Verify candidate continuations under the target’s actual histories

For a fixed committed prefix h, define normalized next-token distributions p for the target and q for the draft over the same finite token vocabulary. A proposed block is generated autoregressively from q: each later proposal conditions on the earlier proposed tokens. The target can teacher-force that whole block through a causal model to compute the next-token distributions for those candidate histories in one verification pass. This is parallel evaluation of known inputs, not simultaneous unconditional sampling of several independent future tokens. Preserve the tokenizer, positions, attention mask, and processed probability convention that define each conditional.

Temperature, top-k or nucleus truncation, repetition penalties, and grammar constraints can change the distribution being sampled. The exactness claim must identify the target decoder after the declared transformations, not silently compare an adjusted proposal with an unrelated raw target softmax. The actual proposal probabilities must match the proposal mechanism used to generate candidates. A draft need not be a perfect model of the target; poor agreement can reduce efficiency while a correct verifier still preserves the target law. Special proposal mechanisms or different tokenizers require their own supported mapping and correctness argument.

Suppose the target scores p 1 at h, p 2 at h plus the first proposed token, and so on. Verification proceeds from the beginning. If the first two proposals pass and the third fails, only the first two proposed histories remain the committed path. Scores and key/value states computed after the rejected third proposal describe a history that will not occur. Do not use a favorable fourth-position score to skip over that rejection. The correction token is chosen from the distribution required at the first failing history; the next round starts from the resulting actual prefix.

If all proposed tokens pass, the scored target distribution after the full proposed block can supply one additional token. The usual no-stop round can therefore emit accepted proposals plus one correction or bonus token. EOS and output-length limits can shorten that count and must be applied consistently with the baseline. A target verification pass may be cheaper than several sequential target calls, especially when a short block improves reuse of weights, but its arithmetic and temporary storage still grow with candidate work. One pass is an execution boundary, not evidence that every block length costs the same time.

Greedy verification can preserve a deterministic target sequence under matched model numerics and tie rules. Stochastic verification instead aims to preserve a probability distribution using a valid acceptance-and-residual scheme. These are different tests: equal seeded strings are not required for two exact stochastic implementations that consume randomness differently. Original speculative-sampling papers give the algorithmic argument under their model; pinned Transformers 4.56.2 exposes assisted generation with explicit mode limitations. Confirm the exact backend and configuration rather than infer support from the existence of a generic speculative option.

The probability lab illustrates a two-token distribution at one fixed history only. Reset, set both p=0.7 and n=1, predict the two bars, then inspect. They represent target masses 0.7 and 0.3 for a deliberately finite example, not a four-token draft or verification pass. The instrument has no conditional histories, target model, or correction sampler. It is useful for keeping a normalized one-step distribution distinct from the product of several conditional probabilities, which must be computed from the actual histories in a real decoder.