Editing Openai/6939b23e-87cc-8001-bdd9-9546d1143ce9 (section)

=== User: rewrite the full King/warrior story ===
rewrite the full King/warrior story

this is the old one:

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Decision-Making Council
The Setup:
The King (the model) must choose the next warrior (token).
Step 0 — The Scribes Compute Warrior Strengths
Before any meeting, the King’s scribes compute each warrior’s strength score (token probability).
The scribes evaluate 10 warriors, assigning probability (likelihood of the King (the model) selecting that warrior (token) as next warrior (token)) scores:
Warrior	Strength 
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 (100%)
Notice:
Warrior A is strongest, but A’s share is only 0.28 (28%), not anywhere near 100%.
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# The Advisor Proposes: TOP-K = 5
The Advisor makes the list:
“Only the top 5 warriors will enter the throne room.”
He admits only:
# A (0.28)
# B (0.22)
# C (0.15)
# D (0.12)
# E (0.08)
Warriors F–J are excluded.
Effect:
Top-K removes all but the highest-ranked 5 warriors.
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# The Mathematician Acts: TOP-P Filtering
The Mathematician considers that showing too many warriors might confuse the King, so he trims the list based on how likely the warriors are to be chosen.
The Mathematician counts the warriors from strongest to weakest, adding up their “chances” one by one.
He says: “We stop selecting more warriors once we’ve covered enough of the King’s likely choices.”
Anything after that is hidden from the King — he won’t consider them at all.
Top-P never promotes weak warriors, it only removes the weaker ones at the end.
Let’s compute cumulative sums:
•	A: 0.28 (cumulative = 0.28)
•	B: 0.22 (cumulative = 0.50)
•	C: 0.15 (cumulative = 0.65)
•	D: 0.12 (cumulative = 0.77)
•	E: 0.08 (cumulative = 0.85)
Now let’s set top-p = 0.80 (example).
The Mathematician says:
“We stop adding warriors when adding reaches at least 0.80 (80%).”
Our cumulative sums:
•	After A: 0.28 < 0.80
•	After B: 0.50 < 0.80
•	After C: 0.65 < 0.80
•	After D: 0.77 < 0.80
•	After E: 0.85 ≥ 0.80 → STOP
So top-p keeps:
•	A (0.28)
•	B (0.22)
•	C (0.15)
•	D (0.12)
•	E (0.08)
In this example, top-p does NOT remove anyone because the top-5 cumulatively reach 0.80 only once E is included.
If instead top-p = 0.70, then the Mathematician would stop at:
•	A + B + C = 0.28 + 0.22 + 0.15 = 0.65 (<0.70)
•	Must include D: cumulative = 0.77 → STOP
So top-p would keep ONLY:
•	A, B, C, D
And E gets kicked out.
Effect:
Top-P just says: “Stop showing more warriors once we’ve covered most of the King’s likely choices.”
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# The King’s Mood: TEMPERATURE
Now the King chooses among whichever warriors have entered the throne room and were filtered by top-k (Advisor) and top-p (Mathematician).
Temperature determines how “strict” the King is:
Temperature = 0
The King always picks the strongest warrior left in the room.
If A is present, he ALWAYS picks A.
Medium Temperature (e.g., 0.7)
The King favors A but is open to B, C, D, or E with decreasing likelihood.
High Temperature (1.0–1.5)
The King treats all remaining warriors more evenly.
Effect:
Temperature adjusts how deterministic or exploratory the King is when picking from the final pool.
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Min-P Sampling
Think of min-p as a floor for the King’s attention:
The King must consider any warrior whose chance is above a certain minimum, no matter what top-k or top-p says.
It ensures very low-probability warriors are ignored, but all slightly likely ones are still eligible.

The King has a rule: “I will at least look at all warriors who have at least X% chance of being chosen, even if the Mathematician or Advisor wants to remove them.”
It’s like a safety net for the King to not completely ignore certain warriors.
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Repeat Penalty

The repeat penalty discourages the King from picking the same warrior repeatedly.
If a warrior has been chosen recently, the King loses a bit of confidence in that warrior.
This lowers the chance the warrior is picked again immediately.

Imagine the King gets bored of picking the same hero over and over.
If he already sent Warrior A on a mission recently, he’s slightly less likely to pick A again, even if A is strong.
This encourages variety in the King’s choices.
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Full Summary (with all 5 Advisors)
Top-K	Only let the strongest K warriors into the room
Top-P	Cut the weakest ones from the remaining warriors until the main group covers most of the King’s likely choices
Temperature	Adjust how strictly the King picks the strongest warrior vs. exploring others
Min-P	Ensure warriors above a minimum chance are considered
Repeat Penalty	Reduce chance of picking a recently used warrior
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