schema: superpaper.ledger/v1
retired_ids: []
paper:
  id: excerpt-toy
  title: A One-Step Predictor
  authors: ["Fixture"]
  year: 2026
  venue: Superpaper examples
  notes_language: zh
  source: {kind: excerpt}
coverage:
  mode: excerpt
  sections_in: ["1"]
questions:
  - {id: Q1, text: "一次前向如何得到预测，损失该放在哪？", source: "excerpt"}
claims:
  - id: C1
    text: "一次前向是 x → f_θ → ŷ；损失在预测之后单独计算"
    kind: contribution
    status: core
    supports: [Q1]
    source: "excerpt"
definitions:
  - {id: D1, name: "one-step predictor", text: "ŷ = f_θ(x)", source: "excerpt"}
assumptions: []
lemmas: []
symbols:
  - {name: x, latex: "x", meaning: "输入", kind: value, introduced: "excerpt"}
  - {name: yhat, latex: "\\hat y", meaning: "预测", kind: value}
  - {name: L, latex: "L", meaning: "损失", kind: scalar}
  - {name: d, latex: "d", meaning: "特征维", kind: "shape parameter"}
derivations:
  - id: DER1
    claim: C1
    title: "缩放来自方差"
    source: "excerpt"
    expand: true
    figure: null
    steps:
      - {id: S1, from: "u^\\top v", to: "u^\\top v / \\sqrt{d}", rule: scale,
         justify: "点积方差随 d 增长"}
figures: []
evidence: []
terms:
  - {canonical: "one-step predictor", aliases: ["一次前向"]}
source_assets: []