Control LLM probability distributions using temperature to modify softmax, top-k/top-p sampling methods, and frequency penalties for precise text generation.
LLMs for the end-user are a black box. We can't see what's going on inside. But we can still control in a limited way the output of the model by changing few parameters.
When a language model generates text, it's not simply "thinking" and producing words. Behind every generated sentence lies a complex decision-making process where the model scores then weighs thousands of possibilities at each step.
The good part is that we can minimally influence these decisions through parameters that control how the model selects its next words.
Think of it like directing a jazz musician. You can ask them to play conservatively (sticking to familiar melodies) or experimentally (exploring creative variations). Similarly, generation parameters let us guide AI models along the spectrum from predictable to creative, from focused to diverse.
Let's examine our text generation process using a concrete example. When generating the continuation of "I love to go...", the model doesn't just pick one word—it calculates logits (raw scores) for the complete vocabulary of possible next tokens:
"Eat" → 5.1 logits
"Your" → 4.5 logits
"Get" → 2.2 logits
"Count" → -0.9 logits
"Trump" → 0.7 logits
...and **hundreds** of thousands more
These logits are then converted to probabilities using the softmax function:
"Eat" → 34% probability
"Your" → 12% probability
"Get" → 5% probability
"Count" → 0.1% probability
"Trump" → 3% probability
...
The question becomes: How do we choose from this probability distribution? This is where generation parameters come into play.
Temperature reshapes the entire probability distribution by modifying the softmax calculation:
Temperature = 0.1 (More Deterministic):
"Eat" → 99% probability
"Your" → 0.9% probability
"Get" → 0.1% probability
"Count" → 0.000% probability
Result: "I love to go eat" (predictable)
Temperature = 1.0 (Normal):
"Eat" → 34% probability
"Your" → 12% probability
"Get" → 5% probability
"Count" → 0.1% probability
Result: "I love to go shopping" (balanced)
Temperature = 100 (More Creative):
"Eat" → 25% probability
"Your" → 22% probability
"Get" → 20% probability
"Count" → 18% probability
Result: "I love to go spelunking" (unexpected)
Temperature acts like a creativity dial — higher values flatten the probability distribution, giving unlikely tokens more chance to be selected.
Instead of considering all possible tokens, top-k limits selection to the k most probable candidates.
For "I love to go" with different k values:
Effect: Smaller k values increase focus and reduce randomness, while larger k values allow more creativity.
Rather than fixing the number of tokens, top-p considers tokens until their cumulative probability reaches a threshold.
For "I love to go" with different p values:
Advantage: Adapts to the probability distribution—narrow distributions use fewer tokens, broad distributions use more.
Reduces the probability of tokens based on how often they've appeared in the generated text.
Formula: [new_logit = original_logit - (frequency_penalty \times token_frequency)]
Example: If "go" has appeared 3 times already:
Reduces the probability of any token that has already appeared, regardless of frequency.
Effect on "I love to go": If we've already used "love" and "go", those tokens become less likely in future selections, encouraging the model to use different vocabulary.
Different parameter combinations create distinct generation personalities:
These generation control concepts aren't just theoretical—they're the foundation of practical text generation through API parameters. Modern LLM providers like OpenAI, Anthropic, Google, and others expose these exact parameters in their APIs, allowing you to apply everything we've discussed:
temperature
controls the creativity dial we exploredtop_p
and top_k
implement the sampling strategiesfrequency_penalty
and presence_penalty
manage repetitionmax_tokens
sets length boundariesBy understanding how these parameters work with examples like "I love to go", you're equipped to make informed decisions when configuring API calls for your specific use cases—whether you need predictable documentation, engaging conversation, or creative content generation.
Generation parameters transform you from a passive user of AI to an active director of its creative process. By understanding how temperature reshapes probability distributions, how sampling methods select from those distributions, and how penalties guide vocabulary choices, you gain precise control over AI output quality and style.
The journey from "I love to go eat" (deterministic) to "I love to go quantum-leaping between parallel universes" (highly creative) is entirely within your control through parameter mastery.
Remember: Parameters are creative tools, not just technical settings. Each adjustment changes how the model weighs possibilities, turning the same input into entirely different expressive & inpredictable outcomes.
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