Supervised Learning · Learn from Answered Examples

01 · 先看练习方式01 · Start with the practice

如果每道题都附着答案，分错一次之后，下一次能不能把分界线挪得更准？If every example comes with an answer, can one mistake tell us how to move the boundary for the next try?

02贴标签并训练Label, Then Train

误差反馈型Error feedback

先告诉模型答案Give the model answer keys

选红色或蓝色，再点画布里的灰点贴标签。贴完后连续点“训练一步”，看分界线和错分数一起变化。Choose red or blue, then select gray points on the canvas. After labeling, press “Train one step” repeatedly and track the boundary and mistake count together.

标签画笔Label brush红色Red

固定种子Fixed seed20260722

教学模拟值，非真实模型输出simulated for teaching — not real model output

已贴标签Labeled

4/8

训练样本training examples

错分Mistakes

—

按当前标签against current labels

训练步数Train steps

次反馈feedback rounds

画布操作：点击散点贴上当前颜色；再训练。灰点没有答案，不参与误差反馈。Canvas action: select a point to apply the current label, then train. Gray points have no answer and provide no feedback.

03一次监督学习的 4 个零件Four Parts of One Supervised Step

答案驱动Answer driven

PART 01

输入样本Input example

每个散点的位置是模型收到的特征。Each point's position is the feature input seen by the model.

PART 02

标准标签Answer label

红蓝颜色告诉模型这个样本应属于哪类。Red or blue states which class the example should belong to.

PART 03

当前预测Current prediction

分界线左侧预测红色，右侧预测蓝色。The boundary predicts red on the left and blue on the right.

PART 04

误差反馈Error feedback

错分数量指出当前分界线还不够好。The mistake count reveals that the current boundary is not good enough.

04最小机制：预测与答案不一致就调整Minimal Mechanism: Adjust When Prediction Disagrees

error = ŷ ≠ y

x → ŷ ; compare(ŷ, y) → error → update

x 是散点位置，y 是你贴的标签，ŷ 是分界线给出的预测。上方错分数就是 ŷ ≠ y 的数量。x is point position, y is the label you apply, and ŷ is the boundary's prediction. The mistake count above is the number of cases where ŷ ≠ y.

贴答案Apply answers样本获得评价依据Examples become scorable

计算错分Count mistakes预测与答案比较Predictions meet labels

移动边界Move boundary下一轮错分减少The next round improves

05边界实验：只给一种答案Boundary Test: Provide Only One Class

主动制造失败Create a failure

删除全部红色标签Remove every red label

模型只看到蓝色答案时，没有证据知道红蓝应在哪里分开。点击后再尝试训练。With blue answers only, the model has no evidence for where red ends and blue begins. Create this state, then try training.

尚未执行。两类答案都存在，分界才有依据。Not run yet. A boundary needs evidence from both classes.

✗ 模型看样本就会自己悟出答案。A model infers the right answer merely by seeing examples. → ✓ 监督学习需要样本与可评价目标配对。Supervised learning pairs examples with scorable targets.

✗ 训练就是把答案背下来。Training simply memorizes the answer key. → ✓ 训练调整输入到目标的预测关系。Training adjusts the mapping from input to target.

✗ 错分为零就证明处处正确。Zero training mistakes proves universal correctness. → ✓ 这里只证明当前已标样本被分对。It only shows that the labeled examples here are classified correctly.

06 · 一句话带走06 · One line to keep

监督学习用带标准答案的样本，让模型根据预测误差调整输入到目标的关系；在上方连续训练，就能检验分界线移动时错分是否下降。Supervised learning uses answered examples to adjust a mapping through prediction error. Train repeatedly above to verify whether moving the boundary reduces mistakes.