QUERY
查询变成向量 Encode the query
把“多久能退”映射为三维教学向量 q⃗。 Map “how long can I return it” into the teaching vector q⃗.
01 · 没写同一个词，也能找到
01 · Different words, nearby meaning
查询写“多久能退”，文档写“退货期限”，没有同词匹配，为什么它仍可能排第一？ The query says “how long can I send it back,” while the document says “return window.” Why can it still rank first?
02 3D 嵌入邻域：移动查询，实时重排 3D Embedding Neighborhood: Move the Query, Rerank Live
查询向量 query vector
最近文档
Nearest document
D1
退货期限
return window
距离
Distance
0.00
‖q⃗ − d⃗‖
邻域变化
Rank changes
0
自上次移动
since last move
正在装载本地 3D 场景…若持续显示，需要 WebGL / three.js 未加载。
Loading the local 3D scene… If this remains visible, WebGL is required or three.js did not load.
拖拽旋转 · 滚轮缩放 · 停手后缓转
drag to orbit · wheel to zoom · idle auto-rotate
03 稠密检索的四个零件 Four Parts of Dense Retrieval
编码 · 距离 · 排名 encode · distance · rankDOCUMENTS
文档预先入空间 Place documents in space
每个文档块也有向量 d⃗，近义表述可能聚在一起。 Every document chunk has a vector d⃗; paraphrases can cluster together.
DISTANCE
距离衡量相近 Distance measures proximity
本页用欧氏距离演示；真实系统常用点积或余弦相似度。 This lesson uses Euclidean distance; real systems often use dot product or cosine similarity.
TOP-K
最近邻形成候选 Nearest neighbors become candidates
距离从小到大排序，前 k 个进入后续筛选或重排。 Sort by increasing distance and pass the first k candidates downstream.
04 最小机制：查询移动会改写每个距离 Minimal Mechanism: Moving the Query Rewrites Every Distance
rank = sort(distance)dist(q⃗,d⃗i) = √Σ(qj − dij)2
拖动 q⃗ 的任一分量，所有 dist 都会重算；最近邻不是固定标签，而是当前位置产生的排序。
Changing any component of q⃗ recomputes every distance. A nearest neighbor is not a permanent label; it is the ranking produced at the current position.
移动 q⃗
Move q⃗
查询语义位置改变
query position changes
重算距离
Recompute distances
dist(q⃗,d⃗i)
重排 Top-3
Rerank Top 3
颜色、连线、卡片同步
color, lines, cards update
05 边界实验：精确编号不等于语义近邻 Boundary Test: An Exact Identifier Is Not Semantic Proximity
主动制造失败 Create a failure查询“ZX-42 故障码” Query “ZX-42 fault code”
把查询移到“故障排查”语义簇。语义相近文档会靠前，但含精确编号 ZX-42 的手册可能仍在后面；这正是稀疏检索能补足的地方。 Move the query into the troubleshooting cluster. Semantically related documents rise, while the manual containing the exact identifier ZX-42 may remain lower. Sparse retrieval can fill that gap.
尚未执行。当前近义“退货期限”位于最近邻。
Not run yet. The paraphrase “return window” is currently nearest.
✗ 稠密检索就是关键词包含。
Dense retrieval is keyword containment.
→ ✓ 它比较查询与文档向量的相似度。
It compares query and document vectors.
✗ 向量最近就一定事实正确。
The nearest vector must be factually correct.
→ ✓ 相近只代表表示接近，仍需筛选与重排。
Proximity means representation similarity; filtering and reranking still matter.
✗ 编号、专名也必然靠语义命中。
Identifiers and names are guaranteed semantic hits.
→ ✓ 精确词项常需要稀疏检索补足。
Exact terms often need sparse retrieval support.
06 · 一句话带走
06 · One line to keep