English

Space filling positionality and the Spiroformer

Machine Learning 2025-07-14 v1 Artificial Intelligence Differential Geometry Dynamical Systems Symplectic Geometry

Abstract

Transformers excel when dealing with sequential data. Generalizing transformer models to geometric domains, such as manifolds, we encounter the problem of not having a well-defined global order. We propose a solution with attention heads following a space-filling curve. As a first experimental example, we present the Spiroformer, a transformer that follows a polar spiral on the 22-sphere.

Keywords

Cite

@article{arxiv.2507.08456,
  title  = {Space filling positionality and the Spiroformer},
  author = {M. Maurin and M. Á. Evangelista-Alvarado and P. Suárez-Serrato},
  journal= {arXiv preprint arXiv:2507.08456},
  year   = {2025}
}

Comments

9 pages, 5 figures. To appear in Geometric Science of Information 2025

R2 v1 2026-07-01T03:56:18.130Z