Space filling positionality and the Spiroformer

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 $2$-sphere.

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