stages (descending and ascending) to determine the optimal search path. The neural network model is used to approach the given fitness value. Specifically, for the descending stage, the integer gradient of the network output with respect the current location is employed to find the next descending point, while for the ascending stage, the fractional gradient is implemented to climb and escape from the local optimal point. We further propose one adaptive learning rate during training which relies on both the current gradient (integer or fractional) information and the fitness value. Finally, a series of numerical experiments verify the effectiveness of the proposed algorithm, Fragmachine. [ABSTRACT FROM AUTHOR]