`BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax` {m : ℕ} (q : ℝ) (k : Fin m → ℝ) (j : Fin m) : packetBorn q k j = scoreSoftmax (1 / 2) (fun l => -(q - k l) ^ 2)

Proved

BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentPositionSpace.

BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax {m : ℕ} (q : ℝ) (k : Fin m → ℝ) (j : Fin m) : packetBorn q k j = scoreSoftmax (1 / 2) (fun l => -(q - k l) ^ 2) j

Formalization note: Lean 4 identifier BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax.

Preamble

-- Generated from ChapterCoherentPositionSpace.lean — theorem BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax
import Definitions.Def_ChapterCoherentOverlap
import Mathlib
import Definitions.Def_ChapterCoherentPositionSpace
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterCoherentPositionSpace


open scoped BigOperators
open MeasureTheory

noncomputable section


open BookProof.ChapterCoherentOverlap BookProof.ChapterSoftmaxSharpness

Formal statement

theorem BookProof.ChapterCoherentPositionSpace.packetBorn_eq_scoreSoftmax {m : ℕ} (q : ℝ) (k : Fin m → ℝ) (j : Fin m) :
    packetBorn q k j = scoreSoftmax (1 / 2) (fun l => -(q - k l) ^ 2) j := by sorry

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