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混合检索与重排 / 4 OF 5

理想重排上界

Perfect labels can improve ordering only inside the candidate pool.

本地计算 / 模拟

本地教学实验，不调用外部 API。合成示例不能替代生产环境测量。

学习指南与本课目录LEARNING CONTRACT

理解 → 实现 → 研究

目标：解释本课机制、复现一个例子、测试一个失败案例。读完不自动代表掌握。

先修路线 →关联实现练习 →

02 · 预测与配置

技术场景说明、参数名称与参考答案目前为英文。

03 · 检查证据

运行实验后查看结果。

方法与参考资料

Lexical score counts matching query terms (not BM25). Dense score is cosine on supplied 2D vectors, not a live embedding model. RRF combines ranks. Optional reranking uses known relevance labels as an oracle upper-bound, not a trained reranker. Empty query ties preserve document order.

Text / 原始公式
score=w/(k+lexicalRank)+(1−w)/(k+denseRank); DCG=Σ(2^rel−1)/log₂(rank+1)

An oracle reranker leaks labels intentionally; never report it as learned model performance.

Reciprocal Rank Fusion · SIGIR 2009 ↗

练习题

retrieval-4 / 01What does “Oracle reranking ceiling” test?

Perfect labels can improve ordering only inside the candidate pool.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 02Which computation produces the result in “Oracle reranking ceiling”?

;

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 03What is the baseline configuration for “Oracle reranking ceiling”?

{"query":"KV cache memory","documents":"[\n {\n \"id\": \"D1\",\n \"text\": \"KV cache stores keys and values for generation\",\n \"vector\": [\n 1,\n 0.1\n ],\n \"relevance\": 3\n },\n {\n \"id\": \"D2\",\n \"text\": \"Cache restaurant menu and opening hours\",\n \"vector\": [\n 0.1,\n 1\n ],\n \"relevance\": 0\n },\n {\n \"id\": \"D3\",\n \"text\": \"Grouped query attention reduces memory\",\n \"vector\": [\n 0.95,\n 0.2\n ],\n \"relevance\": 2\n },\n {\n \"id\": \"D4\",\n \"text\": \"KV cache memory footprint depends on sequence length\",\n \"vector\": [\n 0.8,\n 0.3\n ],\n \"relevance\": 3\n },\n {\n \"id\": \"D5\",\n \"text\": \"Tokenization splits input text\",\n \"vector\": [\n 0.4,\n 0.8\n ],\n \"relevance\": 0\n }\n]","x":1,"y":0.1,"weight":0.5,"k":60,"retrieve":5,"top":3,"rerank":1}

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 04What numerical result should you check for “Oracle reranking ceiling”?

{"Recall@k":1,"nDCG@k":1}

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

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retrieval-4 / 05How would you run a controlled comparison for “Oracle reranking ceiling”?

Keep the supplied fixture and other settings fixed; change weight. Compare Recall@k and nDCG@k while varying candidate pool and fusion weight.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 06What failure could invalidate a conclusion from “Oracle reranking ceiling”?

An oracle reranker leaks labels intentionally; never report it as learned model performance.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 07Is “Oracle reranking ceiling” a benchmark of a deployed language model?

No. Lexical score counts matching query terms (not BM25). Dense score is cosine on supplied 2D vectors, not a live embedding model. RRF combines ranks. Optional reranking uses known relevance labels as an oracle upper-bound, not a trained reranker. Empty query ties preserve document order.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 08Which evidence should you report for “Oracle reranking ceiling”?

Compare Recall@k and nDCG@k while varying candidate pool and fusion weight. Export inputs, engine, result and method; distinguish synthetic fixtures from observed production data.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

打开实验 →
retrieval-4 / 09How can another researcher reproduce “Oracle reranking ceiling”?

Open retrieval-4, reset the preset, retain the exact inputs and run. The calculation is deterministic for identical inputs.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

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retrieval-4 / 10What is the next validation step after “Oracle reranking ceiling”?

An oracle reranker leaks labels intentionally; never report it as learned model performance. Test the hypothesis on a representative held-out workload and document a baseline, success metric and stopping rule before claiming deployment readiness.

Original teaching answer / local derivation. Method reference: Reciprocal Rank Fusion · SIGIR 2009 ↗

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MATHEMATICAL REVIEW · 2026-10-26

假设、参考实现与验收

加权倒数排名融合从排名 1 开始。给定相关性是 oracle 重排器，不是训练模型。零向量余弦采用软件哨兵值；实际检索索引不得泄漏标签。

已复核引擎公式、场景预设及数值保护。固定种子的合成输入不是生产基准。

查询 → 词法与向量排名 → 加权倒数排名融合 → 可选相关性 oracle 重排 → Top-k → 召回率与 nDCG
机制图：从上到下跟踪每次变换。

运行前：预测一个边界情况

Perfect labels can improve ordering only inside the candidate pool.

提示：隔离假设

固定基线输入，只改变一个参数或边界；同时比较数值与声明单位。单例通过仅验证该样例。

最小可运行算例

将算例及所链接模块保存在同一目录。使用 Node.js 22 或更高版本，然后运行 node retrieval-4.mjs. 无需第三方运行依赖。

import {calculate,network} from './academy-core.mjs';
const params={
  "query": "KV cache memory",
  "documents": "[\n  {\n    \"id\": \"D1\",\n    \"text\": \"KV cache stores keys and values for generation\",\n    \"vector\": [\n      1,\n      0.1\n    ],\n    \"relevance\": 3\n  },\n  {\n    \"id\": \"D2\",\n    \"text\": \"Cache restaurant menu and opening hours\",\n    \"vector\": [\n      0.1,\n      1\n    ],\n    \"relevance\": 0\n  },\n  {\n    \"id\": \"D3\",\n    \"text\": \"Grouped query attention reduces memory\",\n    \"vector\": [\n      0.95,\n      0.2\n    ],\n    \"relevance\": 2\n  },\n  {\n    \"id\": \"D4\",\n    \"text\": \"KV cache memory footprint depends on sequence length\",\n    \"vector\": [\n      0.8,\n      0.3\n    ],\n    \"relevance\": 3\n  },\n  {\n    \"id\": \"D5\",\n    \"text\": \"Tokenization splits input text\",\n    \"vector\": [\n      0.4,\n      0.8\n    ],\n    \"relevance\": 0\n  }\n]",
  "x": 1,
  "y": 0.1,
  "weight": 0.5,
  "k": 60,
  "retrieve": 5,
  "top": 3,
  "rerank": 1
};
const result=calculate('retrieval',params);
console.log(result.metrics);
下载本课算例academy-core.mjs

测试与迁移

Perfect labels can improve ordering only inside the candidate pool.

在下方笔记记录输入、代码版本、期望值和实测值；再构造违反上述假设的反例，解释原结论为何不再成立。

下载完整代码包（.tar.gz） · 完整参考代码与回归检查

预测、检验与证据记录

展开答案前先预测一个结果；练习后记录差异和迁移测试。记录仅存本地，在不同语言版本间共用。

打开记录／导出／清除 →

数学复核范围逐篇记录，不代表完成论文实证复现；可在笔记中记录疑似错误。 复核范围