Complexity of multiverse networks and their multilayer generalization

Multiverse networks were recently proposed as a method for promoting more effective transfer learning. While an extensive analysis was proposed, this analysis failed to capture two main aspects of these networks: (i) the rank of the representation is much lower than the rank predicted by the analysis; and (ii) the contribution of increased multiplicity in such networks diminishes quickly. In this work, we propose additional analysis of multiverse networks which addresses both deficits. A major contribution of our work is quantifying the Rademacher complexity of the multiverse network. It is shown that the complexity upper bound of multiverse networks is significantly lower than that of conventional networks, and diminishes by a factor of √k, k being the multiplicity. In addition, we generalize the notion of multiverse networks to multilayer multiverse networks. We derive the Rademacher complexity formula to such networks and present experimental results.