On-line learning in the Ising perceptron
Michal Rosen‐Zvi · Journal of Physics A Mathematical and General · 2000
On-line learning of both binary and continuous rules in an Ising space is studied. Learning is achieved by using an artificial parameter, a weight vector , which is constrained to the surface of a hypersphere (spherical constraint). In the case of a binary rule the generalization error decays to zero super-exponentially as exp (- C α 2 ), where α is the number of examples divided by N , the size of the input vector, and C >0. Much faster learning is obtained in the case of continuous activation functions where the generalization error decays as exp (-e |λ|α ). The number of steps required for perfect learning is estimated for both scenarios and compared with simulations.