  We examine the continuous-time counterpart of mirror descent, namely mirror
flow, on classification problems which are linearly separable. Such problems
are minimised `at infinity' and have many possible solutions; we study which
solution is preferred by the algorithm depending on the mirror potential. For
exponential tailed losses and under mild assumptions on the potential, we show
that the iterates converge in direction towards a $\phi_\infty$-maximum margin
classifier. The function $\phi_\infty$ is the $\textit{horizon function}$ of
the mirror potential and characterises its shape `at infinity'. When the
potential is separable, a simple formula allows to compute this function. We
analyse several examples of potentials and provide numerical experiments
highlighting our results.
