Neural networks can continue learning after training with training data sets, bootstrapping from their initial training to more advanced responses. AlphaGo, Google's machine-learning based Go playing software, was initially trained on large though relatively limited set of game data. Then AlphaGo completed its training by playing against itself. The strategy was so effective that when Go masters saw many of its moves, they thought they were mistakes. It was only after carefully looking at the moves that they realized that AlphaGo was often playing with a unique, and powerful style.
Similarly, Matthew Lai's Giraffe artificial intelligence machine was initially trained on a very large set of chess data. Then, he had Giraffe play against itself. As it played and evaluated the results of its decisions, it trained itself to get much better. Intelligent program can teach themselves to surpass their initial training.
Brain clones will improve their impersonation of you by trying things and then receiving feedback from a companion program about the accuracy of the impersonation. As a result, they will be able to bootstrap beyond the training data that you provide.