Methods and computer systems improve a trained base deep neural network by structurally changing the base deep neural network to create an updated deep neural network, such that the updated deep neural network has no degradation in performance relative to the base deep neural network on the training data. The updated deep neural network is subsequently training. Also, an asynchronous agent for use in a machine learning system comprises a second machine learning system ML2 that is to be trained to perform some machine learning task. The asynchronous agent further comprises a learning coach LC and an optional data selector machine learning system DS. The purpose of the data selection machine learning system DS is to make the second stage machine learning system ML2 more efficient in its learning (by selecting a set of training data that is smaller but sufficient) and/or more effective (by selecting a set of training data that is focused on an important task). The learning coach LC is a machine learning system that assists the learning of the DS and ML2. Multiple asynchronous agents could also be in communication with each others, each trained and grown asynchronously under the guidance of their respective learning coaches to perform different tasks.