  We propose a novel method for the inference of phylogenetic trees that
utilises point configurations on hyperbolic space as its optimisation
landscape. Each taxon corresponds to a point of the point configuration, while
the evolutionary distance between taxa is represented by the geodesic distance
between their corresponding points. The point configuration is iteratively
modified to increase an objective function that additively combines pairwise
log-likelihood terms. After convergence, the final tree is derived from the
inter-point distances using a standard distance-based method. The objective
function, which is shown to mimic the log-likelihood on tree space, is a
differentiable function on a Riemannian manifold. Thus gradient-based
optimisation techniques can be applied, avoiding the need for combinatorial
rearrangements of tree topology.
