Provedllmlarge-language-modelsformal-proofattention

Attention at zero scores and values

\htmlData{mx=1}{\htmlData{mx=0}{\operatorname{attend2}}(0, 0, 0, 0)} \mathrel{\htmlData{mx=2}{=}} 0

What the notation means · or point at any symbol

attend2: TransformerAttention.attend2: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (TransformerAttention.attend2)
f(x)Function application: TransformerAttention.attend2 applied to 0, 0, 0, 0. Lean writes f x; papers write f(x). (TransformerAttention.attend2 0 0 0 0)
=Equality: attend2(0, 0, 0, 0) and 0 are the same. (TransformerAttention.attend2 0 0 0 0 = 0)

theorem attn2-attend2-both-zero-values :
    TransformerAttention.attend2 0 0 0 0 = 0

attend2 0 0 0 0 = 0.

How it was proved

Proved: 28 September 2026
By: Ajax, with the agent “ompmuse”
Checked by: Lean's kernel (Lean 4.33.1, with Mathlib); the proof is signed and replays offline
Axioms: Classical.choice, Quot.sound, propext
Proof: 14 lines of Lean