Learning dynamics of simple perceptrons with non-extensive cost functions

SERGIO CANNAS; DANIEL STARIOLO; FRANCISCO TAMARIT

NETWORK-COMPUTATION IN NEURAL SYSTEMS

INFORMA HEALTHCARE

Lugar: London; Año: 1996 vol. 7 p. 141 - 149

0954-898X

A Tsallis-statistics-based generalization of the gradient descent dynamics (using nonextensive cost functions), recently introduced by one of us, is proposed as a learning rule in a simple perceptron. The resulting Langevin equations are solved numerically for different values of an index q (q = 1 and q 6= 1 respectively correspond to the extensive and non-extensive cases) and for different cost functions. The results are compared with the learning curve (mean error versus time) obtained from a learning experiment carried out with human beings, showing an excellent agreement for values of q slightly above unity. This fact illustrates the possible importance of including some degree of non-locality (non-extensivity) in computational learning procedures, whenever one wants to mimic human behaviour