Application of different entropy formalisms in a neural network for novel word learning

Abstract

In this paper novel word learning in adults is studied. For this goal, four entropy formalisms are employed to include some degree of non-locality in a neural network. The entropy formalisms are Tsallis, Landsberg-Vedral, Kaniadakis, and Abe entropies. First, we have analytically obtained non-extensive cost functions for the all entropies. Then, we have used a generalization of the gradient descent dynamics as a learning rule in a simple perceptron. The Langevin equations are numerically solved and the error function (learning curve) is obtained versus time for different values of the parameters. The influence of index q and number of neuron N on learning is investigated for the all entropies. It is found that learning is a decreasing function of time for the all entropies. The rate of learning for the Landsberg-Vedral entropy is slower than other entropies. The variation of learning with time for the Landsberg-Vedral entropy is not appreciable when the number of neurons increases. It is said that entropy formalism can be used as a means for studying the learning.