`BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq` (s : Fin m → ℝ) (i : Fin m) : (deriv fun b : ℝ => logPartition b s) = fun b : ℝ => meanScore b s

Proved

BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLogPartitionConvex.

BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq (s : Fin m → ℝ) (i : Fin m) : (deriv fun b : ℝ => logPartition b s) = fun b : ℝ => meanScore b s

Formalization note: Lean 4 identifier BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq.

Preamble

-- Generated from ChapterLogPartitionConvex.lean — theorem BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterLogPartitionConvex
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterLogPartitionConvex


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterLogPartitionConvex.deriv_logPartition_eq (s : Fin m → ℝ) (i : Fin m) :
    (deriv fun b : ℝ => logPartition b s) = fun b : ℝ => meanScore b s := by sorry

View graph