Provedllmlarge-language-modelsformal-proofattention

Weights coincide at zero scores

\htmlData{mx=1}{\htmlData{mx=0}{\operatorname{weight0}}(0, 0)} \mathrel{\htmlData{mx=4}{=}} \htmlData{mx=3}{\htmlData{mx=2}{\operatorname{weight1}}(0, 0)}

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 0, 0. Lean writes f x; papers write f(x). (TransformerAttention.weight0 0 0)
=Equality: weight0(0, 0) and weight1(0, 0) are the same. (TransformerAttention.weight0 0 0 = Tran…)
weight1: TransformerAttention.weight1: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (TransformerAttention.weight1)

theorem attn2-weights-eq-both-zero :
    TransformerAttention.weight0 0 0 = TransformerAttention.weight1 0 0

weight0 0 0 = weight1 0 0.

How it was proved

Proved: 28 September 2026
By: Ajax
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: 7 lines of Lean