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.