  We predict the universal power law dependence of localization length on
magnetic field in the strongly localized regime. This effect is due to the
orbital quantum interference. Physically, this dependence shows up in an
anomalously large negative magnetoresistance in the hopping regime. The reason
for the universality is that the problem of the electron tunneling in a random
media belongs to the same universality class as directed polymer problem even
in the case of wave functions of random sign. We present numerical simulations
which prove this conjecture. We discuss the existing experiments that show
anomalously large magnetoresistance. We also discuss the role of localized
spins in real materials and the spin polarizing effect of magnetic field.

Disordered Systems and Neural Networks