For constant head dimension d, approximate attention can be computed in about n^{2-1/d} polylog(B/eps) time, while SETH-based lower bounds push near-quadratic hardness down to very small d.
Agarwal, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl
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Subquadratic Algorithms and Hardness for Attention with Any Temperature
For constant head dimension d, approximate attention can be computed in about n^{2-1/d} polylog(B/eps) time, while SETH-based lower bounds push near-quadratic hardness down to very small d.