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
The paper investigates why hierarchical image retrieval improves when using frozen DINOv2 features. It compares Euclidean and hyperbolic embeddings trained with taxonomy-distance regression or a taxonomy-aware supervised contrastive objective, finding that the choice of loss function (objective family) contributes more to hierarchy-aware performance than the geometry of the embedding space. Semantic alignment of the taxonomy also plays a significant role, while stronger negative curvature does not explain the gains.
By Ling Shi (Southeast University)
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
The paper introduces SurgHiBench, a hierarchy-aware evaluation suite for surgical video understanding that measures recognition, consistency, and severity across different granularity levels. It also presents HyperSurg, a hyperbolic model that enforces phase-step containment using entailment cones, evaluated on four datasets covering three procedure types. The study shows that models with identical accuracy can differ significantly in error severity, and that hyperbolic geometry improves predictions by aligning them with the procedural hierarchy.
By Ana Manzano Rodr\'iguez, Pascal Mettes, Marlies P. Schijven, Cees G. M. Snoek
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...
Surgical procedures follow a phase-to-step hierarchy, yet the video-language models used to recognize them are evaluated with flat per-level metrics that ignore cross-level coherence and error structu...
arXiv:2606. 24952v1 Announce Type: cross Abstract: A central aspiration of mechanistic interpretability is controllability: if we know where a behavior is represented in a model's activations, we should be able to modify it.
By Cosimo Galeone, Anna Ettorre, Minsu Park, Giuseppe Ettorre, Daniele Ligorio
arXiv:2607. 05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked.
By Noel Thomas
The paper introduces a tool‑augmented framework that enhances a small Vision‑Language Model (Qwen3.5‑4B) with geometric tools—3D object detection, metric depth estimation, and deterministic solvers for distance, size, and bearing—to improve metric spatial reasoning. By moving metric computation from the model’s weights into explicit solvers, the approach achieves significant gains on ReVSI‑Bench tasks, notably increasing absolute distance accuracy from 0.46 to 0.74 MRA and relative direction accuracy from 25.9% to 73.4%. The modular design allows swapping in different detectors, enabling a clear separation between perception and reasoning errors, and the model can autonomously sequence the tools to match a scripted pipeline on most tasks.
By Kai Glantz, Clemens Grange
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
The paper introduces Stiefel Attention, which constrains the query and key projection matrices of transformers to the Stiefel manifold and optimizes them with a Riemannian Adam variant. It demonstrates that this approach yields steepest‑descent updates, is well‑conditioned, and preserves learned attention geometry during weight decay. Empirical results show significant accuracy gains on modular arithmetic grokking and CIFAR‑10 patches, with the improvement attributed to a step‑scale‑free update rule rather than equivariance or projector changes.
By Rub\'en Dar\'io Guerrero
arXiv:2605. 20282v3 Announce Type: replace-cross Abstract: Machine unlearning in Vertical Federated Learning (VFL) has attracted growing interest, yet existing methods certify forgetting solely using output-level metrics.
By Zhenyu Yu, Yangchen Zeng, Chunlei Meng, Guangzhen Yao, Shuigeng Zhou