`BookProof.ChapterSoftmaxMaxEntropy.log_scoreSoftmax` (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : Real.log (scoreSoftmax beta s j) = beta * s j - logPartition beta s

Proved

BookProof.ChapterSoftmaxMaxEntropy.log_scoreSoftmax

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxMaxEntropy.

BookProof.ChapterSoftmaxMaxEntropy.log_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : Real.log (scoreSoftmax beta s j) = beta * s j - logPartition beta s

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

Preamble

-- Generated from ChapterSoftmaxMaxEntropy.lean — theorem BookProof.ChapterSoftmaxMaxEntropy.log_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.log_scoreSoftmax (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    Real.log (scoreSoftmax beta s j) = beta * s j - logPartition beta s := by sorry

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