LEARNING DYNAMICS OF SIMPLE PERCEPTRONS WITH NON-EXTENSIVE COST-FUNCTIONS

A Tsailis-statistics-based generalization of the gradient descent dyna mics (using non-extensive cost functions), recently introduced by one of us, is proposed as a learning rule in a simple perceptron. The resu lting Langevin equations are solved numerically for different values o f an index q (q = 1 and q not equal 1 respectively correspond to the e xtensive and non-extensive cases) and for different cost functions. Th e results are compared with the learning curve (mean error versus time ) obtained from a learning experiment carried out with human beings, s howing an excellent agreement for values of q slightly above unity. Th is fact illustrates the possible importance of including some degree o f non-locality (non-extensivity) in computational learning procedures, whenever one wants to mimic human behaviour.