PART 01
输入样本Input example
底部圆点的位置代表这次输入的特征值。The bottom dot's position represents this example's feature value.
01 · 标签没变，不代表判断没变01 · Same label, different confidence
“红色 51%”和“红色 99%”都报红色，但它们真的是同一种判断吗？“Red 51%” and “red 99%” produce the same label. Are they really the same prediction?
02拖样本穿过 50% 门槛Drag the Example Across 50%
连续概率 + 离散翻转Continuous odds + discrete flip
红色概率Red probability
—
p(red)
蓝色概率Blue probability
—
p(blue)
预测标签Predicted label
—
严格超过 50%strictly above 50%
操作校验：依次点 49%、50%、51% 三个位置。先看两根柱连续变化，再看标签只在越过门槛后改变。Verification: select the 49%, 50%, and 51% presets. First watch both bars move continuously, then confirm the label changes only after the threshold is crossed.
03一次概率预测的 4 个零件Four Parts of a Probabilistic Prediction
保留不确定性Keep uncertaintyPART 02
候选结果Candidate outcomes
本页只有红色与蓝色两个互斥候选。This page has two mutually exclusive candidates: red and blue.
PART 03
概率分配Probability assignment
两根柱同时表达系统对两个候选的相对判断。The two bars jointly express the system's assessment of both candidates.
PART 04
决策门槛Decision threshold
超过 50% 才把连续概率压成一个硬标签。Crossing 50% compresses continuous probabilities into one hard label.
04最小机制：先分配概率，再取较大者Minimal Mechanism: Assign Probabilities, Then Choose
p(red) + p(blue) = 1ŷ = arg max {p(red|x), p(blue|x)}
上方拖拽改变 x，两项概率连续改变且总和恒为
1。只有最大项从一边换到另一边，ŷ 才翻转。Dragging changes x. Both probabilities move continuously and still sum to 1. ŷ flips only when the larger
term changes sides.
移动样本Move example输入特征连续变化Input changes continuously
重算两类概率Recompute both odds一升一降，总和为 1One rises, one falls; sum = 1
越过 50%Cross 50%最大候选改变，标签翻转The winner changes; label flips
05边界实验：在 50% 平局时强报一个答案Boundary Test: Force an Answer at a 50% Tie
主动制造失败Create a failure抹掉不确定性Erase the uncertainty
把样本放在精确 50% 位置，却强制显示“蓝色”。这会把完全平局伪装成确定答案。Place the example at an exact 50% tie, then force “blue.” This disguises a perfect tie as a certain answer.
尚未执行。正常状态下，50% 会明确显示“平局”。Not run yet. The normal state explicitly reports a tie at 50%.
✗ 标签相同，模型判断就完全相同。Matching labels mean identical model judgments.
→ ✓ 51% 与 99% 可给同一标签，却保留不同不确定性。51% and 99% can share a label while carrying different uncertainty.
✗ 概率最高就代表事实一定如此。The highest probability makes an outcome certain.
→ ✓ 它只是在候选中占比最高，不是事实保证。It is only the largest candidate share, not a guarantee of fact.
✗ 概率柱是模型真实置信度。These bars are real model confidence.
→ ✓ 本页数值只用于教学；真实概率还需校准与验证。These are teaching values; real probabilities require calibration and validation.
06 · 一句话带走06 · One line to keep