Geometry of Lightning Self-Attention: Identifiability and Dimension

Nathan W. Henry, Giovanni Luca Marchetti, Kathlén Kohn

Keywords: Lightning Self-Attention, Neuromanifolds, Algebraic Geometry

TL;DR: We study neuromanifolds of lightning self-attention networks, discussing, in particular, dimension and identifiability.

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.

Primary Area: learning theory

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Submission Number: 3541