Models of Artificial Neural Networks play an essential role in Artificial Intelligence. All ANN models must be trained before they are deployed to perform tasks. The majority of AI training is supervised. For large-scale models, there are no known methods to achieve 100% accuracy for supervised training. In this talk, I will discuss a newly discovered method that can train ANN models to perfect precision. I will outline the ideas from Dynamical Systems that guarantee the convergence of the error-free training algorithm, and show simulations on the most popular benchmark data for training algorithms in the field. I will also discuss the relationship between the ANN training problem and the classification problem of finite points in Euclidean space that is based on the Stone–Weierstrass approximation theorem in Analysis.