`BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ a, ∑ b, s a * softmaxJacobian beta s a b * s b = beta * varScore

Proved

BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxJacobian.

BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ a, ∑ b, s a * softmaxJacobian beta s a b * s b = beta * varScore beta s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score.

Preamble

-- Generated from ChapterSoftmaxJacobian.lean — theorem BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxJacobian
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxJacobian


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form_score (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    ∑ a, ∑ b, s a * softmaxJacobian beta s a b * s b = beta * varScore beta s := by sorry

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