2023/12/26 by Bo Deng, Deng, Bo · 1 citation
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.2312.16060
openalex publication_date 2023/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.