`BookProof.ChapterAttentionResponse.deriv_headOutput` (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) : deriv (fun b : ℝ => headOutput b s v) beta = scoreValueCovariance beta s v

Proved

BookProof.ChapterAttentionResponse.deriv_headOutput

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionResponse.

BookProof.ChapterAttentionResponse.deriv_headOutput (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) : deriv (fun b : ℝ => headOutput b s v) beta = scoreValueCovariance beta s v

Formalization note: Lean 4 identifier BookProof.ChapterAttentionResponse.deriv_headOutput.

Preamble

-- Generated from ChapterAttentionResponse.lean — theorem BookProof.ChapterAttentionResponse.deriv_headOutput
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionResponse
import Definitions.Def_ChapterAttentionOutput
open BookProof.ChapterAttentionResponse


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterAttentionOutput

variable {m : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionResponse.deriv_headOutput (beta : ℝ) (s : Fin m → ℝ) (v : Fin m → E) :
    deriv (fun b : ℝ => headOutput b s v) beta = scoreValueCovariance beta s v := by sorry

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