  Following a Four Dimensional Renormalization approach to ultraviolet
divergences (FDR), we extend the concept of predictivity to non-renormalizable
quantum field theories at arbitrarily large perturbative orders. The idea of
topological renormalization is introduced, which keeps a finite value for the
parameters of the theory by trading the usual order-by-order renormalization
procedure for an order-by-order redefinition of the perturbative vacuum. One
additional measurement is then sufficient to systematically compute quantum
corrections at any loop order, with no need of absorbing ultraviolet infinities
in the Lagrangian.
