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 Machine Learning
Oct 3

Attention Manifolds: Steering or Blocking Language Models by Editing Learned B-Spline Surfaces

Attention Manifolds introduce learned 2D B-spline surfaces that modulate each value dimension in transformer attention based on query-key interactions. Applied to LLaMA models, they reduce WikiText-2 perplexity by 2–2.5 points with minimal parameter overhead and alter greedy-decoded outputs in 69–83% of diverse prompts, especially on ambiguous inputs. The surfaces can be edited mechanically to steer or block value flow, offering a geometric tool for improving output quality and potentially enhancing safety.

By Naveen Mysore