In the training of feedforward neural networks,it is usually suggested that the initial weights should be small in magnitude in order to prevent premature saturation.The aim of this paper is to point out the other side of the story:In some cases,the gradient of the error functions is zero not only for infinitely large weights but also for zero weights.Slow convergence in the beginning of the training procedure is often the result of sufficiently small initial weights.Therefore,we suggest that,in these cases,the initial values of the weights should be neither too large,nor too small.For instance,a typical range of choices of the initial weights might be something like(0.4,0.1) ∪(0.1,0.4),rather than(0.1,0.1) as suggested by the usual strategy.Our theory that medium size weights should be used has also been extended to a few commonly used transfer functions and error functions.Numerical experiments are carried out to support our theoretical findings. In the training of feedforward neural networks, it is usually suggest that the initial weights should be small in magnitude in order to prevent premature saturation. The aim of this paper is to point out the other side of the story: In some cases, the gradient of the error functions is zero not only for infinitely large weights but also for zero weights.Slow convergence in the beginning of the training procedure is often the result of small small initial weights.Therefore, we suggest that, in these cases, the initial values of the weights should be neither neither large nor nor too small. For instance, a typical range of choices of the initial weights might be something like (0.4,0.1) ∪ (0.1,0.4), rather than (0.1,0.1) as suggested by the usual strategy. Our theory that medium size weights should be used has also been extended to a few commonly used transfer functions and error functions. Numerical experiments are carried out to support our theoretical findings.