`BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ` (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ j : Fin m, scoreSoftmax beta (Fin.cons s0 s) j.succ = 1 - sinkWeight beta

Proved

BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionSink.

BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ j : Fin m, scoreSoftmax beta (Fin.cons s0 s) j.succ = 1 - sinkWeight beta s0 s

Formalization note: Lean 4 identifier BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ.

Preamble

-- Generated from ChapterAttentionSink.lean — theorem BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ
import Definitions.Def_ChapterObservableExpectation
import Mathlib
import Definitions.Def_ChapterAttentionSink
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionSink


open scoped BigOperators

noncomputable section


open BookProof.ChapterObservableExpectation BookProof.ChapterSoftmaxSharpness

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

Formal statement

theorem BookProof.ChapterAttentionSink.sum_scoreSoftmax_sink_succ (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    ∑ j : Fin m, scoreSoftmax beta (Fin.cons s0 s) j.succ = 1 - sinkWeight beta s0 s := by sorry

View graph