CAPACITY
表达能力低Low capacity
黑线能弯曲的程度不足。The black line cannot bend enough.
01 · 用直尺描弯路01 · Trace a bend with a ruler
一条只能轻微倾斜的直线，能同时贴近这组明显弯曲的红点和蓝点吗？Can a nearly straight line follow a visibly curved pattern across both red and blue points?
02调低曲线能力，看两种误差一起升高Lower Curve Capacity and Raise Both Errors
唯一变量：曲线复杂度One variable: curve complexity
训练误差Training error
—
MSE × 1000
测试误差Test error
—
MSE × 1000
诊断Diagnosis
欠拟合UNDERFIT
能力不足insufficient capacity
S2-18 → S2-19 → S2-20同一数据集 · 同一坐标系 · 红训练 / 蓝测试 / 黑模型same dataset · same axes · red train / blue test / black model
03欠拟合的证据链The Evidence Chain for Underfitting
simple model · missed pattern · high train · high testPATTERN
稳定规律漏掉Pattern missed
不是噪声，而是主趋势也没跟上。It misses the main trend, not just noise.
TRAIN
训练也差Training is poor
红点普遍离黑线较远。Red points remain far from the line.
TEST
测试同样差Testing is poor
蓝点也没有被稳定规律解释。Blue points are not explained either.
04最小机制：能力上限压住了可达到的误差Minimal Mechanism: A Capacity Ceiling Limits the Best Fit
low capacity → high biasEtrain ↑ Etest ↑
训练误差高是关键线索：模型连已见样本都解释不好。提高到足够复杂度时，两种误差会一起下降。High training error is the key clue: the model cannot explain examples it already
saw. Raising capacity enough lowers both errors.
限制复杂度Limit complexity可表达曲线变少fewer shapes available
主规律学不全Pattern is missed红蓝点都偏离red and blue both miss
双误差偏高Both errors high诊断为欠拟合diagnose underfitting
05边界实验：把曲线能力降到 0Boundary Test: Reduce Curve Capacity to Zero
主动制造失败Create a failure用近乎平直的线解释弯曲规律Use an almost flat line for a curved pattern
训练点和测试点会同时远离模型。这个失败告诉你：此时不该继续“防过拟合”，而要先增加表达能力。Both train and test points move away from the model. The remedy is more expressive capacity, not stronger anti-overfitting constraints.
尚未执行。Not run yet.
✗ 测试差就一定是过拟合。Poor testing always means overfitting.
→ ✓ 先看训练误差；训练也差更像欠拟合。Check training error first; poor training suggests underfitting.
✗ 模型越简单越会泛化。Simpler models always generalize better.
→ ✓ 简单过头会漏掉稳定规律。Too simple misses stable structure.
✗ 继续加约束能修复欠拟合。More constraints fix underfitting.
→ ✓ 通常需要增能力、增特征或更好优化。Usually add capacity, features, or better optimization.
06 · 一句话带走06 · One line to keep