FINITE-SIZE-SCALING OF THE BAYESIAN PERCEPTRON

We study numerically the properties of the Bayesian perception through a gradient descent on the optimal cost function. The theoretical dist ribution of stabilities is deduced. It predicts that the optimal gener alizer lies close to the boundary of the space of (error-free) solutio ns. The numerical simulations are in good agreement with the theoretic al distribution. The extrapolation of the generalization error to infi nite input space size agrees with the theoretical results. Finite size corrections are negative and exhibit two different scaling regimes, d epending on the training set size. The variance of the generalization error vanishes for N-->oo confirming the property of self-averaging.