The mass information theory says that information itself has energy, which means it also has mass. So those changes imply the mass of the information.

But I don't know if the mass of the information can exist on its own or if it needs another mass to act on. Sort of like how an electron in a higher orbital has more mass than a lower energy electron because it has more energy in it. But that energy associated with the excited electron can't exist on its own unless it is emitted as a photon... Where it becomes a different form of energy.