Learning by a nerual net in a noisy environment - The pseudo-inverse solution revisited

A recurrent neural net is described that learns a set of patterns {ξ µ } in the presence of noise. The learning rule is of a Hebbian type, and, if noise would be absent during the learning process, the resulting final values of the weights w ij would correspond to the pseudo-inverse solution of the fixed point equation in question. For a non-vanishing noise parameter, an explicit expression for the expectation value of the weights is obtained. This result turns out to be unequal to the pseudo-inverse solution. Furthermore, the stability properties of the system are discussed. Learning by a neural net in a noisy environment – The pseudo-inverse solution revisited2