Finite size scaling in neural networks

We demonstrate that the fraction of pattern sets that can be stored in single- and hidden-layer perceptrons exhibits finite size scaling. This feature allows one to estimate the critical storage capacity α_c from simulations of relatively small systems. We illustrate this approach by determining α_c, together with the finite size scaling exponent υ, for storing Gaussian patterns in committee and parity machines with binary couplings and up to K = 5 hidden units.