Top-k Chooses a Token Pool, Not k Finished Answers

Start with the distribution for one next token

At one decoder-only autoregressive decoding position, consider a probability distribution over vocabulary tokens conditioned on the prompt and the continuation already generated. Its support is the set of tokens with nonzero probability. A sampling filter restricts which tokens remain eligible for the next draw.

The Hugging Face Transformers v4.56.0 generation utilities describe top-k as retaining the highest-probability vocabulary choices and top-p as retaining the smallest leading set whose cumulative probability reaches the threshold. These are versioned interface definitions. Their applicability to an offer depends on its actual serving implementation.

For the single-sequence sampling mechanism examined below, the retained probabilities are normalized to sum to one, and one token is drawn. That token extends the sequence. A later position has its own conditional distribution. Filtering identifies eligible choices before a draw; it does not produce a finished continuation for every eligible token.

References: [P1][H2]

TP-242: two filters retain different probability mass

Original fictional example TP-242 has exactly five possible next tokens, labelled A, B, C, D and E. Their probabilities are respectively 0.40, 0.25, 0.15, 0.12 and 0.08. They are distinct, already ordered from highest to lowest, and sum to 1. These are exact invented probabilities after all other stipulated processing, immediately before the one filter being compared.

Apply top-k with k = 2. A and B remain eligible, retaining mass 0.40 + 0.25 = 0.65. C, D and E are excluded. Explicitly renormalizing this retained support gives A probability 0.40 / 0.65 = 8/13 and B probability 0.25 / 0.65 = 5/13. Their probabilities sum to 1. One sample is drawn from those two choices.

Start again from the original five-token distribution and instead apply top-p with threshold 0.70. A alone contributes 0.40; A and B contribute 0.65, which is below the threshold. Adding C brings the cumulative mass to 0.80. The smallest leading set reaching 0.70 therefore contains A, B and C. D and E are excluded.

For this alternative, explicit renormalization gives A probability 0.40 / 0.80 = 0.50, B probability 0.25 / 0.80 = 0.3125 and C probability 0.15 / 0.80 = 0.1875. Again, one sample is drawn. The retained mass exceeds the threshold because including C takes the cumulative total past 0.70.

The two filters are alternatives in TP-242; they are never applied together. Neither calculation generates two or three complete responses. The labels represent token choices, with no named model, observed scores or task-success outcomes.

Read the probabilities at their stated position

TP-242 makes C eligible under the top-p alternative and excludes it under the top-k alternative. That is a concrete difference in what can be sampled at this position. It establishes no ranking of answer quality. No requirement in the example identifies A, B or C as the beginning of a correct answer.

The value 8/13 describes A's chance in the stipulated filtered draw. It does not describe the probability that the completed answer will satisfy a business task. Likewise, the 0.70 top-p threshold describes retained cumulative token mass before renormalization; it is not a 70% correctness target.

At another position, the distribution can change. For a separate invented distribution of 0.75, 0.10, 0.07, 0.05 and 0.03, the same 0.70 threshold would retain only the first token. This is not a claimed continuation of TP-242. It shows why a mass threshold does not specify a constant token-pool size.

The counts of two and three eligible tokens also provide no billed token total, elapsed time or completed-task count. They cannot establish a cost ratio or throughput advantage.

References: [P1]

Keep mode, length and returned sequences separate

Transformers v4.56.0 documents sampling mode separately from filtering: with one beam, do_sample=True selects multinomial sampling, while do_sample=False selects greedy decoding. A proposal listing top_k therefore still needs to establish the supported mode actually used. The one-draw example here describes sampling, not every generation strategy.

For a decoder-only continuation in that version, max_new_tokens limits generated tokens without counting the prompt; max_length includes the prompt. num_return_sequences concerns returned sequences for each batch element. These controls answer separate questions about output length and sequence count. Their documented values and defaults are not universal defaults for other runtimes, models or current offers.

Use the related pass@k guide for a purchase involving complete candidate solutions and selection of the delivered answer. Use the speculative-decoding guide for proposed draft tokens and their verification. A top-k vocabulary pool supplies neither of those counts, and TP-242 contains no complete-candidate evaluation or draft-verification cycle.

References: [H1]

Compare the policy that produced the evaluation

Suppose two fictional inference offers use the same model name. One uses TP-242's top-k alternative and the other uses its top-p alternative at the stipulated shared prefix. Their eligible next-token sets differ. A quality result measured under one policy is evidence about that tested configuration; the model name alone does not transfer the result to the other.

Ask the appointed application team to identify the exact model revision, tokenizer, serving implementation and version, and supported generation mode. Obtain the effective temperature, active filters and constraints, their application order, and any penalties that affect the distribution. Record disabled controls explicitly. Establish how model configuration, endpoint defaults and request overrides combine into the policy actually evaluated.

Keep the output-length limits, stopping rules and requested returned-sequence count alongside that policy. Where an application chooses among completed sequences, identify that selection rule separately. The response should resolve what is sampled, when generation ends and what reaches the user.

For an intended like-for-like evaluation, agree the task inputs, policy and delivered-output assessment before comparing results. If a supplier proposes a different policy, assess that complete offered configuration on the required tasks and retain the difference in the comparison record. TP-242 supplies no reason to prescribe either filter or any temperature, and no evidence that a setting improves accuracy or diversity.

A response that supplies only a model name and a top-k value leaves the comparison incomplete. The useful next step is a confirmed effective policy and evaluation under the intended conditions. The linked GPU benchmark guide covers the wider workload and system comparison.

Bring an independently identified installation need to the physical team

This generation-policy comparison may be resolved on existing infrastructure. If the chosen application separately establishes an equipment installation requirement, Leviathan's Complete Physical Infrastructure Deployment service is the relevant physical-scope discussion.

Use the related service and project inquiry to share a nonconfidential equipment summary, site, required rack work and IT connections. The service describes agreed receiving, rack integration, onsite deployment, cabling and physical handoff records. Generation-policy tuning and application evaluation remain with the appointed application team; this article does not add those activities to the physical service.

References: [L1]