`BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss` (s : Fin m → ℝ) (y : Fin m) : ConvexOn ℝ Set.univ (fun b : ℝ => crossEntropyLoss b s y)

Proved

BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCrossEntropyGradient.

BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss (s : Fin m → ℝ) (y : Fin m) : ConvexOn ℝ Set.univ (fun b : ℝ => crossEntropyLoss b s y)

Formalization note: Lean 4 identifier BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss.

Preamble

-- Generated from ChapterCrossEntropyGradient.lean — theorem BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterCrossEntropyGradient
open BookProof.ChapterCrossEntropyGradient


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterCrossEntropyGradient.convexOn_crossEntropyLoss (s : Fin m → ℝ) (y : Fin m) :
    ConvexOn ℝ Set.univ (fun b : ℝ => crossEntropyLoss b s y) := by sorry

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