CELL 01
点积 Dot product
Q 的两个分量与 K 的两个分量分别相乘再相加。 Multiply the two Q and K component pairs, then add them.
01 · 粗线背后有账本
01 · Every thick line has a ledger
为什么某条注意力线是 8.1 px，而不是凭感觉画粗一点？ Why is one attention line 8.1 px wide instead of simply “drawn a bit thicker”?
02 点击一条线，展开四格账本 Select a Line and Unfold Its Four-Cell Ledger
点积 → 线宽 Dot product → width
① 点积
① Dot product
—
Q · K
② 缩放
② Scaled
—
÷ √2
③ 权重 → ④ 线宽
③ Weight → ④ Width
—
—
复用 S3 线宽语法：lineWidth = 1.5 + weight × 10。只有 softmax 后的非负权重进入线宽。 S3 line grammar reused: lineWidth = 1.5 + weight × 10. Only nonnegative post-softmax weights enter line width.
03 从匹配值到可见线宽的 4 格 Four Cells from Match Value to Visible Width
逐格可审计 Auditable cell by cellCELL 02
缩放 Scale
除以 √dk，避免维度大时点积过尖。 Divide by √dk so large dimensions do not make scores too sharp.
CELL 03
Softmax
所有候选一起归一化为总和 1 的非负权重。 Normalize all candidates together into nonnegative weights summing to one.
CELL 04
线宽 Line width
统一映射把同一个权重变成可比较的粗细。 One shared mapping turns that weight into comparable thickness.
04 最小机制：三步计算，一步显示 Minimal Mechanism: Three Calculations, One Display
α = softmax(QKT / √dk)Q · Ki → si/√2 → αi → 1.5 + 10αi
点击不同线，前三格来自计算，最后一格只负责把 α 变成画面语言。
Select different lines. The first three cells are computation; the last only translates α into visual language.
Q · K
得到可正可负的匹配值
A signed match value
÷ √dk
控制分数尺度
Control score scale
softmax → px
权重竞争后再画线
Compete, normalize, then draw
05 边界实验：跳过缩放与 softmax 直接画线 Boundary Test: Draw Raw Scores Without Scaling or Softmax
主动制造失败 Create a failure原始点积可能为负，也不保证总和为 1 Raw dot products may be negative and do not sum to one
把三个点积直接当权重。负分无法成为负线宽，正分总和也不等于 100%，可视语法失去统一意义。 Treat the three dot products as weights. A negative score cannot become negative width, and positive scores do not sum to 100%, so the visual grammar loses meaning.
尚未执行。正常线宽只接受 softmax 后权重。
Not run yet. Normal line width uses post-softmax weights only.
✗ 点积就是最终注意力权重。
The dot product is the final attention weight.
→ ✓ 它还要经过缩放与候选间归一化。
It still needs scaling and cross-candidate normalization.
✗ 每条线可以独立做 softmax。
Each line can run softmax alone.
→ ✓ 候选必须一起竞争，总和才为 1。
Candidates compete together so weights sum to one.
✗ 粗细只是装饰。
Thickness is decorative.
→ ✓ 同一公式把权重机械映射成线宽。
One formula mechanically maps weight to width.
06 · 一句话带走
06 · One line to keep