AbslracL The learning of a set of p randam patterns in a linear perceptmn is Sudied in the limit of a large number ( N ) of input unit5 with noise on the weights. inputs and output. The pmblem is formulated in continuous time as a langevin equation, and the fin1 task is to evaluate the response ar Green's function for the system. Whitr noise on the output is shown lo correspond to spatially " e l a t e d weight noise acting only in a subspace of Ule weight space. It is shown that the input noise acts as a simple weight decay with a sue pmponional to the load p m " l e r a = p / N . With no weight decay, the relaxation time diverges at c ( = 1. With B weight decay it k a m e s shoner, and finite for CI = 1, but at the mst of a larger asymptotic learning e m r that is is found analytically. It is shown that a small weight decay decreases the effect of noisz on the weights or outputs.
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