Learning phylogenetic trees as hyperbolic point configurations

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.