Autoregressive models predict the next token from a prefix. During teacher-forced training, that prefix usually comes from the reference sequence. During generation, it contains tokens emitted by the model itself. A prediction error can therefore change the context used for every later prediction.

This difference is often called exposure bias. The useful engineering detail is more specific: training and generation can present different prefix distributions to the same conditional predictor. Token-level validation on clean reference prefixes does not fully characterize behavior after the model enters a prefix that its training data rarely presented.

Teacher forcing changes the source of the prefix

For a target sequence y_1, ..., y_T conditioned on input x, maximum-likelihood training commonly minimizes a token loss of the form:

L = -sum_t log p(y_t | y_<t, x)

The prefix y_<t is the reference prefix. Each position is evaluated with earlier target tokens supplied from data, even when the model would have generated a different token at an earlier position.

Autoregressive generation uses a different recurrence:

y_hat_t ~ p(. | y_hat_<t, x)

Now the next conditional distribution depends on y_hat_<t, the model-produced prefix. If y_hat_4 differs from the reference token, position 5 is conditioned on a context that the teacher-forced loss did not use at that example.

This distinction does not make maximum likelihood invalid. The factorization defines a valid sequence likelihood, and teacher forcing gives direct supervision at every target position. The mismatch concerns the contexts encountered during rollout, not the mathematical validity of the likelihood objective.

Local token errors can alter later contexts

A next-token error has two effects during generation. The immediate output differs from the desired sequence, and the changed token becomes part of the next input context.

The second effect can persist. Suppose a model generates a closing delimiter too early. Later predictions are no longer conditioned on the reference structure. Even if the model has low loss on the clean reference prefix, that measurement says little about its conditional behavior after the premature delimiter.

The effect is not necessarily a monotonic cascade. A model can recover from an altered prefix, or multiple continuations can remain acceptable. The central issue is that recovery behavior is not directly exercised by teacher-forced evaluation on intact prefixes.

This matters especially when an application requires long coherent rollouts, structured syntax, or state that must remain consistent across many generated tokens. A small per-token error rate alone does not specify the probability that a complete sequence satisfies those constraints.

Clean-prefix metrics and rollout metrics answer different questions

Teacher-forced cross-entropy measures probability assigned to reference next tokens under reference prefixes. Perplexity is derived from the same conditional probabilities. Both are useful for measuring the modeled distribution under those contexts.

Free-running evaluation measures another object: sequences produced after the model repeatedly consumes its own outputs. Decoding policy also enters the result. Greedy decoding, beam search, temperature sampling, and truncation methods can expose different generated prefixes even with identical model parameters.

A practical evaluation can therefore separate at least two conditions:

clean prefix:
reference tokens -> model -> next-token score

rollout prefix:
model tokens     -> model -> sequence-level behavior

For applications sensitive to recovery, a third condition can be informative: deliberately perturb a valid prefix and measure whether later outputs return to an acceptable state. The perturbation should represent a plausible generation error rather than arbitrary noise. A swapped identifier, missing delimiter, or locally plausible wrong token can reveal behavior that clean-prefix scoring cannot.

The resulting measurements should not be collapsed into one number without a clear reason. Clean-prefix likelihood, rollout quality, and recovery after corruption describe different conditional regimes.

Scheduled sampling changes the training distribution, not just the input

Scheduled sampling was proposed to mix model-generated tokens into prefixes during training. At selected positions, the next prediction can be conditioned on a token produced by the model rather than exclusively on the reference token.

That modification narrows one visible part of the training-generation gap because the model encounters some non-reference prefixes. It also changes the training objective. The sampled prefix depends on model behavior, and the target token still comes from the reference sequence even when the sampled history has diverged from it.

This creates a subtle semantic issue. After a divergent prefix, the original next reference token may no longer be the sole coherent continuation. A training procedure that inserts generated history but retains the fixed reference target can pair a plausible alternate prefix with a target chosen for another history.

Scheduled sampling therefore should not be treated as a generic correction with guaranteed sequence-level improvement. Its effect depends on the sampling schedule, task structure, model state, and evaluation criterion. It is more precise to view it as one way to alter which prefixes appear during optimization.

Prefix perturbations need task semantics

Testing arbitrary corruptions can overstate fragility. Replacing a token with an impossible symbol creates a context that normal decoding may never produce. Conversely, only testing clean prefixes can hide failures that occur after plausible mistakes.

Useful perturbations preserve enough task structure to resemble reachable model states. For code generation, that might mean a valid identifier with the wrong binding or a syntactically plausible operator. For constrained text, it might mean an early section marker or a repeated field. For sequence labeling expressed autoregressively, it might mean one valid but incorrect prior label.

The perturbation rate also matters. A model facing one altered token in a long prefix is being tested under a different condition from a model facing repeated corruption. Reporting the corruption process alongside the metric keeps the result interpretable.

The gap is a property of the full generation system

Prefix distribution shift is often discussed as a training issue, but deployment behavior also depends on decoding and external controls. Constrained decoding can prevent some invalid states from entering the prefix. Retrieval or tool outputs can inject new context between generated segments. A validator can reject a partial structure before generation continues.

Those mechanisms do not erase the distinction between reference and model-produced histories. They change which histories are reachable and which errors can propagate.

For developers, the useful boundary is the prefix actually presented to the model at each generation point. If evaluation covers only reference prefixes while deployment mostly consumes model-produced ones, an observable part of system behavior remains unmeasured. Treating prefix source as an explicit evaluation dimension makes that gap visible without assuming that any single training modification resolves it.

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