Geometry of Lightning Self-Attention: Identifiability and Dimension
Nathan W. Henry, Giovanni Luca Marchetti, Kathlén Kohn
Abstract
We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.
BibTeX
@inproceedings{
henry2025geometry,
title={Geometry of Lightning Self-Attention: Identifiability and Dimension},
author={Nathan W. Henry and Giovanni Luca Marchetti and Kathl{\'e}n Kohn},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=XtY3xYQWcW}
}