分页碎片
One extra token allocates an additional page per sequence.
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。
- 理解层：写明假设、形状/单位和一个反例。
- 实现层：复算数值例子并检查边界。
- 研究层：在匹配预算下比较一个替代方法。
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
方法与参考资料
32 layers, head dimension 128. Dense cache only; excludes model weights, activations, block tables and sharing. Per-sequence allocation rounds up to the next page.
Text / 原始公式
KV bytes=2×layers×KV heads×head dimension×sequence×batch×bytes/value
An estimated cache footprint is not a measured GPU throughput or total memory requirement.
GQA (2023); PagedAttention (2023) ↗练习题
kv-5 / 01What does “Page fragmentation” test?
One extra token allocates an additional page per sequence.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 02Which computation produces the result in “Page fragmentation”?
KV
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 03What is the baseline configuration for “Page fragmentation”?
{"sequence":4097,"batch":1,"heads":8,"bytes":2,"block":256}
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 04What numerical result should you check for “Page fragmentation”?
{"KV cache (GiB)":0.5001220703125,"Allocated KV (GiB)":0.53125,"Padding tokens":255}
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 05How would you run a controlled comparison for “Page fragmentation”?
Keep the supplied fixture and other settings fixed; change sequence. Compare logical KV GiB, allocated GiB and padding tokens.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 06What failure could invalidate a conclusion from “Page fragmentation”?
An estimated cache footprint is not a measured GPU throughput or total memory requirement.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 07Is “Page fragmentation” a benchmark of a deployed language model?
No. 32 layers, head dimension 128. Dense cache only; excludes model weights, activations, block tables and sharing. Per-sequence allocation rounds up to the next page.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 08Which evidence should you report for “Page fragmentation”?
Compare logical KV GiB, allocated GiB and padding tokens. Export inputs, engine, result and method; distinguish synthetic fixtures from observed production data.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 09How can another researcher reproduce “Page fragmentation”?
Open kv-5, reset the preset, retain the exact inputs and run. The calculation is deterministic for identical inputs.
Original teaching answer / local derivation. Method reference: GQA (2023); PagedAttention (2023) ↗
打开实验 →kv-5 / 10What is the next validation step after “Page fragmentation”?
An estimated cache footprint is not a measured GPU throughput or total memory requirement. 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: GQA (2023); PagedAttention (2023) ↗
打开实验 →假设、参考实现与验收
同时计 K/V，使用 KV 头数而不是 query 头数；序列×批次仅乘一次。字节公式不含激活、权重、分配碎片和注意力工作区。
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。
运行前：预测一个边界情况
One extra token allocates an additional page per sequence.
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 kv-5.mjs. 无需第三方运行依赖。
import {calculate,network} from './academy-core.mjs';
const params={
"sequence": 4097,
"batch": 1,
"heads": 8,
"bytes": 2,
"block": 256
};
const result=calculate('kv',params);
console.log(result.metrics);测试与迁移
One extra token allocates an additional page per sequence.
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