`BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum` (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta s j = 1 / ∑ l, Real.exp (beta * (s l - s j))

Proved

BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxSharpness.

BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta s j = 1 / ∑ l, Real.exp (beta * (s l - s j))

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum.

Preamble

-- Generated from ChapterSoftmaxSharpness.lean — theorem BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness


open scoped BigOperators

noncomputable section


open Filter Topology BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxSharpness.scoreSoftmax_eq_inv_sum (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    scoreSoftmax beta s j = 1 / ∑ l, Real.exp (beta * (s l - s j)) := by sorry

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