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We extend our study of phase transitions in the generalization behaviour ofmultilayer perceptrons with non-overlapping receptive fields to the problem ofthe influence of noise, concerning e.g. the input units and/or the couplingsbetween the input units and the hidden units of the second layer (='inputnoise'), or the final output unit (='output noise'). Without output noise, theoutput itself is given by a general, permutation-invariant Boolean function ofthe outputs of the hidden units. As a result we find that the phasetransitions, which we found in the deterministic case, mostly persist in thepresence of noise. The influence of the noise on the position of the phasetransition, as well as on the behaviour in other regimes of the loadingparameter $\alpha$, can often be described by a simple rescaling of $\alpha$depending on strength and type of the noise. We then consider the problem ofthe optimal noise level for Gibbsian and Bayesian learning, looking on replicasymmetry breaking as well. Finally we consider the question why learning witherrors is useful at all.Comment: LaTex, 39 pages, including 12 attached .eps-figure pages. To appear  in J. Phys.

Phase transitions in the generalization behaviour of multilayer perceptrons: II. The influence of noise