Group equivariant non-expansive operators and deep learning

In this talk we illustrate a new mathematical model for machine learning, which follows from the assumption that data cannot be studied directly, but only through the action of agents that transform them. In our framework each agent is represented by a group equivariant non-expansive operator acting on data. After endowing the space of agents with a suitable metric, we describe the main topological and geometrical properties of this space by means of methods developed for topological data analysis.