arXiv Machine Learning August 27, 2026 By Peter Flo, Luca Grossmann

Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off

Read the original on arXiv Machine Learning →

The paper investigates whether placing class prototypes on a hyperbolic manifold (Poincaré ball) rather than a Euclidean space improves the satisfaction of a tree‑structured regularizer in hierarchical classification. Experiments on WikiArt show that hyperbolic prototypes better preserve nearest‑neighbor topology (higher sibling and cousin recall) across multiple tree definitions, while Euclidean prototypes perform similarly to logistic regression on raw features and only hyperbolic models improve local retrieval. The study provides empirical evidence that the choice of latent geometry can affect the fidelity of tree‑structured regularization in real data.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Hugging Face Trending Papers

Aug 25

Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off

We study a tree-structured regularizer over class-prototype layouts in a hierarchical-classification model and ask whether the choice of latent manifold for the prototypes (Euclidean R^d vs. the Poinc...

rag diffusion

arXiv Computer Vision

Aug 25

Hyper^2: Unleashing Hyperbolic Geometry's Full Potential via Dual-Space Consistency

The paper introduces Hyper^2, a dual‑space consistency framework that applies hyperbolic geometry consistently to both the loss and the encoder in point‑cloud completion tasks. By reusing the same arcosh(1+αd²) function as a positional bias in refinement attention and as the Chamfer loss, Hyper^2 achieves significant Chamfer error reductions—up to 22.9% on ShapeNet‑55 and 37.5% on unseen ShapeNet‑34—while adding only ~1.6% FLOPs. The authors demonstrate that geometric consistency across encoder and loss, rather than either component alone, is key to effective hyperbolic supervision, supported by two model‑agnostic indicators that peak only when both are hyperbolic.

By Guantian Zheng, Haiyang Xu, Tianyu Gao

safety

arXiv Computer Vision

Sep 22

Hierarchical Prompt Learning for Hyperbolic Vision-Language Models

arXiv:2609.24276v1 Announce Type: new Abstract: Hyperbolic vision-language models (VLMs) represent image and text features in a geometry naturally suited to hierarchy, but their adaptation to downstr...

By Andro Erdelez, Pascal Mettes, Behzad Bozorgtabar

llms rag multimodal benchmarks

arXiv Machine Learning

Jun 10

$k$-Nearest Neighbors in Gromov--Wasserstein Space

arXiv:2606. 10295v1 Announce Type: cross Abstract: The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry.

By Kaitlyn Hohmeier, Nicolas Fraiman, Caroline Moosmueller

rag

Hugging Face Trending Papers

Sep 23

Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces

Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason...

llms computer-vision fine-tuning efficiency

arXiv AI

Jun 3

Representational Capacity: Geometric Limits on Feature Representation in Transformer Language Models

arXiv:2606. 02765v1 Announce Type: cross Abstract: Model dimension ($d_{model}$) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored.

By Alexander Guha

llms rag diffusion

One email a morning, machine-written

Related stories

Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off

Hyper^2: Unleashing Hyperbolic Geometry's Full Potential via Dual-Space Consistency

Hierarchical Prompt Learning for Hyperbolic Vision-Language Models

$k$-Nearest Neighbors in Gromov--Wasserstein Space

Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces

Representational Capacity: Geometric Limits on Feature Representation in Transformer Language Models