Self-Attention

TL;DR for operators Long context becomes expensive for a specific architectural reason: standard self-attention allows every position to interact with every other position. In the usual formulation, that means $O(n^2 d)$ computation and $O(n^2)$ storage for attention-related matrices as sequence length $n$ grows. Hasi Hays’s mathematical monograph on attention1 is useful because it connects that deployment constraint directly to the mechanism that makes attention powerful in the first place. ...

TL;DR for operators When a model behaves unexpectedly, teams often inspect attention maps to see where information flowed. Those maps show which source tokens were selected and how strongly, but not how the retrieved features were transformed before reaching the destination token. The paper proves that multi-head attention is exactly representable as a scaled, edge-dependent connection walk: token routing is supplied by attention weights, while feature transport is supplied by an attention-gated mixture of the heads’ value-output maps. Two layers can therefore display similar attention patterns while computing materially different transformations. ...