Communication Dans Un Congrès Année : 2025

Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity

Résumé

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 δhyperbolicity. 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 δ-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.

Fichier principal
Vignette du fichier
camera_ready_neurips2025.pdf (1.01 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05088161 , version 1 (28-05-2025)
hal-05088161 , version 2 (30-10-2025)

Licence

Identifiants

  • HAL Id : hal-05088161 , version 2

Citer

Pierre Houedry, Nicolas Courty, Florestan Martin-Baillon, Laetitia Chapel, Titouan Vayer. Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity. NeurIPS 2025 - 39th Annual Conference on Neural Information Processing Systems, Dec 2025, San diego (Californie), United States. ⟨hal-05088161v2⟩
1002 Consultations
417 Téléchargements

Partager

  • More