arXiv Machine Learning By Timo Klein, Thomas Lang, Yllka Velaj, Sebastian Tschiatschek

hyperbolix: Hyperbolic Deep Learning in JAX

Read the original on arXiv Machine Learning →

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.

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.

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
arXiv AI
Sep 18

Riemannian--Lorentz Fusion of Vision Transformers and State-Space Models

The paper introduces Riemannian–Lorentz Parameter Fusion (RLPF), a method for merging a Vision Transformer and a state‑space model without gradient descent. RLPF aligns parameter groups by semantic role, projects them onto a common coordinate system, lifts selected coordinates to the Lorentz hyperboloid, computes a regularized geodesic barycenter, and decodes the result back into the two branches, with a learned gate combining their logits. The resulting fine‑tuned system achieves 82.37 % on CIFAR‑10, 75.04 % on Oxford‑IIIT Pet, and 78.58 % top‑1 accuracy on ImageNet‑1K, surpassing the best‑parent accuracies of 76.54 %, 71.42 %, and 76.42 % respectively.

By Badri N. Patro, Vijay S. Agneeswaran
arXiv AI
Jul 22

Riemannian Deep Learning:Modules, Networks, and Geometries

arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.

By Chen Ziheng