`BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq` (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : bornWeight q k j = sc

Proved

BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentGeometry.

BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : bornWeight q k j = scoreSoftmax 1 (fun l => -‖q - k l‖ ^ 2) j

Formalization note: Lean 4 identifier BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq.

Preamble

-- Generated from ChapterCoherentGeometry.lean — theorem BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq
import Definitions.Def_ChapterCoherentOverlap
import Mathlib
import Definitions.Def_ChapterCoherentGeometry
import Definitions.Def_ChapterSoftmaxBorn
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxBorn
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterCoherentGeometry


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlap BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentGeometry.bornWeight_eq_scoreSoftmax_neg_dist_sq (q : EuclideanSpace ℝ (Fin n))
    (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) :
    bornWeight q k j = scoreSoftmax 1 (fun l => -‖q - k l‖ ^ 2) j := by sorry

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