`BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax` (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, l ≠ j → s l < s j) : Tendsto (fun b : ℝ => shannonEntropy (fun l =>

Proved

BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionEntropy.

BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, l ≠ j → s l < s j) : Tendsto (fun b : ℝ => shannonEntropy (fun l => scoreSoftmax b s l)) atTop (𝓝 0)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax.

Preamble

-- Generated from ChapterAttentionEntropy.lean — theorem BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionEntropy


open scoped BigOperators

noncomputable section


open Filter Topology BookProof.ChapterSoftmaxBorn BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionEntropy.tendsto_shannonEntropy_scoreSoftmax (s : Fin m → ℝ) (j : Fin m)
    (hmax : ∀ l, l ≠ j → s l < s j) :
    Tendsto (fun b : ℝ => shannonEntropy (fun l => scoreSoftmax b s l)) atTop (𝓝 0) := by sorry

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