Reprinted from JOURNAL OF ST.'TISTICAL PHYSICS Vol. I, No.2.1~69 Printed in Bel,.~m

Learning of patterns by neural networks obeying general rules of sensory transductl and of converting membrane potentials to spiking frequencies is considered. A finite number of cells Ol can sample a pattern playing on any finite number of cells without causing irrevocable sampling bias if Ol = f:H or Ol () f:H = 1". Total eneJ transfer from inputs of Ol to outputs of f:H depends on the entropy of the input distril tion. Pattern completion on recall trials can occur without destroying perfect mem< even if Ol = f:H by choosing the signal thresholds sufficiently large. The mathemati results are global limit and oscillation theorems for a class of nonlinear functiolJ differential systems. a.l-