The Role of Generator Access in Autoregressive Post-Training

Amit Kiran Rege

cs.LGApr 6, 2026

The Role of Generator Access in Autoregressive Post-Training

Authors: Amit Kiran Rege

Organizations: Department of Computer Science, University of Colorado Boulder, Boulder, Colorado 80309

Abstract

We study how generator access constrains autoregressive post-training. The central question is whether the learner is confined to fresh root-start rollouts or can return to previously built prefixes and query the next-token rule there. In the root-start regime, output sampling, generated-token log probabilities, top- $k$ reports, and full next-token distributions along sampled trajectories all reduce to one canonical experiment, limited by the on-policy probability of reaching informative prefixes. Weak prefix control breaks this barrier, and once control is available, richer observations such as conditional sampling or logits can outperform top- $1$ access. Changing only the generator interface creates an exponential gap for KL-regularized outcome-reward post-training.

Figures & tables

	Limited observation	Rich observation
No prefix control	Output-only sampling	Generated-token log probabilities, top-log-probability lists, or full next-token distributions on visited prefixes
Prefix control	Top token at a chosen prefix	Chosen-prefix sampling, chosen-prefix logits, or teacher-forced sequence scores

Table 1: The taxonomy studied in this paper. The main point is that the horizontal distinction comes first. Once the learner is confined to root-start rollouts, richer trajectory-local observations do not overcome the need to reach informative prefixes on policy.

Language Model Post-Training

Language model post-training adapts pretrained models to follow instructions, reason, use tools, and meet task-specific or human-defined goals.

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Autoregressive pretraining increasingly draws on heterogeneous data, making it important to understand how a model learns from an individual token. The next-token prediction objective naturally identifies a token's contribution with its own loss. However, each token is not only a prediction target but also context for what follows. Using controlled corruption, we decouple these two roles and find a reversal: making a noisy token easier to predict reduces its damage as a target but increases it as context. The same decoupling helps explain text generated by language models: generation selects each token by its fit to the prefix, while its role as context is never tested against an independently determined continuation, because that continuation is generated to fit it. At known corrupted positions, acting through the context can reduce damage that removing the token's own loss does not. Understanding and controlling what a model learns from a token therefore requires decoupling its roles.

Abstract

Language Model Post-Training

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