(Neurips 2025) One paper on a differentiable Gromov Hyperbolicity accepted
Work first authored by Pierre Houédry during his post-doc
Title: Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Abstract: ‘Trees and the associated shortest-path tree metrics provide a powerful framework for representing hierarchical and combinatorial structures in data. Given an arbitrary metric space, its deviation from a tree metric can be quantified by Gromov’s \delta-hyperbolicity. Nonetheless, designing algorithms that bridge an arbitrary metric to its closest tree metric is still a vivid subject of interest, as most common approaches are either heuristical and lack guarantees, or perform moderately well. In this work, we introduce a novel differentiable optimization framework, coined DeltaZero, that solves this problem. Our method leverages a smooth surrogate for Gromov’s \delta-hyperbolicity which enables a gradient-based optimization, with a tractable complexity. The corresponding optimization procedure is derived from a problem with better worst case guarantees than existing bounds, and is justified statistically. Experiments on synthetic and real-world datasets demonstrate that our method consistently achieves state-of-the-art distortion.’
