`BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic` (beta : ℝ) (S : Fin m → Fin m → ℝ) : IsStochastic (attentionMatrix beta S)

Proved

BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMarkov.

BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic (beta : ℝ) (S : Fin m → Fin m → ℝ) : IsStochastic (attentionMatrix beta S)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic.

Preamble

-- Generated from ChapterAttentionMarkov.lean — theorem BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMarkov
open BookProof.ChapterAttentionMarkov


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionMarkov.attentionMatrix_isStochastic (beta : ℝ) (S : Fin m → Fin m → ℝ) :
    IsStochastic (attentionMatrix beta S) := by sorry

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