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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Space Filling Positionality and the Spiroformer

  • M. Maurin,
  • M. Á. Evangelista-Alvarado,
  • P. Suárez-Serrato

摘要

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.