Large language models choose words by assigning a probability to many possible next tokens, then selecting one according to a sampling rule. Top-k and top-p sampling are two common ways to control that choice so the output is not too random or too repetitive. They matter because small changes in sampling can make an AI response feel more creative, more focused, or more predictable.
Understanding these methods connects computer science with probability and statistics.
Understanding AI & Machine Learning: Top-k and Top-p Sampling Explained
Before a model can choose a token, it produces a score for every token in its vocabulary. These raw scores are not yet probabilities. A calculation called softmax turns them into positive values that total one.
Tokens can be whole words, parts of words, punctuation, or spaces. This matters because the model is not choosing from a neat list of complete English words.
It may be deciding between a comma, the ending of a word, or the first part of a rare name. The context changes the scores at every step, so the available choices can look very different from one token to the next.
Top-k uses a fixed limit on the number of candidates. If k is ten, the model considers ten candidates whether the next word is obvious or uncertain. This can be useful when a system needs steady, controlled behavior.
Its weakness appears when the probability distribution changes shape. After a clear prompt, one token may be far more likely than the rest, so keeping ten choices adds little useful variety.
After an open-ended creative prompt, ten choices may be too few. Top-p responds to this difference because its candidate set can grow when many tokens have similar chances and shrink when one answer strongly stands out.
The final selection remains random unless a system uses greedy decoding, which always takes the most likely token. Random selection does not mean the model ignores probability. A token with a larger adjusted probability is selected more often over many trials.
Individual results can still differ. This is why asking the same model for a story several times may produce different wording, examples, or endings.
For tasks such as extracting a date from a document or producing program code, too much variation can cause errors. For brainstorming, dialogue, or fiction, some variation can prevent the text from becoming dull and repetitive.
Sampling settings work together with temperature. Temperature changes how sharply the model favors its leading choices before top-k or top-p filters are applied. A low temperature makes the leading tokens dominate.
A high temperature gives less likely tokens more influence. Using a high temperature with a large top-p value can produce surprising text, though it can also make the response wander away from the task. A low temperature with a small candidate set can make wording repeat.
Students should treat these controls as trade-offs, not quality switches. Good settings depend on whether accuracy, consistency, variety, or natural phrasing matters most.
When testing a model, change one setting at a time and keep the prompt unchanged. Compare several outputs rather than judging one result. Notice factual accuracy, repeated phrases, tone, and whether the answer follows instructions.
A fluent sentence is not proof that its information is correct. Sampling only controls which plausible continuation is chosen from the model's learned patterns.
It does not give the model new knowledge or a way to verify claims. For schoolwork, use focused settings when clarity matters, then check important facts against reliable sources.
Key Facts
- A language model predicts P(next token | previous tokens), the probability of each possible next token.
- Top-k sampling keeps only the k highest-probability tokens before sampling from them.
- Top-p sampling keeps the smallest set of tokens whose total probability is at least p.
- After filtering, probabilities are renormalized so the kept tokens add to 1.
- If kept probabilities are 0.40, 0.30, and 0.10, the renormalized probabilities are 0.50, 0.375, and 0.125.
- Lower k or lower p usually makes output more focused, while higher k or higher p usually makes output more varied.
Vocabulary
- Token
- A token is a piece of text, such as a word, part of a word, number, or punctuation mark, that an AI model processes.
- Probability distribution
- A probability distribution lists possible outcomes and the probability of each outcome, with all probabilities adding to 1.
- Top-k sampling
- Top-k sampling is a method that keeps only the k most likely next tokens and randomly chooses from that smaller group.
- Top-p sampling
- Top-p sampling, also called nucleus sampling, keeps the most likely tokens until their total probability reaches a chosen cutoff p.
- Renormalization
- Renormalization is the process of rescaling the remaining probabilities so they add up to 1 after some options are removed.
Common Mistakes to Avoid
- Thinking top-k always chooses the single most likely word. This is wrong because top-k filters the list, then still samples randomly from the remaining k tokens.
- Forgetting to renormalize after filtering. This is wrong because the remaining probabilities no longer add to 1 until they are rescaled.
- Assuming top-p always keeps the same number of tokens. This is wrong because the number kept depends on the shape of the probability distribution.
- Using very low k or p and expecting creative writing. This is wrong because strict filtering removes many surprising or unusual word choices.
Practice Questions
- 1 A model assigns next-token probabilities: cat = 0.35, dog = 0.25, bird = 0.15, fish = 0.10, car = 0.08, moon = 0.07. With top-k sampling and k = 3, which tokens are kept, and what are their renormalized probabilities?
- 2 A model assigns probabilities in order: A = 0.42, B = 0.21, C = 0.14, D = 0.10, E = 0.08, F = 0.05. With top-p sampling and p = 0.80, which tokens are kept, and what is the total probability before renormalization?
- 3 A chatbot is giving dull, repetitive answers. Explain whether increasing k, increasing p, or both could help, and describe one possible risk of making the values too high.