Correction exponents in the Gross - Neveu - Yukawa model at $1\mathrm{/}{N}^2$

We calculate the critical exponents ${\omega }_{\pm }$ in the $d$-dimensional Gross-Neveu model in $1\mathrm{/}N$ expansion with $1\mathrm{/}{N}^2$ accuracy. These exponents are related to the slopes of the $\beta$-functions at the critical point in the Gross - Neveu - Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations.