  In this paper, we explicitly prove that statistical manifolds, related to
exponential families and with flat structure connection have a Frobenius
manifold structure. This latter object, at the interplay of beautiful
interactions between topology and quantum field theory, raises natural
questions, concerning the existence of Gromov--Witten invariants for those
statistical manifolds. We prove that an analog of Gromov--Witten invariants for
those statistical manifolds (GWS) exists. Similarly to its original version,
these new invariants have a geometric interpretation concerning intersection
points of para-holomorphic curves. However, it also plays an important role in
the learning process, since it determines whether a system has succeeded in
learning or failed.
