Top k, Top p, Temperature of LLM Models

 Excellent question — understanding nucleus sampling (top-p) and top-k sampling is key to knowing how generative AI models decide what to output next (like in ChatGPT, Claude, or any LLM).

Let’s go step by step 👇

---

🧠 Background — How Language Models Generate Text

When a language model (like GPT, Claude, or Titan) generates text, it predicts one token (word or sub-word) at a time.

For each step:

1. The model calculates a probability distribution over its vocabulary — e.g.
   “The cat sat on the ___”

   • mat: 0.60

   • sofa: 0.20

   • table: 0.10

   • dog: 0.05

   • … etc.

2. The model must choose the next token.

If it always picks the most likely token (“mat”), it’s called greedy decoding — but that makes text repetitive and boring.

👉 To add creativity and variability, models use sampling techniques like top-k and top-p (nucleus) sampling.

---

🔢 1. Top-K Sampling

🔍 Definition

Top-k sampling means the model:

• Looks at the k most probable next tokens,

• Randomly samples one of them proportionally to their probabilities.

Everything outside the top-k tokens is ignored (set to probability 0).

---

⚙️ Example

Token	Probability	Kept (Top-k=3)?
“mat”	0.60	✅
“sofa”	0.20	✅
“table”	0.10	✅
“dog”	0.05	❌
“carpet”	0.03	❌

Now the model samples only among “mat”, “sofa”, “table”.

So instead of always picking “mat”, it might choose “sofa” occasionally.

---

⚙️ Parameter Meaning

• k = 1 → deterministic (greedy)

• k = 10–50 → typical for creative text generation

• Higher k → more randomness and diversity

---

🔮 2. Nucleus Sampling (Top-P Sampling)

🔍 Definition

Instead of fixing k, nucleus sampling chooses from the smallest possible set of tokens whose cumulative probability ≥ p (e.g., 0.9 or 0.95).

So the number of tokens considered changes dynamically depending on how concentrated or spread out the probability distribution is.

---

⚙️ Example

Token	Probability	Cumulative	Included?
“mat”	0.60	0.60	✅
“sofa”	0.20	0.80	✅
“table”	0.10	0.90	✅
“dog”	0.05	0.95	❌ (if p=0.9)

Here, since 0.9 cumulative probability is reached at “table”,
only the top 3 tokens are considered — same result as top-k=3, but adaptive.

If the model is uncertain (probabilities spread out), more tokens are included.
If it’s confident (one token has high probability), fewer tokens are included.

---

⚙️ Parameter Meaning

• p = 1.0 → keep all tokens (pure sampling, max randomness)

• p = 0.9 → typical value for balanced creativity

• p = 0.7 → more deterministic and focused

---

⚖️ Top-K vs. Top-P (Nucleus Sampling)

Feature	Top-K Sampling	Top-P (Nucleus) Sampling
How it works	Keeps the k most probable tokens	Keeps smallest set whose cumulative probability ≥ p
Fixed or Dynamic?	Fixed number of tokens	Dynamic number (depends on distribution)
Control Type	Hard cutoff by count	Soft cutoff by probability mass
When Useful	When you want a consistent “breadth” of choices	When you want adaptive diversity (context-sensitive)
Typical Range	k = 20–100	p = 0.8–0.95
Output Style	Can produce abrupt randomness if k large	Usually smoother and more coherent outputs

---

🧩 Combined Usage (Top-K + Top-P Together)

Many modern LLMs (like GPT-4 or Claude) use both together:

• First apply Top-K to limit candidates (say top 50 tokens).

• Then apply Top-P to keep only the most probable subset within those 50.

This balances efficiency, coherence, and creativity.

---

🧠 Other Related Parameter — Temperature

Alongside top-k/top-p, models also use temperature to scale randomness.

• Temperature = 1.0 → normal sampling

• Temperature < 1.0 → sharper, more focused probabilities (less creativity)

• Temperature > 1.0 → flatter, more random probabilities (more creative)

All three (temperature, top-k, top-p) work together to control creativity vs. precision.

---

🧭 Summary

Concept	Description	Typical Range	Effect
Top-K	Pick from top k probable tokens	k = 20–100	Fixed breadth; more or less random
Top-P (Nucleus)	Pick from tokens covering p of total probability	p = 0.8–0.95	Adaptive breadth; smoother control
Temperature	Scales probabilities before sampling	0.7–1.2	Higher → more creative; lower → more deterministic

---

💬 In Simple Terms

Top-K: “Consider only the top K words.”
Top-P: “Consider enough words to cover P of total probability.”
Temperature: “How bold or cautious should I be while choosing?”

---

Would you like me to show you a visual diagram or Python example demonstrating how top-k and top-p affect word selection probabilities step by step?