Training Artificial Neural Networks with Reduced Computational Complexity

At least some embodiments of the present disclosure relate to a method of training an artificial neural network (ANN) for an artificial intelligence recognition. The method includes producing, by an ANN, outputs by feeding inputs of a training data set to the ANN; determining errors of the generated outputs from target outputs of the training data set; generating a first-order derivative matrix including first-order derivatives of the errors and a second-order derivative matrix including second-order derivatives of the errors; obtaining an approximation of the first-order derivative matrix or an approximation of the second-order derivative matrix by compressing the first-order derivative matrix or the second-order derivative matrix; and updating weights of the ANN based on the approximation of the first-order derivative matrix or the approximation of the second-order derivative matrix.