Theory of impossible worlds: Toward a physics of information

In this paper, we introduce an innovative approach to the fusion between datasets in terms of attributes and observations, even when they are not related at all. With our technique, starting from datasets representing independent worlds, it is possible to analyze a single global dataset, and transferring each dataset onto the others is always possible. This procedure allows a deeper perspective in the study of a problem, by offering the chance of looking into it from other, independent points of view. Even unrelated datasets create a metaphoric representation of the problem, useful in terms of speed of convergence and predictive results, preserving the fundamental relationships in the data. In order to extract such knowledge, we propose a new learning rule named double backpropagation, by which an auto-encoder concurrently codifies all the different worlds. We test our methodology on different datasets and different issues, to underline the power and flexibility of the Theory of Impossible Worlds.