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.

传统的人工神经网络训练方法无法系统地实现大数据的零错误率。一种新的训练方法包括三个步骤：首先从传统训练的参数创建一个辅助数据，其对应于克隆数据的损失函数的全局最小值；其次，创建辅助数据和原始数据的一个参数连续（混合）；第三，通过保持每次迭代的零错误训练率，从混合数据的辅助数据端到原始数据端迭代地训练模型。这种连续化方法通过将人工神经网络训练问题转换为训练参数空间中参数化变换的不动点的连续化问题，以动力系统中统一收缩映射定理来保证数值上的收敛。