  Conventional training methods for artificial neural network (ANN) models
never achieve zero error rate systematically for large data. A new training
method consists of three steps: first create an auxiliary data from
conventionally trained parameters which correspond exactly to a global minimum
for the loss function of the cloned data; second create a one-parameter
homotopy (hybrid) of the auxiliary data and the original data; and third train
the model for the hybrid data iteratively from the auxiliary data end of the
homotopy parameter to the original data end while maintaining the zero-error
training rate at every iteration. This continuationmethod is guaranteed to
converge numerically by a theorem which converts the ANN training problem into
a continuation problem for fixed points of a parameterized transformation in
the training parameter space to which the Uniform Contraction Mapping Theorem
from dynamical systems applies.
