`BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : HasDerivAt (fun b : ℝ => attentionEntropy b s) (-(beta * varScore beta s)

Proved

BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropyTemperature.

BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : HasDerivAt (fun b : ℝ => attentionEntropy b s) (-(beta * varScore beta s)) beta

Formalization note: Lean 4 identifier BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy.

Preamble

-- Generated from ChapterEntropyTemperature.lean — theorem BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterEntropyTemperature
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterEntropyTemperature


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterEntropyTemperature.hasDerivAt_attentionEntropy (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    HasDerivAt (fun b : ℝ => attentionEntropy b s) (-(beta * varScore beta s)) beta := by sorry

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