You Could Have Come Up with Kimi Delta Attention

This technical article explains the mathematical derivation of Kimi Delta Attention, a variant of linear attention mechanisms. It uses bra-ket notation to simplify the understanding of complex state update equations in modern AI models.
Why it matters
Understanding these efficient attention mechanisms is crucial for developers working on optimizing large language model inference and architecture.
You Could Have Come Up With Kimi Delta Attention Jamie Dborin Founder & Member of Technical Staff, Doubleword Math notation ⟨k|q⟩ kᵀq A note on notation: this article defaults to bra-ket notation because (in my quantum-inspired opinion) it makes the shapes in this derivation very clear. The Math notation switch above rewrites every equation using conventional bold vectors and explicit transposes instead. In bra-ket mode, ∣ q ⟩ \lvert q\rangle ∣ q ⟩ is a column vector, ⟨ k ∣ \langle k\rvert ⟨ k ∣ is a row vector, ⟨ k ∣ q ⟩ \langle k\rvert q\rangle ⟨ k ∣ q ⟩ is a number, and ∣ v ⟩ ⟨ k ∣ \lvert v\rangle\langle k\rvert ∣ v ⟩ ⟨ k ∣ is a matrix. Vectors face right by default, while keys face left when written into the linear-attention state.
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