  Motivated by the study of big crunch singularities in asymptotically $AdS_4$
spacetimes, we consider a marginal triple trace deformation of ABJM theory. The
deformation corresponds to adding a potential which is unbounded below. In a 't
Hooft large N limit, the beta function for the triple trace deformation
vanishes, which is consistent with the near-boundary behavior of the bulk
fields. At the next order in the 1/N expansion, the triple trace couplings
exhibit non-trivial running, which we analyze explicitly in the limit of zero
't Hooft coupling, in which the model reduces to an $O(N)\times O(N)$ vector
model with large N. In this limit, we establish the existence of a perturbative
UV fixed point, and we comment on possible non-perturbative effects. We also
show that the bulk analysis leading to big crunch singularities extends to the
$\Zbar_k$ orbifold models dual to ABJM theory.
