We define a new network structure to realize a continuous version of t
he Boltzmann machine (BM). Based on mean field (MF) theory for continu
ous and multidimensional elements named ''rotors,'' we derive the corr
esponding MF learning algorithm. Simulations demonstrate the learning
capability of this network for continuous and piecewise continuous map
pings. The rotor neurons ave specially suited for cyclic problems of a
rbitrary dimension.