Generalization performances of perceptrons

This paper presents new results about the confidence bounds on the generalization performances of perceptrons. It deals with regression problems. It is shown that the probability to get a generalization error greater than the empirical error plus a precision E, depends on the number of inputs and on the magnitude of the coefficients of the combination. The result presented does not require to bound a priori the magnitude of these coefficients, the size and the number of layers.