Prove2Me

`BookProof.ChapterSoftmaxDivergence.deriv_meanScore_eq_fisherInformation` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : deriv (fun b : ℝ => meanScore b s) beta = fisherInformation beta

Proved
BookProof.ChapterSoftmaxDivergence.deriv_meanScore_eq_fisherInformation

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxDivergence.

BookProof.ChapterSoftmaxDivergence.deriv_meanScore_eq_fisherInformation (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : deriv (fun b : ℝ => meanScore b s) beta = fisherInformation beta s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxDivergence.deriv_meanScore_eq_fisherInformation.

Preamble
-- Generated from ChapterSoftmaxDivergence.lean — theorem BookProof.ChapterSoftmaxDivergence.deriv_meanScore_eq_fisherInformation
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterSoftmaxDivergence
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxDivergence


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

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

View graph