`BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift` {m : ℕ} (beta : ℝ) (w : Fin n → ℝ) (p t : ℝ) (k : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta (fun l => peInner w

Proved

BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSinusoidalPosition.

BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift {m : ℕ} (beta : ℝ) (w : Fin n → ℝ) (p t : ℝ) (k : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta (fun l => peInner w (p + t) (k l + t)) j = scoreSoftmax beta (fun l => peInner w p (k l)) j

Formalization note: Lean 4 identifier BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift.

Preamble

-- Generated from ChapterSinusoidalPosition.lean — theorem BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSinusoidalPosition
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSinusoidalPosition


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {n : ℕ}

Formal statement

theorem BookProof.ChapterSinusoidalPosition.scoreSoftmax_sinusoidal_shift {m : ℕ} (beta : ℝ) (w : Fin n → ℝ) (p t : ℝ)
    (k : Fin m → ℝ) (j : Fin m) :
    scoreSoftmax beta (fun l => peInner w (p + t) (k l + t)) j
      = scoreSoftmax beta (fun l => peInner w p (k l)) j := by sorry

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