ITEM
离散对象Discrete item
词卡先只是一个可识别的类别。A word card begins as an identifiable category.
01 · 从安排座位开始01 · Start with a seating plan
如果“猫”和“小猫”永远坐得比“猫”和“发票”近，机器能否把这种关系变成可计算的位置？ If “cat” and “kitten” consistently sit closer than “cat” and “invoice,” can a machine turn that relationship into computable positions?
02拖词卡，给“相近 / 不相近”反馈 Drag Word Cards into Similar / Dissimilar Feedback
唯一变量：反馈关系One variable: feedback relation锚点Anchor
猫cat
embedding [0.00, 0.00]
已选词
Selected
小猫
kitten
distance 2.65
反馈轮数Feedback rounds
0
位置逐轮更新
positions update by round
已选“小猫”。把它拖到“相近”，观察两个词点聚拢。
“Kitten” is selected. Drop it on “Similar” and watch the points converge.
03一次反馈更新的 4 个零件 Four Parts of One Feedback Update
identity → vector → relation → updateVECTOR
稠密向量 Dense vector
两个连续坐标把词放进可移动平面。 Two continuous coordinates place the word in a movable plane.
FEEDBACK
关系反馈 Relational feedback
“相近 / 不相近”给出移动方向。 “Similar / dissimilar” supplies an update direction.
TRACE
更新痕迹 Update trace
箭头记录刚才是哪条反馈造成移动。 An arrow records which feedback caused the latest move.
04最小机制：反馈沿距离方向更新坐标 Minimal Mechanism: Feedback Updates Along the Distance Direction
e ← e + Δe similar: e ← e + η(a − e)
dissimilar: e ← e + η(e − a)
dissimilar: e ← e + η(e − a)
a 是“猫”的锚点，η=0.35 是教学步长。反复拖同一词卡，距离会逐轮缩短或拉长。
a is the “cat” anchor and η=0.35 is a teaching step size. Repeated drops shrink or expand distance round by round.
拖入反馈区
Drop into a zone确定拉近或推远
choose pull or push
计算 ΔeCompute Δe
沿锚点连线更新update along anchor line
词点移动Point moves
关系变成可计算距离relation becomes distance
05边界实验：错误反馈也会被“学会” Boundary Test: Wrong Feedback Can Also Be Learned
主动制造失败Create a failure强行把“发票”标成与“猫”相近 Force “invoice” to be similar to “cat”
坐标会忠实地靠近，但错误标签不会因为变成向量就变正确。训练数据决定表示能学到什么偏差。 The coordinate will obediently move closer, but a wrong label does not become correct by becoming a vector. Training data determines which biases the representation learns.
尚未执行。先用正确反馈移动“小猫”。
Not run yet. Move “kitten” with correct feedback first.
✗
embedding 是词的唯一真实含义。An embedding is a word's one true meaning.
→ ✓ 它是由目标和数据学出的任务表示。
It is a task representation learned from objectives and data.
✗ 点靠近就证明事实关系成立。
Nearby points prove a factual relationship. → ✓
靠近只反映训练出的表示关系。Proximity reflects a learned representational relationship.
✗ 稠密向量天然无偏。
Dense vectors are naturally unbiased. → ✓
错误或偏斜反馈会进入坐标。
Wrong or skewed feedback enters the coordinates.
06 · 一句话带走 · S1 表示链收官
06 · One line to keep · representation finale