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A Spectral Theory of Token Communication
Operators, Amplification and the Architecture of Transformers
Abstract
A monograph on attention as an averaging operator: what attention needs in order to work, why the transformer block supplies those needs cheaply, and where the design can still move. It gathers the results of one research programme with their evidence, and each claim of its opening chapter carries a label that says whether it is proved, measured, partial or pending. Its parts: The object; What attention needs; When averaging feeds back; Why the transformer sits where it does; Where the design can still move.
These are working drafts, not final versions. They are unpolished in places, incomplete in others, and keep exploratory material a polished paper would leave out, because it helps decide what comes next and shows the program's big picture more fully. Please read them with that in mind: the work will be refined further.
To cite: Neil D. B. Bruce. A Spectral Theory of Token Communication: Operators, Amplification and the Architecture of Transformers. Zenodo, version 0.1, 2026. https://doi.org/10.5281/zenodo.23541723. Open access under a CC BY 4.0 licence.