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Decision-Making Council: A Metaphor for Top-K, Top-P, Temperature, Min-P, and Repeat Penalty
The Setup:
The King (the model) must choose the next warrior (token) to send on a mission.
Step 0 — The Scribes Compute Warrior Strengths:
Before the council meets, the King’s scribes calculate each warrior’s strength (token probability). Here’s an example with 10 warriors:
Warrior	Strength (Probability)
A	0.28
B	0.22
C	0.15
D	0.12
E	0.08
F	0.05
G	0.04
H	0.03
I	0.02
J	0.01
Total	1.00
Notice that Warrior A is the strongest, but no warrior is certain to be chosen.
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# The Advisor Proposes: Top-K
The Advisor says: “Only the top K strongest warriors may enter the throne room.”
Example: Top-K = 5 → only Warriors A, B, C, D, and E are allowed in.
•	Effect: Top-K removes all but the highest-ranked K warriors.
•	Note: Warriors F–J are excluded no matter their probabilities.
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# The Mathematician Acts: Top-P
The Mathematician says: “We only need to show enough warriors to cover the King’s likely choices.”
•	Top-P adds warriors from strongest to weakest, stopping once cumulative probability reaches a threshold.
•	Example: Top-P = 0.70
o	Cumulative sums:
	A: 0.28 → 0.28
	B: 0.22 → 0.50
	C: 0.15 → 0.65
	D: 0.12 → 0.77 → exceeds 0.70 → stop
o	Result: Only A, B, C, D are considered; E is excluded.
Key distinction:
•	Top-P is independent of Top-K. Top-K removes warriors based on rank count; Top-P removes warriors based on cumulative probability coverage. They can work together or separately.
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# The King’s Minimum Attention: Min-P
The King has a rule: “I will at least look at any warrior with a strength above X%, no matter what the Advisor or Mathematician says.”
•	Min-P acts as a safety net for slightly likely warriors.
•	Example: Min-P = 0.05 → any warrior with probability ≥ 0.05 cannot be excluded, even if Top-K or Top-P would normally remove them.
Effect: Ensures slightly likely warriors are always eligible for consideration.
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# The King’s Mood: Temperature
The King now chooses from the warriors allowed in by the Advisor and Mathematician.
•	Temperature = 0: The King always picks the strongest warrior. Deterministic.
•	Medium Temperature (e.g., 0.7): The King favors the strongest but may explore other warriors.
•	High Temperature (1.0–1.5): The King treats all remaining warriors more evenly, making more adventurous choices.
Effect: Temperature controls determinism vs exploration in the King’s choice.
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# The King’s Boredom: Repeat Penalty
The King dislikes sending the same warrior repeatedly.
•	If Warrior A was recently chosen, the King temporarily loses confidence in A.
•	Example: A’s probability drops from 0.28 → 0.20 due to recent selection.
•	Effect: Encourages variety in the King’s choices while still respecting warrior strengths.
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Full Summary (with all 5 Advisors)
Mechanism	Role in the Council
Top-K	Only the strongest K warriors are allowed into the throne room
Top-P	Remove the weakest warriors until cumulative probability covers most likely choices
Min-P	Ensures warriors above a minimum probability are always considered
Temperature	Determines how strictly the King favors the strongest warrior vs exploring others
Repeat Penalty	Reduces chance of picking recently chosen warriors to encourage variety

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