[eutropia]

I think you meant to say that the mass accelerates opposite to forces acting upon it.

An idealized -M + M = 0 pair of particles (one normal, one negative mass) could experience runaway acceleration. Author touches on this in the paper as a potential source for the incredibly high-energy extra-galactic cosmic rays.

Granted, the paper describes a model in which something that acts like a particle with negative mass exerts this force upon things, but has no claims as to what a physical manifestation of this would look like.