`BookProof.ChapterSoftmaxJacobian.deriv_scoreSoftmax_score` (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) : deriv (fun t : ℝ => scoreSoftmax beta (scorePerturb s i t) j) 0 = softmaxJaco

Proved

BookProof.ChapterSoftmaxJacobian.deriv_scoreSoftmax_score

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxJacobian.

BookProof.ChapterSoftmaxJacobian.deriv_scoreSoftmax_score (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) : deriv (fun t : ℝ => scoreSoftmax beta (scorePerturb s i t) j) 0 = softmaxJacobian beta s i j

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

Preamble

-- Generated from ChapterSoftmaxJacobian.lean — theorem BookProof.ChapterSoftmaxJacobian.deriv_scoreSoftmax_score
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.deriv_scoreSoftmax_score (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) :
    deriv (fun t : ℝ => scoreSoftmax beta (scorePerturb s i t) j) 0
      = softmaxJacobian beta s i j := by sorry

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