Prove2Me

`BookProof.ChapterEntropyTemperature.attentionEntropy_eq` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : attentionEntropy beta s = logPartition beta s - beta * meanScore beta s

Proved
BookProof.ChapterEntropyTemperature.attentionEntropy_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropyTemperature.

BookProof.ChapterEntropyTemperature.attentionEntropy_eq (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : attentionEntropy beta s = logPartition beta s - beta * meanScore beta s

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

Preamble
-- Generated from ChapterEntropyTemperature.lean — theorem BookProof.ChapterEntropyTemperature.attentionEntropy_eq
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.attentionEntropy_eq (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    attentionEntropy beta s = logPartition beta s - beta * meanScore beta s := by sorry

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