Prove2Me

`BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : shannonEntropy (scoreSoftmax beta s) = logPartition beta s - beta * meanSc

Proved
BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxMaxEntropy.

BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : shannonEntropy (scoreSoftmax beta s) = logPartition beta s - beta * meanScore beta s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax.

Preamble
-- Generated from ChapterSoftmaxMaxEntropy.lean — theorem BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax
import Definitions.Def_ChapterAttentionEntropy
import Mathlib
import Definitions.Def_ChapterSoftmaxMaxEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxMaxEntropy


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxMaxEntropy.shannonEntropy_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    shannonEntropy (scoreSoftmax beta s) = logPartition beta s - beta * meanScore beta s := by sorry

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