On attention heads and bilinear forms

Abstract:We study the symmetric and antisymmetric parts of bilinear forms in the attention heads of trained large language models. We introduce an orthogonally invariant profile map from real bilinear forms to a three-dimensional simplex and observe that profiles of trained bilinear forms accumulate near profiles of rank-one bilinear forms. We prove that the symmetric part of a bilinear form in an attention head is the sum of a hyperbolic form and a zero form for a Zariski-dense subset of query-key matrices.

Machine Learning (cs.LG); Spectral Theory (math.SP); Machine Learning (stat.ML)

arXiv:2609.22990 [cs.LG]

(or arXiv:2609.22990v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.22990 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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