  We call an ideal in a polynomial ring robust if it can be minimally generated
by a universal Gr\"obner basis. In this paper we show that robust toric ideals
generated by quadrics are essentially determinantal. We then discuss two
possible generalizations to higher degree, providing a tight classification for
determinantal ideals, and a counterexample to a natural extension for Lawrence
ideals. We close with a discussion of robustness of higher Betti numbers.
