Space filling positionality and the Spiroformer

M. Maurin; M. Á. Evangelista-Alvarado; P. Suárez-Serrato

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arXiv · 2507.08456

Space filling positionality and the Spiroformer

M. Maurin·M. Á. Evangelista-Alvarado·P. Suárez-Serrato

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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.

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M. Maurin, M. Á. Evangelista-Alvarado, P. Suárez-Serrato. 2025-07-11. Space filling positionality and the Spiroformer. https://arxiv.org/abs/2507.08456

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