Recently claimed [1,2,3] anomalous nuclear effects in di-jet production are analyzed in view of multiple interaction of projectile/ejectile partons in nuclear matter. We derive model-independent relations between A-dependence of the cross section and nuclear broadening of transverse momentum. Comparison with the data show that initial/final state interaction of partons participating in hard process is hard as well. This is a solid argument in favor of smallness of a color neutralization radius of a hadronizing highly virtual quark.