  We study the strong coupling limit of AdS/CFT correspondence in the framework
of a recently proposed fermionic formulation of the Bethe Ansatz equations
governing the gauge theory anomalous dimensions. We provide examples of states
that do not follow the Gubser-Klebanov-Polyakov law at large 't Hooft coupling
$\lambda$, in contrast with recent results on the quantum string Bethe
equations valid in that regime. This result indicates that the fermionic
construction cannot be trusted at large $\lambda$, although it remains an
efficient tool to compute the weak coupling expansion of anomalous dimensions.
