Prove2Me

`BookProof.ChapterAttentionOutput.headOutput_eq_sum` (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) : headOutput beta s v = ∑ j, scoreSoftmax beta s j • v j

Proved
BookProof.ChapterAttentionOutput.headOutput_eq_sum

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionOutput.

BookProof.ChapterAttentionOutput.headOutput_eq_sum (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) : headOutput beta s v = ∑ j, scoreSoftmax beta s j • v j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionOutput.headOutput_eq_sum.

Preamble
-- Generated from ChapterAttentionOutput.lean — theorem BookProof.ChapterAttentionOutput.headOutput_eq_sum
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionOutput
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionOutput


open scoped BigOperators

open Filter Topology

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m n : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionOutput.headOutput_eq_sum (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) :
    headOutput beta s v = ∑ j, scoreSoftmax beta s j • v j := by sorry

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