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`BookProof.ChapterSoftmaxFluctuation.deriv_logPartition` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : deriv (fun b : ℝ => logPartition b s) beta = meanScore beta s

Proved
BookProof.ChapterSoftmaxFluctuation.deriv_logPartition

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.deriv_logPartition (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : deriv (fun b : ℝ => logPartition b s) beta = meanScore beta s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxFluctuation.deriv_logPartition.

Preamble
-- Generated from ChapterSoftmaxFluctuation.lean — theorem BookProof.ChapterSoftmaxFluctuation.deriv_logPartition
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxFluctuation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxFluctuation.deriv_logPartition (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    deriv (fun b : ℝ => logPartition b s) beta = meanScore beta s := by sorry

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