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I like this definition. Simple, clean, effective.

Maybe the start of a new field tackling 'travelling wordsman' (smith?) problems.

To anyone knowledgeable: where does geometric deep learning fit in here? Is this paper just another geometric view, or is it an attempt at a formalization for transformer mathematics? I don't see prominent GDL authors in this paper's references (Bronstein, Cohen, Bruna, Veličković, ...).
Geometric learning is more about group- and invariant theory. This paper only goes as far as linear algebra, as far as I see.
I think it could be applicable to developing a novel geometric theory if the dynamics of the word trajectories were better understood.