Provedllmlarge-language-modelsformal-proofattention

Weight0 is one half at tied score at score 1

\htmlData{mx=1}{\htmlData{mx=0}{\operatorname{weight0}}(1, 1)} \mathrel{\htmlData{mx=3}{=}} \htmlData{mx=2}{\frac{1}{2}}

What the notation means · or point at any symbol

weight0: TransformerAttention.weight0: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (TransformerAttention.weight0)
f(x)Function application: TransformerAttention.weight0 applied to 1, 1. Lean writes f x; papers write f(x). (TransformerAttention.weight0 1 1)
=Equality: weight0(1, 1) and 1/2 are the same. (TransformerAttention.weight0 1 1 = 1 / 2)
a/bDivision: 1 divided by 2. In Lean, dividing by 0 gives 0. (1 / 2)

theorem attn2-weight0-tie-one :
    TransformerAttention.weight0 1 1 = 1 / 2

weight0 1 1 = 1/2: any tied pair of scores splits the mass evenly.

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: 15 lines of Lean