hyperbolix is an open‑source library for hyperbolic deep learning in JAX, built on Flax NNX. It provides six manifolds—including Euclidean, Poincaré ball, hyperboloid, κ‑stereographic, mixed‑curvature product, and proper velocity space—through a common interface, and implements a wide range of layer families (linear, convolution, attention, normalization, positional encoding, regression, vector quantization). The library also supplies Riemannian optimizers, wrapped distributions, dimensionality‑reduction techniques, and precision‑tested operations that replace numerically unstable formulas on the hyperboloid, ensuring accurate float32 computations at large distances.
By Timo Klein, Thomas Lang, Yllka Velaj, Sebastian Tschiatschek
arXiv:2607. 05268v1 Announce Type: cross Abstract: Whether a hyperbolic representation model uses its geometry cannot be read off its curvature parameter: what matters is the dimensionless operating point $\sqrt{c}\rho$ and whether the radial and cone machinery is active there.
By Jaeyoung Kim, Eunseok Kim, Dongsuk Jang
arXiv:2608. 10416v1 Announce Type: cross Abstract: We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver).
By Liangchen Ge
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...
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.
By Peter Flo, Luca Grossmann
arXiv:2609.10305v1 Announce Type: new
Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
By Fang Li
arXiv:2609.27988v1 Announce Type: cross
Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
By Andrew Bond, Ege Erdem \"Ozl\"u, Tuna \c{C}imen, Ilkin Umut Melanlioglu, Tolga Birdal, Erkut Erdem, Aykut Erdem
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...
arXiv:2607. 17513v1 Announce Type: cross Abstract: Expert domains are trees; the Euclidean transformer is not, diluting parent-child structure exponentially at depth.
By Kwan Soo Shin, In Seok Kang, Munho Lee
The paper introduces Hyperbolic Multimodal Continual Learning (HMCL), a method that preserves the Lorentz geometry of hyperbolic multimodal models during sequential updates. By restricting all modalities to a shared hyperbolic isometry, HMCL formulates a joint closest‑admissible (CA) correction—along with a minimal‑rotation (MR) variant—to adjust AdamW updates while maintaining task performance. Experiments on a 16‑task classification‑retrieval stream with three hyperbolic backbones show that HMCL-CA achieves the highest overall score, reduces geometric drift by up to 95.5 %, and improves semantic hierarchy preservation on ImageNet‑WordNet.
whyItMatters":"The study demonstrates that explicitly maintaining hyperbolic geometry during continual learning yields superior performance and reduced representation drift compared to existing baselines."
By Jiahong Liu, Ming Shen, Xiaohao Liu, Rex Ying, Menglin Yang, Tat-Seng Chua, Irwin King
arXiv:2602. 07739v2 Announce Type: replace-cross Abstract: Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space.
By Hiren Madhu, Ngoc Bui, Ali Maatouk, Leandros Tassiulas, Smita Krishnaswamy, Menglin Yang, Sukanta Ganguly, Kiran Srinivasan, Rex Ying
arXiv:2609.37817v1 Announce Type: new
Abstract: Geometric representation learning predominantly scaffolds representations onto flat Euclidean subspaces or compact product tori ($\mathbb{T}^K$). Howev...
By Zhongping Ji