`BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq` (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)} (hS : S.Nonempty) (i : Fin m) : l1dist (maskedSoftmax beta s S) (scoreSof

Proved

BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionSparse.

BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)} (hS : S.Nonempty) (i : Fin m) : l1dist (maskedSoftmax beta s S) (scoreSoftmax beta s) = 2 * (1 - attendedMass beta s S)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq.

Preamble

-- Generated from ChapterAttentionSparse.lean — theorem BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionSparse
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterAttentionMarkov
import Definitions.Def_ChapterAttentionMasking
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionSparse


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterAttentionMarkov
open BookProof.ChapterAttentionMasking

variable {m : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionSparse.l1dist_maskedSoftmax_eq (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)}
    (hS : S.Nonempty) (i : Fin m) :
    l1dist (maskedSoftmax beta s S) (scoreSoftmax beta s)
      = 2 * (1 - attendedMass beta s S) := by sorry

View graph