  We calculate the anomalous dimensions of higher spin singlet currents in the
critical $O(N)$ vector model at order $1/N^2$. The results are shown to be in
agreement with the four-loop perturbative computation in $\phi^4$ theory in
$4-2\epsilon$ dimensions. It is known that the order $1/N$ anomalous dimensions
of higher-spin currents happen to be the same in the Gross-Neveu and the
critical vector model. On the contrary, the order $1/N^2$ corrections are
different. The results can also be interpreted as a prediction for the two-loop
computation in the dual higher-spin gravity.
