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`BookProof.ChapterLogPartitionConvex.hasDerivAt_deriv_logPartition` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : HasDerivAt (deriv fun b : ℝ => logPartition b s) (varScore beta s) beta

Proved
BookProof.ChapterLogPartitionConvex.hasDerivAt_deriv_logPartition

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLogPartitionConvex.

BookProof.ChapterLogPartitionConvex.hasDerivAt_deriv_logPartition (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : HasDerivAt (deriv fun b : ℝ => logPartition b s) (varScore beta s) beta

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

Preamble
-- Generated from ChapterLogPartitionConvex.lean — theorem BookProof.ChapterLogPartitionConvex.hasDerivAt_deriv_logPartition
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.hasDerivAt_deriv_logPartition (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    HasDerivAt (deriv fun b : ℝ => logPartition b s) (varScore beta s) beta := by sorry

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