PART 01
概率排序 Probability order
候选仍先按概率从高到低排列。 Candidates are still sorted from highest to lowest probability.
01 · 装满八成水就停
01 · Stop once the cup reaches eighty percent
同样要求装到 80%，为什么大水杯可能只倒两勺，小水杯却要倒五勺？ For the same 80% target, why can one distribution need two scoops while another needs five?
02 拖 p 并切换分布，追踪累计截点 Move p, Switch Distributions, and Track the Cutoff
自适应核 Adaptive nucleus
状态 A
Metric A
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状态 B
Metric B
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状态 C
Metric C
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概率与输出均为固定种子的教学模拟，不代表真实模型。拖回主变量即可复核结论。 Probabilities and outputs are fixed-seed teaching simulations, not real model output. Move the main variable back to verify the conclusion.
03 把变化拆成 4 个零件 Break the Change into Four Parts
Top-p SamplingPART 02
累计曲线 Cumulative curve
从头部逐项相加，曲线单调向 1 上升。 Probabilities accumulate from the top, producing a curve that rises toward one.
PART 03
最小集合 Smallest set
刚好让累计质量达到或超过 p 时停止收集。 Collection stops as soon as cumulative mass reaches or exceeds p.
PART 04
自适应数量 Adaptive count
尖锐分布用少量候选，平坦分布需要更多候选。 Sharp distributions need fewer candidates; flat ones need more.
04 最小机制：找第一个累计概率越过 p 的位置 Minimal Mechanism: Find the First Cumulative Point Crossing p
Top-p Samplingk* = min{k : Σi≤k pi ≥ p}
p 是概率质量阈值，k* 是由当前分布算出的候选数量，不是手工固定值。
p is a probability-mass threshold. k* is derived from the current distribution, not fixed by hand.
拖动 p
Move p
累计目标改变
cumulative target changes
切换分布
Switch shape
曲线陡峭度改变
curve steepness changes
移动截点
Move cutoff
保留数量自适应
retained count adapts
05 边界实验：平坦分布配高 p Boundary Test: Pair a Flat Distribution with High p
主动制造失败 Create a failure采样核几乎吞下整个词表尾部 The nucleus nearly swallows the whole tail
切到平坦分布并设 p = 0.95。累计曲线很慢才越线，弱候选也会进入保留集合。 Use the flat distribution and p = 0.95. The cumulative curve crosses late, admitting weak candidates into the retained set.
尚未执行。先在主交互中观察正常机制。
Not run yet. Observe the normal mechanism in the main interaction first.
✗
Top-p 永远保留固定数量。
Top-p always keeps a fixed count.
→ ✓
它固定概率质量，数量随分布改变。
It fixes probability mass; count changes with the distribution.
✗
p = 0.8 就恰好保留 80%。
p = 0.8 keeps exactly 80%.
→ ✓
最后一个完整候选可能让累计值略高于 p。
The final whole candidate may push cumulative mass above p.
✗
Top-p 会修改模型 logits。
Top-p modifies model logits.
→ ✓
它在概率生成后裁剪并重归一化。
It prunes and renormalizes after probabilities are produced.
06 · 一句话带走
06 · One line to keep