  We present a general geometrical approach to the problem of escape from a
metastable state in the presence of noise. The accompanying analysis leads to a
simple condition, based on the norm of the drift field, for determining whether
caustic singularities alter the escape trajectories when detailed balance is
absent. We apply our methods to systems lacking detailed balance, including a
nanomagnet with a biaxial magnetic anisotropy and subject to a spin transfer
torque. The approach described within allows determination of the regions of
experimental parameter space that admit caustics.
