HyperTree: Scalable Unsupervised Hierarchy Discovery in Hyperbolic Space

Real-world image datasets are deeply hierarchical, yet unsupervised hierarchical representation learning remains underdeveloped. Hyperbolic space is geometrically ideal for embedding trees with low distortion due to its exponential volume growth, but existing unsupervised hyperbolic methods either fail to scale beyond a few thousand points or depend heavily on class supervision. We bridge this gap with HyperTree, a fully unsupervised, scalable, and capacity-efficient framework for hierarchical representation learning in hyperbolic space, built on three contributions: (i) a geometrically consistent, closed-form definition of the hyperbolic Lowest Common Ancestor, valid across hyperbolic manifolds of arbitrary curvatures; (ii) a differentiable hierarchical objective based on Dasgupta's cost that is bounded and invariant to dataset scale; and (iii) a sample-complexity guarantee that enables scaling to datasets such as ImageNet-1k and iNaturalist-2018. Across four benchmarks, HyperTree outperforms Euclidean baselines by wide margins on hierarchical dendrogram purity, matches supervised hyperbolic baselines on CIFAR-100, and surpasses them on TinyImageNet at 16 dimensions — a highly capacity-efficient regime where competing methods collapse.