Finite Size Scaling in Neural Networks
Walter Nadler, Wolfgang Fink · Physical Review Letters · 1997
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 ${\ensuremath{\alpha}}_{c}$ from simulations of relatively small systems. We illustrate this approach by determining ${\ensuremath{\alpha}}_{c}$, together with the finite size scaling exponent $\ensuremath{ u}$, for storing Gaussian patterns in committee and parity machines with binary couplings and up to $K\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5$ hidden units.