A crucial element in the ability of artificial systems to include mechanisms for anticipation, inclusion and novelty search is the ability to efficiently explore the space of the Adjacent Possible introduced by S. Kauffman. Such a search requires the ability to explore the space of the possible using the information currently stored in the artificial system, along with a generative mechanism for including and selecting novel elements to improve the learning of the non-stationary reference system. To this end, we introduce the Dreaming Learning technique aimed to equip a neural network with an explorative tool for anticipating and predicting the potential new items or sequences per the previously stored knowledge. This method offers many advantages regarding resilience to unexpected paradigm shifts, non-stationary sequences, and auto-correlation. This latter is specifically relevant for improving the textual coherence in language models. However, this technique has the limitation that it can only operate on one-dimensional discrete-valued time sequences. To overcome this problem, we sought to exploit the nature of chaotic systems to make trajectories diverge on specific manifolds and be dissipative simultaneously. We then constructed artificial neural networks capable of controlling the spectrum of Lyapunov exponents as a regularization technique to be coupled with traditional learning algorithms based on backpropagation. The results are encouraging both in terms of defining chaotic attractors through their macroscopic features and making neural network learning of multi-dimensional non-stationary sequences much more prone to include and anticipate novelties.