A single-layer attention-only transformer's fact-storage capacity can be estimated by the rank of a 3-tensor built from its weights, with the value-output dimension dominating the query-key dimension in capacity.
Tensor rank is NP-complete.Journal of algorithms, 11(4):644– 654, 1990
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Paying Attention to Facts: Quantifying the Knowledge Capacity of Attention Layers
A single-layer attention-only transformer's fact-storage capacity can be estimated by the rank of a 3-tensor built from its weights, with the value-output dimension dominating the query-key dimension in capacity.