A split result
An arXiv preprint comparing Euclidean and Poincare-ball class prototypes found a clear split between classification and local hierarchy. When the best configuration for each geometry was selected, Euclidean prototypes had a 5.3 percentage-point advantage in top-1 accuracy, a 2.4-point edge when the five highest-ranked choices were counted, and a 0.108 higher Spearman correlation with the default reference tree. Hyperbolic prototypes led on the local measures: sibling recall@5 was 0.052 higher and cousin recall@5 was 0.047 higher. Seed bands did not overlap on those five headline measures.
Put plainly, the geometry that was strongest at naming a painting's style was not the one that most consistently kept nearby styles together in the learned neighborhood.
What the models were asked to do
The question was whether Euclidean or Poincare-ball prototypes would change the cost of satisfying a tree-structured regularizer without distorting the model's data likelihood. In ordinary language, the regularizer is a training rule that encourages distances between class representatives to follow a reference tree. Both conditions used frozen CLIP ViT-B/16 features, an MLP head and a prototype classifier. Only the manifold used for the classifier output changed.
The experiment used WikiArt-Refined, with approximately 81,446 paintings across 27 styles and a supplied 70/30 training-validation split. The imbalance was severe: Impressionism had 13,060 examples, compared with 77 for Analytical Cubism, a 133.3-fold difference.
Rather than rely on a single setting, the authors ran 150 seed-replicated configurations. They varied the embedding dimension across 2, 4, 8, 16, 32 and 64; the curvature setting across 0.1, 0.3, 1 and 3; the regularizer strength across 0, 0.1, 0.3, 1 and 3; and used three reference-tree variants. Training used Adam for the MLP and Riemannian Adam for the hyperbolic prototypes, with 30 epochs.
Classification and local retrieval pull apart
On a raw frozen-CLIP logistic-regression baseline, top-1 accuracy was 64.1%. Euclidean prototypes reached 64.3% at dimension 8, essentially matching that baseline. Hyperbolic prototypes were 4 to 6 percentage points lower. The comparison puts the Euclidean result close to the performance of the raw features before the prototype geometry was added.
The local retrieval measure reversed the ordering. At dimension 8, sibling recall@5 was 0.195 for hyperbolic prototypes, 0.149 for Euclidean prototypes and 0.160 for k-NN-5 applied to raw CLIP features. Here, recall@5 tracks how often the five nearest validation-embedding neighbours include styles that are siblings in the reference hierarchy. On that measure, the hyperbolic prototype space was ahead of both the Euclidean model and the raw-feature baseline.
That local gap was not limited to the selected winners. Across 18 paired seed configurations, hyperbolic prototypes recorded sibling recall 8.7 percentage points higher and cousin recall 15.2 points higher than Euclidean prototypes. The sign of the difference agreed in 94% of the pairings, and the paired t-test gave p < 10^-4.
The global picture is harder to read
The dimension sweep added a wrinkle. On the default tree, hyperbolic sibling recall@5 stayed near 0.19 from dimensions 2 through 64. Euclidean recall started higher, at 0.221 in two dimensions, but fell to 0.142 at 64 dimensions.
The local advantage also survived changes to the reference tree. At dimension 8, Euclidean sibling recall@5 was 0.149 on the default tree, 0.356 on the CLIP-empirical tree and 0.322 on the DINOv2-empirical tree. The corresponding hyperbolic values were 0.195, 0.416 and 0.380. The ordering was the same for all three tree choices.
Global tree fidelity was less settled. Default-tree Spearman correlation, which compares the ranking of learned distances with the reference ranking, showed no reliable separation: p = 0.68 and sign agreement was 0.50. A different global measure, mean tree distortion, favoured Euclidean by 0.040 with p < 10^-4. Since the two measures disagreed, the study did not identify a stable winner for global fidelity.
The choice of training emphasis mattered too. As regularizer strength rose, tree-Spearman climbed from about 0.3 to about 0.7, while classification collapsed at strengths of 1 or above. The pattern shows why a model can look more tree-faithful on one score while performing worse at assigning the correct style.
A sensitivity rerun used inverse-frequency class weights on the dimension-8 winners with three seeds. The direction of the split stayed intact: top-1 remained 5 percentage points higher for Euclidean, sibling recall remained 4 points higher for hyperbolic, and the balanced-accuracy gap narrowed from 11.9 to 3.5 points. The weighting changed the size of one gap, but not which geometry led on the two headline tasks.
A result bounded by its setup
The document is an arXiv version-1 preprint. The evidence comes from the 27-style WikiArt-Refined task, with frozen CLIP ViT-B/16 features and the MLP head and prototype classifier shared between conditions. Only the classifier-output manifold varied. It does not establish that hyperbolic prototypes improve overall classification or that either geometry consistently wins on global tree fidelity.
The acknowledgements disclose that Anthropic's Claude, version 4.7, assisted with experimental infrastructure, analysis brainstorming and preliminary prose that the authors substantially revised.
Paper data and sources
Original title: Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off
Authors: Peter Flo, Luca Grossmann
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
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