`BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form` (beta : ℝ) (s x : Fin m → ℝ) : ∑ i, ∑ j, x i * softmaxJacobian beta s i j * x j = beta * weightedVar beta s x

Proved

BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form

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 (beta : ℝ) (s x : Fin m → ℝ) : ∑ i, ∑ j, x i * softmaxJacobian beta s i j * x j = beta * weightedVar beta s x

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxJacobian.softmaxJacobian_quadratic_form (beta : ℝ) (s x : Fin m → ℝ) :
    ∑ i, ∑ j, x i * softmaxJacobian beta s i j * x j = beta * weightedVar beta s x := by sorry

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