Error-free Training for Artificial Neural Network
This addresses the challenge of systematic error-free training in machine learning, which is incremental as it builds on existing methods with a theoretical guarantee.
The paper tackles the problem of achieving zero error rate in training artificial neural networks for large datasets, and presents a continuation method that guarantees convergence to a global minimum by constructing a homotopy between auxiliary and original data.
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.