Comment on noncommutative deformation of instantons

It was argued in Y. Maeda, A. Sako, Noncommutative deformation of instantons, J. Geom. Phys. 58 (2008) 1784] that the noncommutative deformation of instantons on a 4-torus T⁴$T^4$ should alter the instanton numbers for arbitrary noncommutativity parameter θ$\theta$. We show that this is not the case for the U(N²)$U\left(N^2\right)$ theory discussed there. And we discuss the instanton numbers in general gauge theories on the noncommutative T⁴$T^4$.