Prove2Me

`BookProof.ChapterSoftmaxFluctuation.hasDerivAt_scoreSoftmax` (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : HasDerivAt (fun b : ℝ => scoreSoftmax b s j) (scoreSoftmax beta s j * (s j -

Proved
BookProof.ChapterSoftmaxFluctuation.hasDerivAt_scoreSoftmax

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.hasDerivAt_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : HasDerivAt (fun b : ℝ => scoreSoftmax b s j) (scoreSoftmax beta s j * (s j - meanScore beta s)) beta

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

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxFluctuation.hasDerivAt_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    HasDerivAt (fun b : ℝ => scoreSoftmax b s j)
      (scoreSoftmax beta s j * (s j - meanScore beta s)) beta := by sorry

View graph